From 1f6b7597ca843ff5d8b932e70955d7ff561e93ba Mon Sep 17 00:00:00 2001 From: acp29 Date: Thu, 4 Jan 2024 10:59:25 +0000 Subject: [PATCH] Moved manual to docs folder and publish page using GitHub pages --- README.md | 2 +- docs/description.json | 6 +- docs/function/boot.html | 114 +++ docs/function/boot1way.html | 373 ++++++++ docs/function/bootbayes.html | 65 ++ docs/function/bootci.html | 281 ++++++ docs/function/bootclust.html | 248 +++++ docs/function/bootknife.html | 489 ++++++++++ docs/function/bootlm.html | 1156 ++++++++++++++++++++++++ docs/function/bootmode.html | 72 ++ docs/function/bootstrp.html | 69 ++ docs/function/bootwild.html | 67 ++ docs/function/images/boot1way_101.png | Bin 0 -> 25968 bytes docs/function/images/boot1way_201.png | Bin 0 -> 25966 bytes docs/function/images/boot1way_301.png | Bin 0 -> 24892 bytes docs/function/images/boot1way_401.png | Bin 0 -> 26388 bytes docs/function/images/boot1way_501.png | Bin 0 -> 26259 bytes docs/function/images/boot1way_601.png | Bin 0 -> 24386 bytes docs/function/images/boot1way_701.png | Bin 0 -> 24677 bytes docs/function/images/bootlm_1001.png | Bin 0 -> 68815 bytes docs/function/images/bootlm_101.png | Bin 0 -> 54916 bytes docs/function/images/bootlm_1101.png | Bin 0 -> 59020 bytes docs/function/images/bootlm_1201.png | Bin 0 -> 65286 bytes docs/function/images/bootlm_201.png | Bin 0 -> 53379 bytes docs/function/images/bootlm_301.png | Bin 0 -> 60987 bytes docs/function/images/bootlm_401.png | Bin 0 -> 64526 bytes docs/function/images/bootlm_501.png | Bin 0 -> 55970 bytes docs/function/images/bootlm_601.png | Bin 0 -> 58088 bytes docs/function/images/bootlm_701.png | Bin 0 -> 79764 bytes docs/function/images/bootlm_801.png | Bin 0 -> 66845 bytes docs/function/images/bootlm_901.png | Bin 0 -> 77766 bytes docs/function/randtest2.html | 104 +++ docs/function/sampszcalc.html | 62 ++ docs/index.html | 6 +- docs/readme.html | 8 +- man/generate_manual_helper.sh | 84 -- man/{generate_manual.m => make_docs.m} | 11 +- man/make_docs_helper.sh | 80 ++ manual | 1 - manual.lnk | Bin 1491 -> 0 bytes 40 files changed, 3198 insertions(+), 100 deletions(-) create mode 100644 docs/function/images/boot1way_101.png create mode 100644 docs/function/images/boot1way_201.png create mode 100644 docs/function/images/boot1way_301.png create mode 100644 docs/function/images/boot1way_401.png create mode 100644 docs/function/images/boot1way_501.png create mode 100644 docs/function/images/boot1way_601.png create mode 100644 docs/function/images/boot1way_701.png create mode 100644 docs/function/images/bootlm_1001.png create mode 100644 docs/function/images/bootlm_101.png create mode 100644 docs/function/images/bootlm_1101.png create mode 100644 docs/function/images/bootlm_1201.png create mode 100644 docs/function/images/bootlm_201.png create mode 100644 docs/function/images/bootlm_301.png create mode 100644 docs/function/images/bootlm_401.png create mode 100644 docs/function/images/bootlm_501.png create mode 100644 docs/function/images/bootlm_601.png create mode 100644 docs/function/images/bootlm_701.png create mode 100644 docs/function/images/bootlm_801.png create mode 100644 docs/function/images/bootlm_901.png delete mode 100755 man/generate_manual_helper.sh rename man/{generate_manual.m => make_docs.m} (80%) create mode 100755 man/make_docs_helper.sh delete mode 120000 manual delete mode 100644 manual.lnk diff --git a/README.md b/README.md index 3a99f43b..dea18b6e 100755 --- a/README.md +++ b/README.md @@ -46,7 +46,7 @@ To install (or test) the statistics-resampling package at it's existing location ### Usage -All help and demos are documented on the 'Function Reference' page in the documentation. For the best experience navigating the manual, please ensure that javascript is enabled in your browser. +All help and demos are documented on the 'Function Reference' page in the [manual](https://gnu-octave.github.io/statistics-resampling/). If you do not see the navigation pane on the manual web pages, please enable javascript in your browser. Function help can also be requested from the Octave/MATLAB command prompt, by typing `help function-name`. diff --git a/docs/description.json b/docs/description.json index fde82d3b..59f75668 100644 --- a/docs/description.json +++ b/docs/description.json @@ -5,10 +5,10 @@ "package": { "name": "statistics-resampling", - "version": "5.5.3", + "version": "5.5.4", "description": "The statistics-resampling package is an Octave package and Matlab toolbox that can be used to overcome a wide variety of statistics problems using non-parametric resampling methods. In particular, the functions included can be used to estimate bias, uncertainty (standard errors and confidence intervals), prediction error, and test hypotheses (p-values). Variations of the resampling methods are included that improve the accuracy of the statistics for small samples and samples with complex dependence structures.", "shortdescription": "The statistics-resampling package is an Octave package and Matlab toolbox that can be used to overcome a wide variety of statistics problems using non-parametric resampling methods", - "date": "2024-01-03", + "date": "2024-01-04", "title": "A statistics package with a variety of resampling tools", "author": "Andrew Penn ", "maintainer": "Andrew Penn ", @@ -33,7 +33,7 @@ "has_index": true, "has_license": true, "has_website_files": true, - "has_demos": false + "has_demos": true }, "paths": { diff --git a/docs/function/boot.html b/docs/function/boot.html index 08601c9a..e52fea05 100644 --- a/docs/function/boot.html +++ b/docs/function/boot.html @@ -100,6 +100,120 @@ You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/ +

Demonstration 1

+
+

The following code

+
+
+ % N as input; balanced bootstrap resampling with replacement
+ boot(3, 20, false)
+

Produces the following output

+
ans =
+
+   2   2   3   3   1   1   2   2   3   2   2   3   3   1   3   2   1   2   3   1
+   2   3   3   2   1   1   1   2   3   3   3   1   1   2   3   3   2   1   1   2
+   3   2   3   3   2   2   2   1   3   3   1   1   1   1   2   1   2   1   3   1
+
+

Demonstration 2

+
+

The following code

+
+
+ % N as input; (unbiased) balanced bootknife resampling with replacement
+ boot(3, 20, true)
+

Produces the following output

+
ans =
+
+   3   3   2   3   1   2   2   1   1   3   3   1   2   3   2   2   1   2   2   3
+   2   1   1   2   1   1   3   1   1   3   3   2   3   1   1   3   1   2   2   2
+   2   3   1   3   3   2   3   1   1   3   3   1   3   3   1   2   1   2   2   2
+
+

Demonstration 3

+
+

The following code

+
+ 
+ % N as input; balanced resampling with replacement; setting the random seed
+ boot(3, 20, false, 1) % Set random seed
+ boot(3, 20, false, 1) % Reset random seed, BOOTSAM is the same
+ boot(3, 20, false)    % Without setting random seed, BOOTSAM is different
+

Produces the following output

+
ans =
+
+   3   3   3   3   1   2   3   3   1   1   2   2   1   2   2   2   1   2   1   1
+   3   1   2   2   3   1   3   1   2   2   3   3   2   3   3   3   3   1   1   2
+   3   2   3   1   3   1   1   1   3   1   2   3   2   1   2   2   2   1   2   1
+
+ans =
+
+   3   3   3   3   1   2   3   3   1   1   2   2   1   2   2   2   1   2   1   1
+   3   1   2   2   3   1   3   1   2   2   3   3   2   3   3   3   3   1   1   2
+   3   2   3   1   3   1   1   1   3   1   2   3   2   1   2   2   2   1   2   1
+
+ans =
+
+   3   2   2   3   2   3   1   2   2   3   1   2   3   1   2   3   2   3   2   3
+   1   3   1   1   2   3   3   3   1   2   1   1   2   1   3   1   1   3   3   2
+   1   3   3   1   1   1   2   3   2   2   2   1   2   3   3   1   1   2   2   1
+
+

Demonstration 4

+
+

The following code

+
+ % Vector (X) as input; balanced resampling with replacement; setting weights
+ x = [23; 44; 36];
+ boot(x, 10, false, 1)            % equal weighting
+ boot(x, 10, false, 1, [20;0;10]) % unequal weighting, no x(2) in BOOTSAM
+

Produces the following output

+
ans =
+
+   44   23   23   36   44   23   44   36   36   23
+   36   23   36   23   44   36   36   23   44   44
+   36   36   23   44   23   44   23   36   44   44
+
+ans =
+
+   23   23   23   36   23   23   23   36   36   23
+   36   23   36   23   23   36   36   23   23   23
+   36   36   23   23   23   23   23   36   23   23
+
+

Demonstration 5

+
+

The following code

+
+ 
+ % N as input; resampling without replacement; 3 trials
+ boot(6, 1, false, 1) % Sample 1; Set random seed for first sample only
+ boot(6, 1, false)    % Sample 2
+ boot(6, 1, false)    % Sample 3
+

Produces the following output

+
ans =
+
+   4
+   2
+   3
+   5
+   4
+   6
+
+ans =
+
+   4
+   3
+   4
+   6
+   6
+   2
+
+ans =
+
+   5
+   6
+   3
+   4
+   1
+   6
+

Package: statistics-resampling

diff --git a/docs/function/boot1way.html b/docs/function/boot1way.html index fa9f7328..bf07c614 100644 --- a/docs/function/boot1way.html +++ b/docs/function/boot1way.html @@ -159,6 +159,379 @@ You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/ +

Demonstration 1

+
+

The following code

+
+
+ ## EXAMPLE 1A: 
+ ## ONE-WAY ANOVA WITH EQUAL SAMPLE SIZES: Treatment vs. Control (1)
+
+ y = [111.39 110.21  89.21  76.64  95.35  90.97  62.78;
+      112.93  60.36  92.29  59.54  98.93  97.03  79.65;
+       85.24 109.63  64.93  75.69  95.28  57.41  75.83;
+      111.96 103.40  75.49  76.69  77.95  93.32  78.70];
+ g = [1 2 3 4 5 6 7;
+      1 2 3 4 5 6 7;
+      1 2 3 4 5 6 7;
+      1 2 3 4 5 6 7];
+
+ boot1way (y(:),g(:),'ref',1,'nboot',4999);
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
Summary of bootstrap multiple comparison tests in a one-way layout
+*****************************************************************************
+Bootstrap settings: 
+ Function: mean
+ Bootstrap resampling method: Balanced, bootstrap resampling
+ Number of bootstrap resamples: 4999 
+ Method for estimating standard errors: Calculated without resampling
+ Multiple comparison method: Single-step maxT procedure based on Dunnett 
+ Reference group used for comparisons: 1 (1) 
+
+-----------------------------------------------------------------------------
+| Comparison |     Test # |      Ref # | Difference |          t |        p |
+|------------|------------|------------|------------|------------|----------|
+|          1 |          2 |          1 |     -9.480 |      -0.93 |     .859 |
+|          2 |          3 |          1 |     -24.90 |      -2.43 |     .098 |
+|          3 |          4 |          1 |     -33.24 |      -3.24 |     .018 |*
+|          4 |          5 |          1 |     -13.50 |      -1.32 |     .603 |
+|          5 |          6 |          1 |     -20.70 |      -2.02 |     .205 |
+|          6 |          7 |          1 |     -31.14 |      -3.04 |     .028 |*
+
+-----------------------------------------------------------------------------
+|    GROUP # |                                       GROUP label |        N |
+|------------|---------------------------------------------------|----------|
+|          1 |                                                 1 |        4 |
+|          2 |                                                 2 |        4 |
+|          3 |                                                 3 |        4 |
+|          4 |                                                 4 |        4 |
+|          5 |                                                 5 |        4 |
+|          6 |                                                 6 |        4 |
+|          7 |                                                 7 |        4 |
+

and the following figure

+

+ + + + +
Figure 1
+

+
+

Demonstration 2

+
+

The following code

+
+
+ ## EXAMPLE 1B: 
+ ## ROBUST ONE-WAY ANOVA WITH EQUAL SAMPLE SIZES: Treatment vs. Control (1)
+
+ y = [111.39 110.21  89.21  76.64  95.35  90.97  62.78;
+      112.93  60.36  92.29  59.54  98.93  97.03  79.65;
+       85.24 109.63  64.93  75.69  95.28  57.41  75.83;
+      111.96 103.40  75.49  76.69  77.95  93.32  78.70];
+ g = [1 2 3 4 5 6 7;
+      1 2 3 4 5 6 7;
+      1 2 3 4 5 6 7;
+      1 2 3 4 5 6 7];
+
+ boot1way (y(:), g(:), 'ref', 1, 'nboot', 4999, 'bootfun', 'robust');
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
Summary of bootstrap multiple comparison tests in a one-way layout
+*****************************************************************************
+Bootstrap settings: 
+ Function: robust
+ Bootstrap resampling method: Balanced, bootstrap resampling
+ Number of bootstrap resamples: 4999 
+ Method for estimating standard errors: Leave-one-out jackknife
+ Multiple comparison method: Single-step maxT procedure based on Dunnett 
+ Reference group used for comparisons: 1 (1) 
+
+-----------------------------------------------------------------------------
+| Comparison |     Test # |      Ref # | Difference |          t |        p |
+|------------|------------|------------|------------|------------|----------|
+|          1 |          2 |          1 |     -6.664 |      -0.82 |     .909 |
+|          2 |          3 |          1 |     -30.18 |      -3.73 |     .018 |*
+|          3 |          4 |          1 |     -35.63 |      -4.40 |     .006 |**
+|          4 |          5 |          1 |     -16.21 |      -2.00 |     .275 |
+|          5 |          6 |          1 |     -19.95 |      -2.46 |     .132 |
+|          6 |          7 |          1 |     -34.86 |      -4.30 |     .006 |**
+
+-----------------------------------------------------------------------------
+|    GROUP # |                                       GROUP label |        N |
+|------------|---------------------------------------------------|----------|
+|          1 |                                                 1 |        4 |
+|          2 |                                                 2 |        4 |
+|          3 |                                                 3 |        4 |
+|          4 |                                                 4 |        4 |
+|          5 |                                                 5 |        4 |
+|          6 |                                                 6 |        4 |
+|          7 |                                                 7 |        4 |
+

and the following figure

+

+ + + + +
Figure 1
+

+
+

Demonstration 3

+
+

The following code

+
+
+ ## EXAMPLE 2A:
+ ## COMPARISON OF TWO INDEPENDENT GROUPS WITH UNEQUAL SAMPLE SIZES 
+ ## (analagous to Student's t-test)
+
+ y =    [54       43
+         23       34
+         45       65
+         54       77
+         45       46
+        NaN       65];
+ g = {'male' 'female'
+      'male' 'female'
+      'male' 'female'
+      'male' 'female'
+      'male' 'female'
+      'male' 'female'};
+
+ boot1way (y(:), g(:), 'ref', 'male', 'nboot', 4999);
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
Summary of bootstrap multiple comparison tests in a one-way layout
+*****************************************************************************
+Bootstrap settings: 
+ Function: mean
+ Bootstrap resampling method: Balanced, bootstrap resampling
+ Number of bootstrap resamples: 4999 
+ Method for estimating standard errors: Calculated without resampling
+ Multiple comparison method: Single-step maxT procedure based on Dunnett 
+ Reference group used for comparisons: 2 (male) 
+
+-----------------------------------------------------------------------------
+| Comparison |     Test # |      Ref # | Difference |          t |        p |
+|------------|------------|------------|------------|------------|----------|
+|          1 |          1 |          2 |     +10.80 |      +1.20 |     .255 |
+
+-----------------------------------------------------------------------------
+|    GROUP # |                                       GROUP label |        N |
+|------------|---------------------------------------------------|----------|
+|          1 |                                            female |        6 |
+|          2 |                                              male |        5 |
+

and the following figure

+

+ + + + +
Figure 1
+

+
+

Demonstration 4

+
+

The following code

+
+
+ ## EXAMPLE 2B:
+ ## ONE-WAY ANOVA WITH UNEQUAL SAMPLE SIZES: pairwise comparisons
+
+ y = [54  87  45
+      23  98  39
+      45  64  51
+      54  77  49
+      45  89  50
+      47 NaN  55];
+ g = [ 1   2   3
+       1   2   3
+       1   2   3 
+       1   2   3
+       1   2   3
+       1   2   3];
+
+ boot1way (y(:), g(:), 'nboot', 4999);
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
Summary of bootstrap multiple comparison tests in a one-way layout
+*****************************************************************************
+Bootstrap settings: 
+ Function: mean
+ Bootstrap resampling method: Balanced, bootstrap resampling
+ Number of bootstrap resamples: 4999 
+ Method for estimating standard errors: Calculated without resampling
+ Multiple comparison method: Single-step maxT procedure based on Tukey-Kramer 
+
+-----------------------------------------------------------------------------
+| Comparison |     Test # |      Ref # | Difference |          t |        p |
+|------------|------------|------------|------------|------------|----------|
+|          1 |          2 |          1 |     +38.33 |      +6.17 |    <.001 |***
+|          2 |          3 |          1 |     +3.500 |      +0.59 |     .825 |
+|          3 |          3 |          2 |     -34.83 |      -5.60 |    1.000 |
+
+-----------------------------------------------------------------------------
+|    GROUP # |                                       GROUP label |        N |
+|------------|---------------------------------------------------|----------|
+|          1 |                                                 1 |        6 |
+|          2 |                                                 2 |        5 |
+|          3 |                                                 3 |        6 |
+

and the following figure

+

+ + + + +
Figure 1
+

+
+

Demonstration 5

+
+

The following code

+
+
+ ## EXAMPLE 2C:
+ ## COMPARE STANDARD DEVIATIONS BETWEEN 3 GROUPS: pairwise comparisons
+
+ y = [54  87  45
+      23  98  39
+      45  64  51
+      54  77  49
+      45  89  50
+      47 NaN  55];
+ g = [ 1   2   3
+       1   2   3
+       1   2   3
+       1   2   3
+       1   2   3
+       1   2   3];
+ p = boot1way (y(:),g(:),'bootfun',{@std,1});
+

Produces the following output

+
Summary of bootstrap multiple comparison tests in a one-way layout
+*****************************************************************************
+Bootstrap settings: 
+ Function: std
+ Bootstrap resampling method: Balanced, bootstrap resampling
+ Number of bootstrap resamples: 999 
+ Method for estimating standard errors: Balanced, bootknife resampling
+ Number of bootknife resamples used to estimate standard errors: 99 
+ Multiple comparison method: Single-step maxT procedure based on Tukey-Kramer 
+
+-----------------------------------------------------------------------------
+| Comparison |     Test # |      Ref # | Difference |          t |        p |
+|------------|------------|------------|------------|------------|----------|
+|          1 |          2 |          1 |     +1.207 |      +0.26 |     .965 |
+|          2 |          3 |          1 |     -5.356 |      -1.20 |     .502 |
+|          3 |          3 |          2 |     -6.563 |      -1.40 |     .427 |
+
+-----------------------------------------------------------------------------
+|    GROUP # |                                       GROUP label |        N |
+|------------|---------------------------------------------------|----------|
+|          1 |                                                 1 |        6 |
+|          2 |                                                 2 |        5 |
+|          3 |                                                 3 |        6 |
+

and the following figure

+

+ + + + +
Figure 1
+

+
+

Demonstration 6

+
+

The following code

+
+
+ ## EXAMPLE 3:
+ ## COMPARE CORRELATION COEFFICIENTS BETWEEN 2 DATA SETS
+ Y = randn (20, 2); g = [zeros(10, 1); ones(10, 1)];
+ func = @(M) cor (M(:,1), M(:,2));
+
+ boot1way (Y, g, 'bootfun', func);
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
Summary of bootstrap multiple comparison tests in a one-way layout
+*****************************************************************************
+Bootstrap settings: 
+ Function: @(M) cor (M (:, 1), M (:, 2))
+ Bootstrap resampling method: Balanced, bootstrap resampling
+ Number of bootstrap resamples: 999 
+ Method for estimating standard errors: Balanced, bootknife resampling
+ Number of bootknife resamples used to estimate standard errors: 99 
+ Multiple comparison method: Single-step maxT procedure based on Tukey-Kramer 
+
+-----------------------------------------------------------------------------
+| Comparison |     Test # |      Ref # | Difference |          t |        p |
+|------------|------------|------------|------------|------------|----------|
+|          1 |          2 |          1 |    -0.2781 |      -0.54 |     .588 |
+
+-----------------------------------------------------------------------------
+|    GROUP # |                                       GROUP label |        N |
+|------------|---------------------------------------------------|----------|
+|          1 |                                                 0 |       10 |
+|          2 |                                                 1 |       10 |
+

and the following figure

+

+ + + + +
Figure 1
+

+
+

Demonstration 7

+
+

The following code

+
+
+ ## EXAMPLE 4:
+ ## COMPARE SLOPES FROM LINEAR REGRESSION ON 2 DATA SETS
+ y = randn (20, 1); x = randn (20, 1); X = [ones(20, 1), x];
+ g = [zeros(10, 1); ones(10, 1)];
+ func = @(M) subsref (M(:,2:end) \ M(:,1), ...
+                      struct ('type', '()', 'subs', {{2}}));
+
+ boot1way ([y, X], g, 'bootfun', func);
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
Summary of bootstrap multiple comparison tests in a one-way layout
+*****************************************************************************
+Bootstrap settings: 
+ Function: @(M) subsref (M (:, 2:end) \ M (:, 1), struct ('type', '()', 'subs', {{2}}))
+ Bootstrap resampling method: Balanced, bootstrap resampling
+ Number of bootstrap resamples: 999 
+ Method for estimating standard errors: Balanced, bootknife resampling
+ Number of bootknife resamples used to estimate standard errors: 99 
+ Multiple comparison method: Single-step maxT procedure based on Tukey-Kramer 
+
+-----------------------------------------------------------------------------
+| Comparison |     Test # |      Ref # | Difference |          t |        p |
+|------------|------------|------------|------------|------------|----------|
+|          1 |          2 |          1 |    +0.1700 |      +0.23 |     .749 |
+
+-----------------------------------------------------------------------------
+|    GROUP # |                                       GROUP label |        N |
+|------------|---------------------------------------------------|----------|
+|          1 |                                                 0 |       10 |
+|          2 |                                                 1 |       10 |
+

and the following figure

+

+ + + + +
Figure 1
+

+

Package: statistics-resampling

diff --git a/docs/function/bootbayes.html b/docs/function/bootbayes.html index 23cad63e..e7975e05 100644 --- a/docs/function/bootbayes.html +++ b/docs/function/bootbayes.html @@ -158,6 +158,71 @@ You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/ +

Demonstration 1

+
+

The following code

+
+
+ ## Input univariate dataset
+ heights = [183, 192, 182, 183, 177, 185, 188, 188, 182, 185].';
+
+ ## 95% credible interval for the mean 
+ bootbayes(heights);
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
Summary of Bayesian bootstrap estimates of bias and precision for linear models
+*******************************************************************************
+
+Bootstrap settings: 
+ Function: sum (w .* Y)
+ Resampling method: Bayesian bootstrap
+ Prior: Symmetric Dirichlet distribution (a = 0.8)
+ Number of resamples: 1999 
+ Credible interval (CI) type: Shortest probability interval
+ Credible interval: 95%
+
+Posterior Statistics: 
+ original     bias         median       stdev       CI_lower      CI_upper
+ +184.5       -0.05229     +184.4       1.309       +182.1        +187.3
+
+

Demonstration 2

+
+

The following code

+
+
+ ## Input bivariate dataset
+ X = [ones(43,1),...
+     [01,02,03,04,05,06,07,08,09,10,11,...
+      12,13,14,15,16,17,18,19,20,21,22,...
+      23,25,26,27,28,29,30,31,32,33,34,...
+      35,36,37,38,39,40,41,42,43,44]'];
+ y = [188.0,170.0,189.0,163.0,183.0,171.0,185.0,168.0,173.0,183.0,173.0,...
+     173.0,175.0,178.0,183.0,192.4,178.0,173.0,174.0,183.0,188.0,180.0,...
+     168.0,170.0,178.0,182.0,180.0,183.0,178.0,182.0,188.0,175.0,179.0,...
+     183.0,192.0,182.0,183.0,177.0,185.0,188.0,188.0,182.0,185.0]';
+
+ ## 95% credible interval for the regression coefficents
+ bootbayes(y,X);
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
Summary of Bayesian bootstrap estimates of bias and precision for linear models
+*******************************************************************************
+
+Bootstrap settings: 
+ Function: pinv (X' * W * X) * (X' * W * y)
+ Resampling method: Bayesian bootstrap
+ Prior: Symmetric Dirichlet distribution (a = 1)
+ Number of resamples: 1999 
+ Credible interval (CI) type: Shortest probability interval
+ Credible interval: 95%
+
+Posterior Statistics: 
+ original     bias         median       stdev       CI_lower      CI_upper
+ +175.5       -0.05320     +175.3       2.376       +171.2        +180.2    
+ +0.1904      +0.0005658   +0.1935      0.07863     +0.04389      +0.3476
+

Package: statistics-resampling

diff --git a/docs/function/bootci.html b/docs/function/bootci.html index 60448b1e..14c7ded2 100644 --- a/docs/function/bootci.html +++ b/docs/function/bootci.html @@ -167,6 +167,287 @@ You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/ +

Demonstration 1

+
+

The following code

+
+
+ ## Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41].';
+
+ ## 95% BCa bootstrap confidence intervals for the mean
+ ci = bootci (1999, @mean, data)
+

Produces the following output

+
ci =
+
+   23.825
+   34.411
+
+

Demonstration 2

+
+

The following code

+
+
+ ## Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41].';
+
+ ## 95% calibrated percentile bootstrap confidence intervals for the mean
+ ci = bootci (1999, {@mean, data}, 'type', 'cal','nbootcal',199)
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
ci =
+
+   23.462
+   34.651
+
+

Demonstration 3

+
+

The following code

+
+
+ ## Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41].';
+
+ ## 95% calibrated percentile bootstrap confidence intervals for the median
+ ## with smoothing
+ ci = bootci (1999, {@smoothmedian, data}, 'type', 'cal', 'nbootcal', 199)
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
ci =
+
+   24.811
+   36.698
+
+

Demonstration 4

+
+

The following code

+
+
+ ## Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41].';
+
+ ## 90% percentile bootstrap confidence intervals for the variance
+ ci = bootci (1999, {{@var,1}, data}, 'type', 'per', 'alpha', 0.1)
+

Produces the following output

+
ci =
+
+   100.29
+   233.90
+
+

Demonstration 5

+
+

The following code

+
+
+ ## Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41].';
+
+ ## 90% BCa bootstrap confidence intervals for the variance
+ ci = bootci (1999, {{@var,1}, data}, 'type', 'bca', 'alpha', 0.1)
+

Produces the following output

+
ci =
+
+   116.40
+   265.89
+
+

Demonstration 6

+
+

The following code

+
+
+ ## Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41]';
+
+ ## 90% Studentized bootstrap confidence intervals for the variance
+ ci = bootci (1999, {{@var,1}, data}, 'type', 'stud', ...
+                                              'nbootstd', 50, 'alpha', 0.1)
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
ci =
+
+   106.75
+   290.95
+
+

Demonstration 7

+
+

The following code

+
+
+ ## Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41].';
+
+ ## 90% calibrated percentile bootstrap confidence intervals for the variance
+ ci = bootci (1999, {{@var,1}, data}, 'type', 'cal', 'nbootcal', ...
+              199, 'alpha', 0.1)
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
ci =
+
+   115.81
+   278.35
+
+

Demonstration 8

+
+

The following code

+
+
+ ## Input bivariate dataset
+ x = [2.12,4.35,3.39,2.51,4.04,5.1,3.77,3.35,4.1,3.35, ...
+      4.15,3.56, 3.39,1.88,2.56,2.96,2.49,3.03,2.66,3].';
+ y  = [2.47,4.61,5.26,3.02,6.36,5.93,3.93,4.09,4.88,3.81, ...
+       4.74,3.29,5.55,2.82,4.23,3.23,2.56,4.31,4.37,2.4].';
+
+ ## 95% BCa bootstrap confidence intervals for the correlation coefficient
+ ci = bootci (1999, @cor, x, y)
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
ci =
+
+   0.5167
+   0.8730
+
+

Demonstration 9

+
+

The following code

+
+
+ ## Spatial Test Data from Table 14.1 of Efron and Tibshirani (1993)
+ ## An Introduction to the Bootstrap in Monographs on Statistics and Applied 
+ ## Probability 57 (Springer)
+
+ ## AIM:
+ ## To construct 90% nonparametric bootstrap confidence intervals for var(A,1)
+ ## var(A,1) = 171.5
+ ## Exact intervals based on Normal theory are [118.4, 305.2].
+
+ ## Calculations using Matlab's 'Statistics and Machine Learning toolbox'
+ ## (R2020b)
+ ##
+ ## A = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+ ##      0 33 28 34 4 32 24 47 41 24 26 30 41].';
+ ## varfun = @(A) var(A, 1);
+ ## rng('default'); % For reproducibility
+ ## rng('default'); ci1 = bootci (19999,{varfun,A},'alpha',0.1,'type','norm');
+ ## rng('default'); ci2 = bootci (19999,{varfun,A},'alpha',0.1,'type','per');
+ ## rng('default'); ci4 = bootci (19999,{varfun,A},'alpha',0.1,'type','bca');
+ ## rng('default'); ci5 = bootci (19999,{varfun,A},'alpha',0.1,'type','stud');
+ ##
+ ## Summary of results from Matlab's 'Statistics and Machine Learning toolbox'
+ ## (R2020b)
+ ##
+ ## method             |   0.05 |   0.95 | length | shape |  
+ ## -------------------|--------|--------|--------|-------|
+ ## ci1 - normal       |  108.9 |  247.4 |  138.5 |  1.21 |
+ ## ci2 - percentile   |   97.6 |  235.8 |  138.2 |  0.87 |
+ ## ci4 - BCa          |  114.9 |  260.5 |  145.6 |  1.57 |*
+ ## ci5 - bootstrap-t  |   46.7 |  232.5 |  185.8 |  0.49 |** 
+ ## -------------------|--------|--------|--------|-------|
+ ## parametric - exact |  118.4 |  305.2 |  186.8 |  2.52 |
+ ##
+ ## * Bug in the fx0 subfunction of bootci
+ ## ** Bug in the bootstud subfunction of bootci
+
+ ## Calculations using the 'boot' and 'bootstrap' packages in R
+ ## 
+ ## library (boot)       # Functions from Davison and Hinkley (1997)
+ ## A <- c(48,36,20,29,42,42,20,42,22,41,45,14,6, ...
+ ##         0,33,28,34,4,32,24,47,41,24,26,30,41);
+ ## n <- length(A)
+ ##  var.fun <- function (d, i) { 
+ ##        # Function to compute the population variance
+ ##        n <- length (d); 
+ ##        return (var (d[i]) * (n - 1) / n) };
+ ##  boot.fun <- function (d, i) {
+ ##        # Compute the estimate
+ ##        t <- var.fun (d, i);
+ ##        # Compute sampling variance of the estimate using Tukey's jackknife
+ ##        n <- length (d);
+ ##        U <- empinf (data=d[i], statistic=var.fun, type="jack", stype="i");
+ ##        var.t <- sum (U^2 / (n * (n - 1)));
+ ##        return ( c(t, var.t) ) };
+ ## set.seed(1)
+ ## var.boot <- boot (data=A, statistic=boot.fun, R=19999, sim='balanced')
+ ## ci1 <- boot.ci (var.boot, conf=0.90, type="norm")
+ ## ci2 <- boot.ci (var.boot, conf=0.90, type="perc")
+ ## ci3 <- boot.ci (var.boot, conf=0.90, type="basic")
+ ## ci4 <- boot.ci (var.boot, conf=0.90, type="bca")
+ ## ci5 <- boot.ci (var.boot, conf=0.90, type="stud")
+ ##
+ ## library (bootstrap)  # Functions from Efron and Tibshirani (1993)
+ ## set.seed(1); 
+ ## ci4a <- bcanon (A, 19999, var.fun, alpha=c(0.05,0.95))
+ ## set.seed(1); 
+ ## ci5a <- boott (A, var.fun, nboott=19999, nbootsd=499, perc=c(.05,.95))
+ ##
+ ## Summary of results from 'boot' and 'bootstrap' packages in R
+ ##
+ ## method             |   0.05 |   0.95 | length | shape |  
+ ## -------------------|--------|--------|--------|-------|
+ ## ci1  - normal      |  109.6 |  246.7 |  137.1 |  1.22 |
+ ## ci2  - percentile  |   97.9 |  234.8 |  136.9 |  0.86 |
+ ## ci3  - basic       |  108.3 |  245.1 |  136.8 |  1.16 |
+ ## ci4  - BCa         |  116.0 |  260.7 |  144.7 |  1.60 |
+ ## ci4a - BCa         |  115.8 |  260.6 |  144.8 |  1.60 |
+ ## ci5  - bootstrap-t |  112.0 |  291.8 |  179.8 |  2.02 |
+ ## ci5a - bootstrap-t |  116.1 |  290.9 |  174.8 |  2.16 |
+ ## -------------------|--------|--------|--------|-------|
+ ## parametric - exact |  118.4 |  305.2 |  186.8 |  2.52 |
+ 
+ ## Calculations using the 'statistics-resampling' package for Octave/Matlab
+ ##
+ ## A = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+ ##      0 33 28 34 4 32 24 47 41 24 26 30 41].';
+ ## ci1 = bootci (19999,{{@var,1},A},'alpha',0.1,'type','norm','seed',1);
+ ## ci2 = bootci (19999,{{@var,1},A},'alpha',0.1,'type','per','seed',1);
+ ## ci3 = bootci (19999,{{@var,1},A},'alpha',0.1,'type','basic','seed',1);
+ ## ci4 = bootci (19999,{{@var,1},A},'alpha',0.1,'type','bca','seed',1);
+ ## ci5 = bootci (19999,{{@var,1},A},'alpha',0.1,'type','stud',...
+ ##                                              'nbootstd',100,'seed',1);
+ ## ci6 = bootci (19999,{{@var,1},A},'alpha',0.1,'type','cal', ...
+ ##                                              'nbootcal',499,'seed',1);
+ ##
+ ## Summary of results from 'statistics-resampling' package for Octave/Matlab
+ ##
+ ## method             |   0.05 |   0.95 | length | shape |  
+ ## -------------------|--------|--------|--------|-------|
+ ## ci1 - normal       |  110.1 |  246.2 |  136.1 |  1.22 |
+ ## ci2 - percentile   |   98.1 |  234.7 |  136.6 |  0.86 |
+ ## ci3 - basic        |  108.4 |  245.0 |  136.1 |  1.17 |
+ ## ci4 - BCa          |  116.1 |  259.3 |  143.2 |  1.59 |
+ ## ci5 - bootstrap-t  |  114.0 |  290.3 |  176.3 |  2.07 |
+ ## ci6 - calibrated   |  115.3 |  276.4 |  161.1 |  1.87 |
+ ## -------------------|--------|--------|--------|-------|
+ ## parametric - exact |  118.4 |  305.2 |  186.8 |  2.52 |
+ ##
+ ## Simulation results for constructing 90% confidence intervals for the
+ ## variance of a population N(0,1) from 1000 random samples of size 26
+ ## (analagous to the situation above). Simulation performed using the
+ ## bootsim script with nboot of 1999.
+ ##
+ ## method               | coverage |  lower |  upper | length | shape |
+ ## ---------------------|----------|--------|--------|--------|-------|
+ ## normal               |    81.5% |   3.0% |  15.5% |   0.77 |  1.21 |
+ ## percentile           |    81.5% |   0.9% |  17.6% |   0.76 |  0.91 |
+ ## basic                |    81.1% |   2.5% |  16.4% |   0.78 |  1.09 |
+ ## BCa                  |    84.2% |   5.4% |  10.4% |   0.86 |  1.82 |
+ ## bootstrap-t          |    89.2% |   4.3% |   6.5% |   0.99 |  2.15 |
+ ## calibrated           |    87.4% |   4.2% |   8.4% |   0.91 |  2.03 |
+ ## ---------------------|----------|--------|--------|--------|-------|
+ ## parametric - exact   |    90.8% |   3.7% |   5.5% |   0.99 |  2.52 |
+

gives an example of how 'bootci' is used.

+

Package: statistics-resampling

diff --git a/docs/function/bootclust.html b/docs/function/bootclust.html index 888bdf3b..f7db5d07 100644 --- a/docs/function/bootclust.html +++ b/docs/function/bootclust.html @@ -147,6 +147,254 @@ You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/ +

Demonstration 1

+
+

The following code

+
+
+ ## Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41].';
+
+ ## 95% expanded BCa bootstrap confidence intervals for the mean
+ bootclust (data, 1999, @mean);
+

Produces the following output

+
Summary of nonparametric cluster bootstrap estimates of bias and precision
+******************************************************************************
+
+Bootstrap settings: 
+ Function: mean
+ Resampling method: Balanced, bootstrap cluster resampling 
+ Number of resamples: 1999 
+ Confidence interval (CI) type: Expanded bias-corrected and accelerated (BCa) 
+ Nominal coverage (and the percentiles used): 95% (1.1%, 97.3%)
+
+Bootstrap Statistics: 
+ original     bias         std_error    CI_lower     CI_upper  
+ +29.65       -3.197e-14   +2.682       +23.16       +34.58
+
+

Demonstration 2

+
+

The following code

+
+
+ ## Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41].';
+ clustid = {'a';'a';'b';'b';'a';'c';'c';'d';'e';'e';'e';'f';'f'; ...
+            'g';'g';'g';'h';'h';'i';'i';'j';'j';'k';'l';'m';'m'};
+
+ ## 95% expanded BCa bootstrap confidence intervals for the mean with
+ ## cluster resampling
+ bootclust (data, 1999, @mean, [0.025,0.975], clustid);
+

Produces the following output

+
Summary of nonparametric cluster bootstrap estimates of bias and precision
+******************************************************************************
+
+Bootstrap settings: 
+ Function: mean
+ Resampling method: Balanced, bootstrap cluster resampling 
+ Number of resamples: 1999 
+ Confidence interval (CI) type: Expanded bias-corrected and accelerated (BCa) 
+ Nominal coverage (and the percentiles used): 95% (1.2%, 98.9%)
+
+Bootstrap Statistics: 
+ original     bias         std_error    CI_lower     CI_upper  
+ +29.65       -0.03231     +2.917       +22.85       +36.07
+
+

Demonstration 3

+
+

The following code

+
+
+ ## Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41].';
+
+ ## 90% equal-tailed percentile bootstrap confidence intervals for
+ ## the variance
+ bootclust (data, 1999, {@var, 1}, 0.1);
+

Produces the following output

+
Summary of nonparametric cluster bootstrap estimates of bias and precision
+******************************************************************************
+
+Bootstrap settings: 
+ Function: var
+ Resampling method: Balanced, bootstrap cluster resampling 
+ Number of resamples: 1999 
+ Confidence interval (CI) type: Percentile (equal-tailed)
+ Nominal coverage (and the percentiles used): 90% (5.0%, 95.0%)
+
+Bootstrap Statistics: 
+ original     bias         std_error    CI_lower     CI_upper  
+ +171.5       -6.652       +41.58       +97.78       +233.6
+
+

Demonstration 4

+
+

The following code

+
+
+ ## Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41].';
+ clustid = {'a';'a';'b';'b';'a';'c';'c';'d';'e';'e';'e';'f';'f'; ...
+            'g';'g';'g';'h';'h';'i';'i';'j';'j';'k';'l';'m';'m'};
+
+ ## 90% equal-tailed percentile bootstrap confidence intervals for
+ ## the variance
+ bootclust (data, 1999, {@var, 1}, 0.1, clustid);
+

Produces the following output

+
Summary of nonparametric cluster bootstrap estimates of bias and precision
+******************************************************************************
+
+Bootstrap settings: 
+ Function: var
+ Resampling method: Balanced, bootstrap cluster resampling 
+ Number of resamples: 1999 
+ Confidence interval (CI) type: Percentile (equal-tailed)
+ Nominal coverage (and the percentiles used): 90% (5.0%, 95.0%)
+
+Bootstrap Statistics: 
+ original     bias         std_error    CI_lower     CI_upper  
+ +171.5       -9.315       +33.34       +104.3       +214.2
+
+

Demonstration 5

+
+

The following code

+
+
+ ## Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41].';
+
+ ## 90% BCa bootstrap confidence intervals for the variance
+ bootclust (data, 1999, {@var, 1}, [0.05 0.95]);
+

Produces the following output

+
Summary of nonparametric cluster bootstrap estimates of bias and precision
+******************************************************************************
+
+Bootstrap settings: 
+ Function: var
+ Resampling method: Balanced, bootstrap cluster resampling 
+ Number of resamples: 1999 
+ Confidence interval (CI) type: Bias-corrected and accelerated (BCa) 
+ Nominal coverage (and the percentiles used): 90% (13.0%, 98.9%)
+
+Bootstrap Statistics: 
+ original     bias         std_error    CI_lower     CI_upper  
+ +171.5       -6.872       +42.05       +116.6       +265.5
+
+

Demonstration 6

+
+

The following code

+
+
+ ## Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41].';
+ clustid = {'a';'a';'b';'b';'a';'c';'c';'d';'e';'e';'e';'f';'f'; ...
+            'g';'g';'g';'h';'h';'i';'i';'j';'j';'k';'l';'m';'m'};
+
+ ## 90% BCa bootstrap confidence intervals for the variance
+ bootclust (data, 1999, {@var, 1}, [0.05 0.95], clustid);
+

Produces the following output

+
Summary of nonparametric cluster bootstrap estimates of bias and precision
+******************************************************************************
+
+Bootstrap settings: 
+ Function: var
+ Resampling method: Balanced, bootstrap cluster resampling 
+ Number of resamples: 1999 
+ Confidence interval (CI) type: Bias-corrected and accelerated (BCa) 
+ Nominal coverage (and the percentiles used): 90% (12.1%, 98.5%)
+
+Bootstrap Statistics: 
+ original     bias         std_error    CI_lower     CI_upper  
+ +171.5       -9.500       +33.19       +121.5       +227.0
+
+

Demonstration 7

+
+

The following code

+
+
+ ## Input dataset
+ y = randn (20,1); x = randn (20,1); X = [ones(20,1), x];
+
+ ## 90% BCa confidence interval for regression coefficients 
+ bootclust ({y,X}, 1999, @(y,X) X\y, [0.05 0.95]); % Could also use @regress
+

Produces the following output

+
Summary of nonparametric cluster bootstrap estimates of bias and precision
+******************************************************************************
+
+Bootstrap settings: 
+ Function: @(y, X) X \ y
+ Resampling method: Balanced, bootstrap cluster resampling 
+ Number of resamples: 1999 
+ Confidence interval (CI) type: Bias-corrected and accelerated (BCa) 
+ Nominal coverage: 90%
+
+Bootstrap Statistics: 
+ original     bias         std_error    CI_lower     CI_upper  
+ -0.02091     +0.0007003   +0.1936      -0.3307      +0.2989    
+ -0.2575      +0.01285     +0.2040      -0.5555      +0.09648
+
+

Demonstration 8

+
+

The following code

+
+
+ ## Input dataset
+ y = randn (20,1); x = randn (20,1); X = [ones(20,1), x];
+ clustid = [1;1;1;1;2;2;2;3;3;3;3;4;4;4;4;4;5;5;5;6];
+
+ ## 90% BCa confidence interval for regression coefficients 
+ bootclust ({y,X}, 1999, @(y,X) X\y, [0.05 0.95], clustid);
+

Produces the following output

+
Summary of nonparametric cluster bootstrap estimates of bias and precision
+******************************************************************************
+
+Bootstrap settings: 
+ Function: @(y, X) X \ y
+ Resampling method: Balanced, bootstrap cluster resampling 
+ Number of resamples: 1999 
+ Confidence interval (CI) type: Bias-corrected and accelerated (BCa) 
+ Nominal coverage: 90%
+
+Bootstrap Statistics: 
+ original     bias         std_error    CI_lower     CI_upper  
+ +0.2887      -0.01050     +0.2209      -0.03247     +0.7051    
+ -0.02806     +0.07045     +0.1821      -0.2984      +0.1488
+
+

Demonstration 9

+
+

The following code

+
+
+ ## Input bivariate dataset
+ x = [576 635 558 578 666 580 555 661 651 605 653 575 545 572 594].';
+ y = [3.39 3.3 2.81 3.03 3.44 3.07 3 3.43 ...
+      3.36 3.13 3.12 2.74 2.76 2.88 2.96].';
+ clustid = [1;1;3;1;1;2;2;2;2;3;1;3;3;3;2];
+
+ ## 95% BCa bootstrap confidence intervals for the correlation coefficient
+ bootclust ({x, y}, 1999, @cor, [], clustid);
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
Summary of nonparametric cluster bootstrap estimates of bias and precision
+******************************************************************************
+
+Bootstrap settings: 
+ Function: cor
+ Resampling method: Balanced, bootstrap cluster resampling 
+ Number of resamples: 1999 
+ Confidence interval (CI) type: Bias-corrected and accelerated (BCa) 
+ Nominal coverage (and the percentiles used): 95% (1.9%, 97.0%)
+
+Bootstrap Statistics: 
+ original     bias         std_error    CI_lower     CI_upper  
+ +0.7764      -0.02325     +0.1414      +0.4133      +0.9950
+

Package: statistics-resampling

diff --git a/docs/function/bootknife.html b/docs/function/bootknife.html index 24872abb..162e576f 100644 --- a/docs/function/bootknife.html +++ b/docs/function/bootknife.html @@ -199,6 +199,495 @@ You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/ +

Demonstration 1

+
+

The following code

+
+
+ ## Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41].';
+
+ ## 95% expanded BCa bootstrap confidence intervals for the mean
+ bootknife (data, 1999, @mean);
+

Produces the following output

+
Summary of nonparametric bootstrap estimates of bias and precision
+******************************************************************************
+
+Bootstrap settings: 
+ Function: mean
+ Resampling method: Balanced, bootknife resampling 
+ Number of resamples (outer): 1999 
+ Number of resamples (inner): 0 
+ Confidence interval (CI) type: Expanded bias-corrected and accelerated (BCa) 
+ Nominal coverage (and the percentiles used): 95% (1.2%, 97.0%)
+
+Bootstrap Statistics: 
+ original     bias         std_error    CI_lower     CI_upper  
+ +29.65       +5.329e-14   +2.630       +23.35       +34.43
+
+

Demonstration 2

+
+

The following code

+
+
+ ## Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41].';
+
+ ## 95% calibrated percentile bootstrap confidence intervals for the mean
+ bootknife (data, [1999, 199], @mean);
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
Summary of nonparametric bootstrap estimates of bias and precision
+******************************************************************************
+
+Bootstrap settings: 
+ Function: mean
+ Resampling method: Iterated, balanced, bootknife resampling 
+ Number of resamples (outer): 1999 
+ Number of resamples (inner): 199 
+ Confidence interval (CI) type: Calibrated percentile
+ Nominal coverage (and the percentiles used): 95% (1.1%, 97.4%)
+
+Bootstrap Statistics: 
+ original     bias         std_error    CI_lower     CI_upper  
+ +29.65       -4.974e-14   +2.702       +23.38       +34.61
+
+

Demonstration 3

+
+

The following code

+
+
+ ## Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41].';
+
+ ## 95% calibrated percentile bootstrap confidence intervals for the median
+ ## with smoothing.
+ bootknife (data, [1999, 199], @smoothmedian);
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
Summary of nonparametric bootstrap estimates of bias and precision
+******************************************************************************
+
+Bootstrap settings: 
+ Function: smoothmedian
+ Resampling method: Iterated, balanced, bootknife resampling 
+ Number of resamples (outer): 1999 
+ Number of resamples (inner): 199 
+ Confidence interval (CI) type: Calibrated percentile
+ Nominal coverage (and the percentiles used): 95% (1.9%, 98.2%)
+
+Bootstrap Statistics: 
+ original     bias         std_error    CI_lower     CI_upper  
+ +30.86       -0.05204     +3.075       +24.23       +37.11
+
+

Demonstration 4

+
+

The following code

+
+
+ ## Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41].';
+
+ ## 90% equal-tailed percentile bootstrap confidence intervals for
+ ## the variance
+ bootknife (data, 1999, {@var, 1}, 0.1);
+

Produces the following output

+
Summary of nonparametric bootstrap estimates of bias and precision
+******************************************************************************
+
+Bootstrap settings: 
+ Function: var
+ Resampling method: Balanced, bootknife resampling 
+ Number of resamples (outer): 1999 
+ Number of resamples (inner): 0 
+ Confidence interval (CI) type: Percentile (equal-tailed)
+ Nominal coverage (and the percentiles used): 90% (5.0%, 95.0%)
+
+Bootstrap Statistics: 
+ original     bias         std_error    CI_lower     CI_upper  
+ +171.5       -6.877       +43.94       +95.65       +240.7
+
+

Demonstration 5

+
+

The following code

+
+
+ ## Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41].';
+
+ ## 90% BCa bootstrap confidence intervals for the variance
+ bootknife (data, 1999, {@var, 1}, [0.05 0.95]);
+

Produces the following output

+
Summary of nonparametric bootstrap estimates of bias and precision
+******************************************************************************
+
+Bootstrap settings: 
+ Function: var
+ Resampling method: Balanced, bootknife resampling 
+ Number of resamples (outer): 1999 
+ Number of resamples (inner): 0 
+ Confidence interval (CI) type: Bias-corrected and accelerated (BCa) 
+ Nominal coverage (and the percentiles used): 90% (11.5%, 98.6%)
+
+Bootstrap Statistics: 
+ original     bias         std_error    CI_lower     CI_upper  
+ +171.5       -6.585       +43.85       +111.9       +265.8
+
+

Demonstration 6

+
+

The following code

+
+
+ ## Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41].';
+
+ ## 90% calibrated equal-tailed percentile bootstrap confidence intervals for
+ ## the variance.
+ bootknife (data, [1999, 199], {@var, 1}, 0.1);
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
Summary of nonparametric bootstrap estimates of bias and precision
+******************************************************************************
+
+Bootstrap settings: 
+ Function: var
+ Resampling method: Iterated, balanced, bootknife resampling 
+ Number of resamples (outer): 1999 
+ Number of resamples (inner): 199 
+ Confidence interval (CI) type: Calibrated percentile (equal-tailed)
+ Nominal coverage (and the percentiles used): 90% (2.5%, 97.5%)
+
+Bootstrap Statistics: 
+ original     bias         std_error    CI_lower     CI_upper  
+ +171.5       -6.574       +43.76       +87.30       +252.1
+
+

Demonstration 7

+
+

The following code

+
+
+ ## Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41].';
+
+ ## 90% calibrated percentile bootstrap confidence intervals for the variance
+ bootknife (data, [1999, 199], {@var, 1}, [0.05, 0.95]);
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
Summary of nonparametric bootstrap estimates of bias and precision
+******************************************************************************
+
+Bootstrap settings: 
+ Function: var
+ Resampling method: Iterated, balanced, bootknife resampling 
+ Number of resamples (outer): 1999 
+ Number of resamples (inner): 199 
+ Confidence interval (CI) type: Calibrated percentile
+ Nominal coverage (and the percentiles used): 90% (12.1%, 99.5%)
+
+Bootstrap Statistics: 
+ original     bias         std_error    CI_lower     CI_upper  
+ +171.5       -7.397       +44.13       +114.4       +279.9
+
+

Demonstration 8

+
+

The following code

+
+
+ ## Input dataset
+ y = randn (20,1); x = randn (20,1); X = [ones(20,1), x];
+
+ ## 90% BCa confidence interval for regression coefficients 
+ bootknife ({y,X}, 1999, @(y,X) X\y, [0.05 0.95]); % Could also use @regress
+

Produces the following output

+
Summary of nonparametric bootstrap estimates of bias and precision
+******************************************************************************
+
+Bootstrap settings: 
+ Function: @(y, X) X \ y
+ Resampling method: Balanced, bootknife resampling 
+ Number of resamples (outer): 1999 
+ Number of resamples (inner): 0 
+ Confidence interval (CI) type: Bias-corrected and accelerated (BCa) 
+ Nominal coverage: 90%
+
+Bootstrap Statistics: 
+ original     bias         std_error    CI_lower     CI_upper  
+ +0.4012      -0.001857    +0.2266      +0.006121    +0.7530    
+ -0.1871      +0.0007758   +0.1541      -0.4090      +0.1068
+
+

Demonstration 9

+
+

The following code

+
+
+ ## Input bivariate dataset
+ x = [576 635 558 578 666 580 555 661 651 605 653 575 545 572 594].';
+ y = [3.39 3.3 2.81 3.03 3.44 3.07 3 3.43 ...
+      3.36 3.13 3.12 2.74 2.76 2.88 2.96].'; 
+
+ ## 95% BCa bootstrap confidence intervals for the correlation coefficient
+ bootknife ({x, y}, 1999, @cor);
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
Summary of nonparametric bootstrap estimates of bias and precision
+******************************************************************************
+
+Bootstrap settings: 
+ Function: cor
+ Resampling method: Balanced, bootknife resampling 
+ Number of resamples (outer): 1999 
+ Number of resamples (inner): 0 
+ Confidence interval (CI) type: Bias-corrected and accelerated (BCa) 
+ Nominal coverage (and the percentiles used): 95% (0.6%, 93.9%)
+
+Bootstrap Statistics: 
+ original     bias         std_error    CI_lower     CI_upper  
+ +0.7764      -0.005924    +0.1392      +0.3173      +0.9495
+
+

Demonstration 10

+
+

The following code

+
+
+ ## Air conditioning failure times (x) in Table 1.2 of Davison A.C. and
+ ## Hinkley D.V (1997) Bootstrap Methods And Their Application. (Cambridge
+ ## University Press)
+
+ ## AIM: to construct 95% nonparametric bootstrap confidence intervals for
+ ## the mean failure time from the sample x (n = 12). The mean(x,1) = 108.1 
+ ## and exact intervals based on an exponential model are [65.9, 209.2].
+
+ ## Calculations using the 'bootstrap' and 'resample' packages in R
+ ##
+ ## x <- c(3, 5, 7, 18, 43, 85, 91, 98, 100, 130, 230, 487);
+ ##
+ ## library (bootstrap)  # Functions from Efron and Tibshirani (1993)
+ ## set.seed(1);
+ ## ci1 <- boott (x, mean, nboott=19999, nbootsd=499, perc=c(.025,.975))
+ ## set.seed(1); 
+ ## ci2a <- bcanon (x, 19999, mean, alpha = c(0.025,0.975))
+ ##
+ ## library (resample)  # Functions from Hesterberg, Tim (2014)
+ ## bootout <- bootstrap (x, mean, R=19999, seed=1)
+ ## ci2b <- CI.bca (bootout, confidence=0.95, expand=FALSE)
+ ## ci3 <- CI.bca (bootout, confidence=0.95, expand=TRUE)
+ ## ci4 <- CI.percentile (bootout, confidence=0.95, expand=FALSE)
+ ## ci5 <- CI.percentile (bootout, confidence=0.95, expand=TRUE)
+ ##
+ ## Confidence intervals from 'bootstrap' and 'resample' packages in R
+ ##
+ ## method                                |   0.05 |   0.95 | length | shape |  
+ ## --------------------------------------|--------|--------|--------|-------|
+ ## ci1  - bootstrap-t (bootstrap)        |   45.2 |  301.6 |  256.4 |  3.08 |
+ ## ci2a - BCa (bootstrap)                |   57.1 |  226.5 |  169.4 |  2.32 |
+ ## ci2b - BCa (resample)                 |   57.5 |  223.4 |  165.9 |  2.27 |
+ ## ci3  - expanded BCa (resample)        |   52.0 |  252.5 |  200.0 |  2.57 |
+ ## ci4  - percentile (resample)          |   47.7 |  191.8 |  144.1 |  1.39 |
+ ## ci5  - expanded percentile (resample) |   41.1 |  209.0 |  167.9 |  1.51 |
+
+ ## Calculations using the 'statistics-resampling' package for Octave/Matlab
+ ##
+ ## x = [3 5 7 18 43 85 91 98 100 130 230 487]';
+ ## boot (1,1,false,1); ci3 = bootknife (x, 19999, @mean, [.025,.975]);
+ ## boot (1,1,false,1); ci5 = bootknife (x, 19999, @mean, 0.05);
+ ## boot (1,1,false,1); ci6 = bootknife (x, [19999,499], @mean, [.025,.975]);
+ ##
+ ## Confidence intervals from 'statistics-resampling' package for Octave/Matlab
+ ##
+ ## method                                |  0.025 |  0.975 | length | shape |
+ ## --------------------------------------|--------|--------|--------|-------|
+ ## ci3  - expanded BCa                   |   51.4 |  255.6 |  204.2 |  2.60 |
+ ## ci5  - expanded percentile            |   37.3 |  207.4 |  170.1 |  1.40 |
+ ## ci6  - calibrated                     |   50.3 |  245.3 |  194.9 |  2.37 |
+ ## --------------------------------------|--------|--------|--------|-------|
+ ## parametric - exact                    |   65.9 |  209.2 |  143.3 |  3.40 |
+ ##
+ ## Simulation results for constructing 95% confidence intervals for the
+ ## mean of populations with different distributions. The simulation was
+ ## of 1000 random samples of size 12 (analagous to the situation above).
+ ## Simulation performed using the bootsim script with nboot of 1999 (for
+ ## single bootstrap) or [1999,199] (for double bootstrap).
+ ##
+ ## --------------------------------------------------------------------------
+ ## expanded BCa
+ ## --------------------------------------------------------------------------
+ ## Population                 | coverage |  lower |  upper | length | shape |
+ ## ---------------------------|----------|--------|--------|--------|-------|
+ ## Normal N(0,1)              |    94.8% |   2.7% |   2.5% |   1.22 |  0.99 |
+ ## Folded normal |N(0,1)|     |    94.9% |   1.8% |   3.3% |   0.75 |  1.34 |
+ ## Laplace exp(1) - exp(1)    |    92.0% |   3.1% |   4.9% |   1.67 |  0.99 |
+ ## Log-normal exp(N(0,1))     |    87.4% |   0.6% |  12.0% |   1.95 |  1.82 |
+ ## ---------------------------|----------|--------|--------|--------|-------|
+ ##
+ ## --------------------------------------------------------------------------
+ ## expanded percentile
+ ## --------------------------------------------------------------------------
+ ## Population                 | coverage |  lower |  upper | length | shape |
+ ## ---------------------------|----------|--------|--------|--------|-------|
+ ## Normal N(0,1)              |    94.8% |   2.2% |   3.0% |   1.22 |  1.00 |
+ ## Folded normal |N(0,1)|     |    92.1% |   1.5% |   6.4% |   0.71 |  1.10 |
+ ## Laplace exp(1) - exp(1)    |    94.7% |   1.9% |   3.4% |   1.61 |  1.00 |
+ ## Log-normal exp(N(0,1))     |    86.4% |   0.1% |  13.5% |   1.74 |  1.24 |
+ ## ---------------------------|----------|--------|--------|--------|-------|
+ ##
+ ## --------------------------------------------------------------------------
+ ## calibrated percentile (equal-tailed)
+ ## --------------------------------------------------------------------------
+ ## Population                 | coverage |  lower |  upper | length | shape |
+ ## ---------------------------|----------|--------|--------|--------|-------|
+ ## Normal N(0,1)              |    95.5% |   2.9% |   1.6% |   1.30 |  1.00 |
+ ## Folded normal |N(0,1)|     |    95.1% |   0.8% |   4.1% |   0.79 |  1.14 |
+ ## Laplace exp(1) - exp(1)    |    94.7% |   2.3% |   3.0% |   1.76 |  0.99 |
+ ## Log-normal exp(N(0,1))     |    88.8% |   0.3% |  10.9% |   1.99 |  1.39 |
+ ## ---------------------------|----------|--------|--------|--------|-------|
+ ##
+ ## --------------------------------------------------------------------------
+ ## calibrated percentile
+ ## --------------------------------------------------------------------------
+ ## Population                 | coverage |  lower |  upper | length | shape |
+ ## ---------------------------|----------|--------|--------|--------|-------|
+ ## Normal N(0,1)              |    95.5% |   3.1% |   1.4% |   1.28 |  1.01 |
+ ## Folded normal |N(0,1)|     |    95.5% |   0.9% |   3.6% |   0.75 |  1.40 |
+ ## Laplace exp(1) - exp(1)    |    93.3% |   3.4% |   3.3% |   1.74 |  1.02 |
+ ## Log-normal exp(N(0,1))     |    89.4% |   0.9% |   9.7% |   1.97 |  1.78 |
+ ## ---------------------------|----------|--------|--------|--------|-------|
+

gives an example of how 'bootknife' is used.

+
+

Demonstration 11

+
+

The following code

+
+
+ ## Spatial Test Data (A) from Table 14.1 of Efron and Tibshirani (1993)
+ ## An Introduction to the Bootstrap in Monographs on Statistics and Applied 
+ ## Probability 57 (Springer)
+
+ ## AIM: to construct 90% nonparametric bootstrap confidence intervals for
+ ## var(A,1), where var(A,1) = 171.5 and n = 23, and exact intervals based
+ ## on Normal theory are [118.4, 305.2].
+ ##
+ ## (i.e. (n - 1) * var (A, 0) ./ chi2inv (1 - [0.05; 0.95], n - 1))
+
+ ## Calculations using the 'boot' and 'bootstrap' packages in R
+ ## 
+ ## library (boot)       # Functions from Davison and Hinkley (1997)
+ ## A <- c(48,36,20,29,42,42,20,42,22,41,45,14,6, ...
+ ##        0,33,28,34,4,32,24,47,41,24,26,30,41);
+ ## n <- length(A)
+ ## var.fun <- function (d, i) { 
+ ##        # Function to compute the population variance
+ ##        n <- length (d); 
+ ##        return (var (d[i]) * (n - 1) / n) };
+ ## boot.fun <- function (d, i) {
+ ##        # Compute the estimate
+ ##        t <- var.fun (d, i);
+ ##        # Compute sampling variance of the estimate using Tukey's jackknife
+ ##        n <- length (d);
+ ##        U <- empinf (data=d[i], statistic=var.fun, type="jack", stype="i");
+ ##        var.t <- sum (U^2 / (n * (n - 1)));
+ ##        return ( c(t, var.t) ) };
+ ## set.seed(1)
+ ## var.boot <- boot (data=A, statistic=boot.fun, R=19999, sim='balanced')
+ ## ci1 <- boot.ci (var.boot, conf=0.90, type="norm")
+ ## ci2 <- boot.ci (var.boot, conf=0.90, type="perc")
+ ## ci3 <- boot.ci (var.boot, conf=0.90, type="basic")
+ ## ci4 <- boot.ci (var.boot, conf=0.90, type="bca")
+ ## ci5 <- boot.ci (var.boot, conf=0.90, type="stud")
+ ##
+ ## library (bootstrap)  # Functions from Efron and Tibshirani (1993)
+ ## set.seed(1);
+ ## ci4a <- bcanon (A, 19999, var.fun, alpha=c(0.05,0.95))
+ ## set.seed(1); 
+ ## ci5a <- boott (A, var.fun, nboott=19999, nbootsd=499, perc=c(.05,.95))
+ ##
+ ## Confidence intervals from 'boot' and 'bootstrap' packages in R
+ ##
+ ## method                                |   0.05 |   0.95 | length | shape |  
+ ## --------------------------------------|--------|--------|--------|-------|
+ ## ci1  - normal                         |  109.6 |  246.7 |  137.1 |  1.21 |
+ ## ci2  - percentile                     |   97.9 |  234.8 |  136.9 |  0.86 |
+ ## ci3  - basic                          |  108.3 |  245.1 |  136.8 |  1.16 |
+ ## ci4  - BCa                            |  116.0 |  260.7 |  144.7 |  1.60 |
+ ## ci4a - BCa                            |  115.8 |  260.6 |  147.8 |  1.59 |
+ ## ci5  - bootstrap-t                    |  112.0 |  291.8 |  179.8 |  2.02 |
+ ## ci5a - bootstrap-t                    |  116.1 |  290.9 |  174.7 |  2.16 |
+ ## --------------------------------------|--------|--------|--------|-------|
+ ## parametric - exact                    |  118.4 |  305.2 |  186.8 |  2.52 |
+ ##
+ ## Summary of bias statistics from 'boot' package in R
+ ##
+ ## method                             | original |    bias | bias-corrected |
+ ## -----------------------------------|----------|---------|----------------|
+ ## single bootstrap                   |   171.53 |   -6.58 |         178.11 |
+ ## -----------------------------------|----------|---------|----------------|
+ ## parametric - exact                 |   171.53 |   -6.86 |         178.40 |
+
+ ## Calculations using the 'statistics-resampling' package for Octave/Matlab
+ ##
+ ## A = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+ ##      0 33 28 34 4 32 24 47 41 24 26 30 41].';
+ ## boot (1,1,false,1); ci2 = bootknife (A,19999,{@var,1},0.1);
+ ## boot (1,1,false,1); ci4 = bootknife (A,19999,{@var,1},[0.05,0.95]);
+ ## boot (1,1,false,1); ci6a = bootknife (A,[19999,499],{@var,1},0.1);
+ ## boot (1,1,false,1); ci6b = bootknife (A,[19999,499],{@var,1},[0.05,0.95]);
+ ##
+ ## Confidence intervals from 'statistics-resampling' package for Octave/Matlab
+ ##
+ ## method                                |   0.05 |   0.95 | length | shape |
+ ## --------------------------------------|--------|--------|--------|-------|
+ ## ci2  - percentile (equal-tailed)      |   96.1 |  237.0 |  140.9 |  0.87 |
+ ## ci4  - BCa                            |  115.9 |  264.6 |  148.7 |  1.68 |
+ ## ci6a - calibrated (equal-tailed)      |   82.6 |  254.4 |  171.8 |  0.93 |
+ ## ci6b - calibrated                     |  113.4 |  284.9 |  171.5 |  1.95 |
+ ## --------------------------------------|--------|--------|--------|-------|
+ ## parametric - exact                    |  118.4 |  305.2 |  186.8 |  2.52 |
+ ##
+ ## Simulation results for constructing 90% confidence intervals for the
+ ## variance of a population N(0,1) from 1000 random samples of size 26
+ ## (analagous to the situation above). Simulation performed using the
+ ## bootsim script with nboot of 1999 (for single bootstrap) or [1999,499]
+ ## (for double bootstrap).
+ ##
+ ## method                     | coverage |  lower |  upper | length | shape |
+ ## ---------------------------|----------|--------|--------|--------|-------|
+ ## percentile (equal-tailed)  |    81.9% |   1.3% |  16.8% |   0.78 |  0.91 |
+ ## BCa                        |    85.6% |   5.2% |   9.2% |   0.87 |  1.84 |
+ ## calibrated (equal-tailed)  |    90.0% |   0.1% |   9.9% |   1.01 |  1.04 |
+ ## calibrated                 |    90.3% |   4.5% |   5.2% |   0.99 |  2.21 |
+ ## ---------------------------|----------|--------|--------|--------|-------|
+ ## parametric - exact         |    90.8% |   3.7% |   5.5% |   0.99 |  2.52 |
+
+ ## Summary of bias statistics from 'boot' package in R
+ ##
+ ## method                             | original |    bias | bias-corrected |
+ ## -----------------------------------|----------|---------|----------------|
+ ## single bootstrap                   |   171.53 |   -6.70 |         178.24 |
+ ## double bootstrap                   |   171.53 |   -7.12 |         178.65 |
+ ## -----------------------------------|----------|---------|----------------|
+ ## parametric - exact                 |   171.53 |   -6.86 |         178.40 |
+
+ ## The equivalent methods for constructing bootstrap intervals in the 'boot'
+ ## and 'bootstrap' packages (in R) and the statistics-resampling package (in
+ ## Octave/Matlab) produce intervals with very similar end points, length and
+ ## shape. However, all intervals calculated using the 'statistics-resampling'
+ ## package are slightly longer than the equivalent intervals calculated in
+ ## R because the 'statistics-resampling' package uses bootknife resampling.
+ ## The scale of the sampling distribution for small samples is approximated
+ ## better by bootknife (rather than bootstrap) resampling.
+

gives an example of how 'bootknife' is used.

+

Package: statistics-resampling

diff --git a/docs/function/bootlm.html b/docs/function/bootlm.html index af36d2d6..a724f7a0 100644 --- a/docs/function/bootlm.html +++ b/docs/function/bootlm.html @@ -444,6 +444,1162 @@ You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/ +

Demonstration 1

+
+

The following code

+
+
+ ## Two-sample unpaired test on independent samples (equivalent to Welch's
+ ## t-test). 
+
+ score = [54 23 45 54 45 43 34 65 77 46 65]';
+ gender = {'male' 'male' 'male' 'male' 'male' 'female' 'female' 'female' ...
+           'female' 'female' 'female'}';
+
+ ## 95% confidence intervals and p-values for the difference in mean score
+ ## between males and females (computed by wild bootstrap)
+ STATS = bootlm (score, gender, 'display', 'on', 'varnames', 'gender', ...
+                 'dim', 1, 'posthoc','trt_vs_ctrl');
+
+ ## 95% credible intervals for the estimated marginal means of the scores by
+ ## males and females (computed by Bayesian bootstrap)
+ STATS = bootlm (score, gender, 'display', 'on', 'varnames', 'gender', ...
+                 'dim', 1, 'method', 'bayesian', 'prior', 'auto');
+

Produces the following output

+
MODEL FORMULA (based on Wilkinson's notation):
+
+score ~ 1 + gender
+
+MODEL POSTHOC COMPARISONS
+
+name                                   mean        CI_lower    CI_upper    p-adj
+--------------------------------------------------------------------------------
+female - male                          +10.80      -8.650      +30.25       .243
+
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+score ~ 1 + gender
+
+MODEL ESTIMATED MARGINAL MEANS
+
+name                                   mean        CI_lower    CI_upper        N
+--------------------------------------------------------------------------------
+male                                   +44.20      +32.51      +53.02          5
+female                                 +55.00      +42.56      +67.82          6
+

and the following figure

+

+ + + + +
Figure 1
+

+
+

Demonstration 2

+
+

The following code

+
+
+ ## Two-sample paired test on dependent or matched samples equivalent to a
+ ## paired t-test.
+
+ score = [4.5 5.6; 3.7 6.4; 5.3 6.4; 5.4 6.0; 3.9 5.7]';
+ treatment = {'before' 'after'; 'before' 'after'; 'before' 'after';
+              'before' 'after'; 'before' 'after'}';
+ subject = {'GS' 'GS'; 'JM' 'JM'; 'HM' 'HM'; 'JW' 'JW'; 'PS' 'PS'}';
+
+ ## 95% confidence intervals and p-values for the difference in mean score
+ ## before and after treatment (computed by wild bootstrap)
+ STATS = bootlm (score(:), {subject(:), treatment(:)}, ...
+                            'model', 'linear', 'display', 'on', ...
+                            'varnames', {'subject','treatment'}, ...
+                            'dim', 2, 'posthoc','trt_vs_ctrl');
+
+ ## 95% credible intervals for the estimated marginal means of the scores
+ ## before and after treatment (computed by Bayesian bootstrap)
+ STATS = bootlm (score(:), {subject(:), treatment(:)}, ...
+                            'model', 'linear', 'display', 'on', ...
+                            'varnames', {'subject','treatment'}, ...
+                            'dim', 2, 'method','bayesian', 'prior', 'auto');
+

Produces the following output

+
MODEL FORMULA (based on Wilkinson's notation):
+
+Y ~ 1 + subject + treatment
+
+MODEL POSTHOC COMPARISONS
+
+name                                   mean        CI_lower    CI_upper    p-adj
+--------------------------------------------------------------------------------
+after - before                         +1.460      +0.6513     +2.269       .002
+
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+Y ~ 1 + subject + treatment
+
+MODEL ESTIMATED MARGINAL MEANS
+
+name                                   mean        CI_lower    CI_upper        N
+--------------------------------------------------------------------------------
+before                                 +4.560      +4.108      +5.000          5
+after                                  +6.020      +5.577      +6.478          5
+

and the following figure

+

+ + + + +
Figure 1
+

+
+

Demonstration 3

+
+

The following code

+
+
+ ## One-way design. The data is from a study on the strength of structural
+ ## beams, in Hogg and Ledolter (1987) Engineering Statistics. NY: MacMillan
+
+ strength = [82 86 79 83 84 85 86 87 74 82 ...
+            78 75 76 77 79 79 77 78 82 79]';
+ alloy = {'st','st','st','st','st','st','st','st', ...
+          'al1','al1','al1','al1','al1','al1', ...
+          'al2','al2','al2','al2','al2','al2'}';
+
+ ## 95% confidence intervals and p-values for the differences in mean strength
+ ## of three alloys (computed by wild bootstrap)
+ STATS = bootlm (strength, alloy, 'display', 'on', 'varnames', 'alloy', ...
+                 'dim', 1, 'posthoc','pairwise');
+
+ ## 95% credible intervals for the estimated marginal means of the strengths
+ ## of each of the alloys (computed by Bayesian bootstrap)
+ STATS = bootlm (strength, alloy, 'display', 'on', 'varnames', 'alloy', ...
+                 'dim', 1, 'method','bayesian', 'prior', 'auto');
+

Produces the following output

+
MODEL FORMULA (based on Wilkinson's notation):
+
+strength ~ 1 + alloy
+
+MODEL POSTHOC COMPARISONS
+
+name                                   mean        CI_lower    CI_upper    p-adj
+--------------------------------------------------------------------------------
+st - al1                               +7.000      +3.868      +10.13      <.001
+st - al2                               +5.000      +2.542      +7.458      <.001
+al1 - al2                              -2.000      -4.870      +0.8703      .170
+
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+strength ~ 1 + alloy
+
+MODEL ESTIMATED MARGINAL MEANS
+
+name                                   mean        CI_lower    CI_upper        N
+--------------------------------------------------------------------------------
+st                                     +84.00      +82.09      +85.68          8
+al1                                    +77.00      +74.93      +79.40          6
+al2                                    +79.00      +77.72      +80.44          6
+

and the following figure

+

+ + + + +
Figure 1
+

+
+

Demonstration 4

+
+

The following code

+
+
+ ## One-way repeated measures design. The data is from a study on the number
+ ## of words recalled by 10 subjects for three time condtions, in Loftus &
+ ## Masson (1994) Psychon Bull Rev. 1(4):476-490, Table 2.
+
+ words = [10 13 13; 6 8 8; 11 14 14; 22 23 25; 16 18 20; ...
+          15 17 17; 1 1 4; 12 15 17;  9 12 12;  8 9 12];
+ seconds = [1 2 5; 1 2 5; 1 2 5; 1 2 5; 1 2 5; ...
+            1 2 5; 1 2 5; 1 2 5; 1 2 5; 1 2 5;];
+ subject = [ 1  1  1;  2  2  2;  3  3  3;  4  4  4;  5  5  5; ...
+             6  6  6;  7  7  7;  8  8  8;  9  9  9; 10 10 10];
+
+ ## 95% confidence intervals and p-values for the differences in mean number
+ ## of words recalled for the different times (using wild bootstrap).
+ STATS = bootlm (words(:), {subject(:), seconds(:)}, ...
+                            'model', 'linear', 'display', 'on', ...
+                            'varnames', {'subject', 'seconds'}, ...
+                            'dim', 2, 'posthoc', 'pairwise');
+
+ ## 95% credible intervals for the estimated marginal means of the number of
+ ## words recalled for each time (computed using Bayesian bootstrap).
+ STATS = bootlm (words(:), {subject(:), seconds(:)}, ...
+                            'model', 'linear', 'display', 'on', ...
+                            'varnames', {'subject', 'seconds'}, ...
+                            'dim', 2, 'method', 'bayesian', 'prior', 'auto');
+

Produces the following output

+
MODEL FORMULA (based on Wilkinson's notation):
+
+Y ~ 1 + subject + seconds
+
+MODEL POSTHOC COMPARISONS
+
+name                                   mean        CI_lower    CI_upper    p-adj
+--------------------------------------------------------------------------------
+1 - 2                                  -2.000      -2.738      -1.262      <.001
+1 - 5                                  -3.200      -3.848      -2.552      <.001
+2 - 5                                  -1.200      -2.087      -0.3132      .012
+
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+Y ~ 1 + subject + seconds
+
+MODEL ESTIMATED MARGINAL MEANS
+
+name                                   mean        CI_lower    CI_upper        N
+--------------------------------------------------------------------------------
+1                                      +11.00      +10.63      +11.34         10
+2                                      +13.00      +12.51      +13.47         10
+5                                      +14.20      +13.77      +14.65         10
+

and the following figure

+

+ + + + +
Figure 1
+

+
+

Demonstration 5

+
+

The following code

+
+
+ ## Balanced two-way design. The data is yield of cups of popped popcorn from
+ ## different popcorn brands and popper types, in Hogg and Ledolter (1987)
+ ## Engineering Statistics. NY: MacMillan
+
+ popcorn = [5.5, 4.5, 3.5; 5.5, 4.5, 4.0; 6.0, 4.0, 3.0; ...
+            6.5, 5.0, 4.0; 7.0, 5.5, 5.0; 7.0, 5.0, 4.5];
+ brands = {'Gourmet', 'National', 'Generic'; ...
+           'Gourmet', 'National', 'Generic'; ...
+           'Gourmet', 'National', 'Generic'; ...
+           'Gourmet', 'National', 'Generic'; ...
+           'Gourmet', 'National', 'Generic'; ...
+           'Gourmet', 'National', 'Generic'};
+ popper = {'oil', 'oil', 'oil'; 'oil', 'oil', 'oil'; 'oil', 'oil', 'oil'; ...
+           'air', 'air', 'air'; 'air', 'air', 'air'; 'air', 'air', 'air'};
+
+ ## Check regression coefficients corresponding to brand x popper interaction
+ STATS = bootlm (popcorn(:), {brands(:), popper(:)}, ...
+                            'display', 'on', 'model', 'full', ...
+                            'varnames', {'brands', 'popper'});
+
+ ## 95% confidence intervals and p-values for the differences in mean yield of
+ ## different popcorn brands (computed by wild bootstrap).
+ STATS = bootlm (popcorn(:), {brands(:), popper(:)}, ...
+                            'display', 'on', 'model', 'full', ...
+                            'varnames', {'brands', 'popper'}, ...
+                            'dim', 1, 'posthoc', 'pairwise');
+
+ ## 95% credible intervals for the estimated marginal means of the yield for
+ ## each popcorn brand (computed by Bayesian bootstrap).
+ STATS = bootlm (popcorn(:), {brands(:), popper(:)}, ...
+                            'display', 'on', 'model', 'full', ...
+                            'varnames', {'brands', 'popper'}, ...
+                            'dim', 1, 'method', 'bayesian', 'prior', 'auto');
+
+ ## 95% confidence intervals and p-values for the differences in mean yield
+ ## for different popper types (computed by wild bootstrap).
+ STATS = bootlm (popcorn(:), {brands(:), popper(:)}, ...
+                            'display', 'on', 'model', 'full', ...
+                            'varnames', {'brands', 'popper'}, ...
+                            'dim', 2, 'posthoc', 'pairwise');
+
+ ## 95% credible intervals for the estimated marginal means of the yield for
+ ## each popper type (computed by Bayesian bootstrap).
+ STATS = bootlm (popcorn(:), {brands(:), popper(:)}, ...
+                            'display', 'on', 'model', 'full', ...
+                            'varnames', {'brands', 'popper'}, ...
+                            'dim', 2, 'method', 'bayesian', 'prior', 'auto');
+

Produces the following output

+
MODEL FORMULA (based on Wilkinson's notation):
+
+Y ~ 1 + brands + popper + brands:popper
+
+MODEL COEFFICIENTS
+
+name                                   coeff       CI_lower    CI_upper    p-val
+--------------------------------------------------------------------------------
+(Intercept)                            +5.667      +4.794      +6.539      <.001
+brands_1                               -1.333      -1.898      -0.7691      .011
+brands_2                               -2.167      -3.123      -1.210      <.001
+popper_1                               +1.167      +0.5958     +1.738       .016
+brands:popper_1                        -0.3333     -1.074      +0.4077      .338
+brands:popper_2                        -0.1667     -1.260      +0.9266      .726
+
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+Y ~ 1 + brands + popper + brands:popper
+
+MODEL POSTHOC COMPARISONS
+
+name                                   mean        CI_lower    CI_upper    p-adj
+--------------------------------------------------------------------------------
+Gourmet - National                     +1.500      +1.131      +1.869      <.001
+Gourmet - Generic                      +2.250      +1.710      +2.790      <.001
+National - Generic                     +0.7500     +0.1981     +1.302       .011
+
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+Y ~ 1 + brands + popper + brands:popper
+
+MODEL ESTIMATED MARGINAL MEANS
+
+name                                   mean        CI_lower    CI_upper        N
+--------------------------------------------------------------------------------
+Gourmet                                +6.250      +6.066      +6.444          6
+National                               +4.750      +4.563      +4.937          6
+Generic                                +4.000      +3.681      +4.316          6
+
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+Y ~ 1 + brands + popper + brands:popper
+
+MODEL POSTHOC COMPARISONS
+
+name                                   mean        CI_lower    CI_upper    p-adj
+--------------------------------------------------------------------------------
+oil - air                              -1.000      -1.384      -0.6160     <.001
+
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+Y ~ 1 + brands + popper + brands:popper
+
+MODEL ESTIMATED MARGINAL MEANS
+
+name                                   mean        CI_lower    CI_upper        N
+--------------------------------------------------------------------------------
+oil                                    +4.500      +4.316      +4.691          9
+air                                    +5.500      +5.309      +5.679          9
+

and the following figure

+

+ + + + +
Figure 1
+

+
+

Demonstration 6

+
+

The following code

+
+
+ ## Unbalanced two-way design (2x2). The data is from a study on the effects
+ ## of gender and a college degree on starting salaries of company employees,
+ ## in Maxwell, Delaney and Kelly (2018): Chapter 7, Table 15
+
+ salary = [24 26 25 24 27 24 27 23 15 17 20 16, ...
+           25 29 27 19 18 21 20 21 22 19]';
+ gender = {'f' 'f' 'f' 'f' 'f' 'f' 'f' 'f' 'f' 'f' 'f' 'f'...
+           'm' 'm' 'm' 'm' 'm' 'm' 'm' 'm' 'm' 'm'}';
+ degree = [1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0]';
+
+ ## ANOVA (including the main effect of gender averaged over levels of degree)
+ [STATS, BOOTSTAT, AOVSTAT] = bootlm (salary, {degree, gender}, 'model', ...
+                             'full', 'display', 'off', 'varnames', ...
+                             {'degree', 'gender'});
+
+ fprintf ('ANOVA SUMMARY with gender averaged over levels of degree\n')
+ for i = 1:numel(AOVSTAT.F)
+   fprintf ('F(%u,%u) = %.2f, p = %.3g for the model: %s\n', ...
+            AOVSTAT.DF(i), AOVSTAT.DFE, AOVSTAT.F(i), ...
+            AOVSTAT.PVAL(i), AOVSTAT.MODEL{i});
+ end
+
+ ## ANOVA (including the main effect of degree averaged over levels of gender)
+ [STATS, BOOTSTAT, AOVSTAT] = bootlm (salary, {gender, degree}, 'model', ...
+                             'full', 'display', 'off', 'varnames', ...
+                             {'gender', 'degree'});
+
+ fprintf ('\nANOVA SUMMARY with degree averaged over levels of gender\n')
+ for i = 1:numel(AOVSTAT.F)
+   fprintf ('F(%u,%u) = %.2f, p = %.3g for the model: %s\n', ...
+            AOVSTAT.DF(i), AOVSTAT.DFE, AOVSTAT.F(i), ...
+            AOVSTAT.PVAL(i), AOVSTAT.MODEL{i});
+ end
+
+ ## Check regression coefficient corresponding to gender x degree interaction
+ STATS = bootlm (salary, {gender, degree}, 'model', 'full', ...
+                             'display', 'on', 'varnames', ...
+                             {'gender', 'degree'});
+
+ ## 95% confidence intervals and p-values for the differences in mean salary
+ ## between males and females (computed by wild bootstrap).
+ STATS = bootlm (salary, {gender, degree}, 'model', 'full', ...
+                            'display', 'on', 'varnames', ...
+                            {'gender', 'degree'}, 'dim', 1, ...
+                            'posthoc', 'trt_vs_ctrl');
+
+ ## 95% credible intervals for the estimated marginal means for salaries of
+ ## females and males (computed by Bayesian bootstrap).
+ STATS = bootlm (salary, {gender, degree}, 'model', 'full', ...
+                            'display', 'on', 'varnames', ...
+                            {'gender', 'degree'}, 'dim', 1, ...
+                            'method', 'bayesian', 'prior', 'auto');
+
+ ## 95% confidence intervals and p-values for the differences in mean salary
+ ## between employees with or without a degree (computed by wild bootstrap).
+ STATS = bootlm (salary, {gender, degree}, 'model', 'full', ...
+                            'display', 'on', 'varnames', ...
+                            {'gender', 'degree'}, 'dim', 2, ...
+                            'posthoc', 'trt_vs_ctrl');
+
+ ## 95% credible intervals for the estimated marginal means for salaries of
+ ## employees with or without a degree (computed by Bayesian bootstrap).
+ STATS = bootlm (salary, {gender, degree}, 'model', 'full', ...
+                            'display', 'on', 'varnames', ...
+                            {'gender', 'degree'}, 'dim', 2, ...
+                            'method', 'bayesian','prior', 'auto');
+

Produces the following output

+
ANOVA SUMMARY with gender averaged over levels of degree
+F(1,18) = 87.20, p = 0.0001 for the model: salary ~ 1 + degree
+F(1,18) = 10.97, p = 0.00527 for the model: salary ~ 1 + degree + gender
+F(1,18) = 0.42, p = 0.566 for the model: salary ~ 1 + degree + gender + degree:gender
+
+ANOVA SUMMARY with degree averaged over levels of gender
+F(1,18) = 0.11, p = 0.749 for the model: salary ~ 1 + gender
+F(1,18) = 98.06, p = 0.0001 for the model: salary ~ 1 + gender + degree
+F(1,18) = 0.42, p = 0.561 for the model: salary ~ 1 + gender + degree + gender:degree
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+salary ~ 1 + gender + degree + gender:degree
+
+MODEL COEFFICIENTS
+
+name                                   coeff       CI_lower    CI_upper    p-val
+--------------------------------------------------------------------------------
+(Intercept)                            +25.00      +23.65      +26.35      <.001
+gender_1                               +2.000      -0.9424     +4.942       .219
+degree_1                               -8.000      -10.78      -5.218      <.001
+gender:degree_1                        +1.000      -2.937      +4.937       .582
+
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+salary ~ 1 + gender + degree + gender:degree
+
+MODEL POSTHOC COMPARISONS
+
+name                                   mean        CI_lower    CI_upper    p-adj
+--------------------------------------------------------------------------------
+m - f                                  +2.500      +0.5706     +4.429       .015
+
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+salary ~ 1 + gender + degree + gender:degree
+
+MODEL ESTIMATED MARGINAL MEANS
+
+name                                   mean        CI_lower    CI_upper        N
+--------------------------------------------------------------------------------
+f                                      +21.00      +20.08      +22.10         12
+m                                      +23.50      +22.51      +24.46         10
+
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+salary ~ 1 + gender + degree + gender:degree
+
+MODEL POSTHOC COMPARISONS
+
+name                                   mean        CI_lower    CI_upper    p-adj
+--------------------------------------------------------------------------------
+0 - 1                                  -7.500      -9.407      -5.593      <.001
+
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+salary ~ 1 + gender + degree + gender:degree
+
+MODEL ESTIMATED MARGINAL MEANS
+
+name                                   mean        CI_lower    CI_upper        N
+--------------------------------------------------------------------------------
+1                                      +26.00      +25.02      +26.96         11
+0                                      +18.50      +17.53      +19.53         11
+

and the following figure

+

+ + + + +
Figure 1
+

+
+

Demonstration 7

+
+

The following code

+
+
+ ## Unbalanced three-way design (3x2x2). The data is from a study of the
+ ## effects of three different drugs, biofeedback and diet on patient blood
+ ## pressure, adapted* from Maxwell, Delaney and Kelly (2018): Ch 8, Table 12
+
+ drug = {'X' 'X' 'X' 'X' 'X' 'X' 'X' 'X' 'X' 'X' 'X' 'X' ...
+         'X' 'X' 'X' 'X' 'X' 'X' 'X' 'X' 'X' 'X' 'X' 'X';
+         'Y' 'Y' 'Y' 'Y' 'Y' 'Y' 'Y' 'Y' 'Y' 'Y' 'Y' 'Y' ...
+         'Y' 'Y' 'Y' 'Y' 'Y' 'Y' 'Y' 'Y' 'Y' 'Y' 'Y' 'Y';
+         'Z' 'Z' 'Z' 'Z' 'Z' 'Z' 'Z' 'Z' 'Z' 'Z' 'Z' 'Z' ...
+         'Z' 'Z' 'Z' 'Z' 'Z' 'Z' 'Z' 'Z' 'Z' 'Z' 'Z' 'Z'};
+ feedback = [1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0;
+             1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0;
+             1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0];
+ diet = [0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1;
+         0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1;
+         0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1];
+ BP = [170 175 165 180 160 158 161 173 157 152 181 190 ...
+       173 194 197 190 176 198 164 190 169 164 176 175;
+       186 194 201 215 219 209 164 166 159 182 187 174 ...
+       189 194 217 206 199 195 171 173 196 199 180 203;
+       180 187 199 170 204 194 162 184 183 156 180 173 ...
+       202 228 190 206 224 204 205 199 170 160 179 179];
+
+ ## Perform 3-way ANOVA (this design is balanced, thus the order of predictors 
+ ## does not make any difference)
+ [STATS, BOOTSTAT, AOVSTAT] = bootlm (BP(:), {diet(:), drug(:), ...
+                                    feedback(:)}, 'seed', 1, ...
+                                    'model', 'full', 'display', 'off', ...
+                                    'varnames', {'diet', 'drug', 'feedback'});
+
+ fprintf ('ANOVA SUMMARY\n')
+ for i = 1:numel(AOVSTAT.F)
+   fprintf ('F(%u,%u) = %.2f, p = %.3g for the model: %s\n', ...
+            AOVSTAT.DF(i), AOVSTAT.DFE, AOVSTAT.F(i), ...
+            AOVSTAT.PVAL(i), AOVSTAT.MODEL{i});
+ end
+
+ ## Check regression coefficient corresponding to drug x feedback x diet
+ STATS = bootlm (BP(:), {diet(:), drug(:), feedback(:)}, ...
+                                    'model', 'full', ...
+                                    'display', 'on', ...
+                                    'varnames', {'diet', 'drug', 'feedback'});
+
+ ## 95% confidence intervals and p-values for the differences in mean salary
+ ## between males and females (computed by wild bootstrap).
+ STATS = bootlm (BP(:), {diet(:), drug(:), feedback(:)}, 'model', 'full', ...
+                                    'display', 'on', 'dim', [1,2,3], ...
+                                    'posthoc', 'trt_vs_ctrl', ...
+                                    'varnames', {'diet', 'drug', 'feedback'});
+
+ ## 95% credible intervals for the estimated marginal means of salaries of
+ ## females and males (computed by Bayesian bootstrap).
+ STATS = bootlm (BP(:), {diet(:), drug(:), feedback(:)}, 'model', 'full', ...
+                                    'display', 'on', 'dim', [1,2,3], ...
+                                    'method', 'bayesian', 'prior', 'auto', ...
+                                    'varnames', {'diet', 'drug', 'feedback'});
+

Produces the following output

+
ANOVA SUMMARY
+F(1,60) = 33.20, p = 0.0001 for the model: Y ~ 1 + diet
+F(2,60) = 11.73, p = 0.000179 for the model: Y ~ 1 + diet + drug
+F(1,60) = 13.07, p = 0.000561 for the model: Y ~ 1 + diet + drug + feedback
+F(2,60) = 2.88, p = 0.0628 for the model: Y ~ 1 + diet + drug + feedback + diet:drug
+F(1,60) = 0.20, p = 0.648 for the model: Y ~ 1 + diet + drug + feedback + diet:drug + diet:feedback
+F(2,60) = 0.83, p = 0.434 for the model: Y ~ 1 + diet + drug + feedback + diet:drug + diet:feedback + drug:feedback
+F(2,60) = 3.43, p = 0.0388 for the model: Y ~ 1 + diet + drug + feedback + diet:drug + diet:feedback + drug:feedback + diet:drug:feedback
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+Y ~ 1 + diet + drug + feedback + diet:drug + diet:feedback + drug:feedback + diet:drug:feedback
+
+MODEL COEFFICIENTS
+
+name                                   coeff       CI_lower    CI_upper    p-val
+--------------------------------------------------------------------------------
+(Intercept)                            +168.0      +157.9      +178.1      <.001
+diet_1                                 +1.000      -15.70      +17.70       .883
+drug_1                                 +36.00      +21.99      +50.01      <.001
+drug_2                                 +21.00      +6.751      +35.25       .008
+feedback_1                             +20.00      +7.057      +32.94       .006
+diet:drug_1                            -33.00      -53.28      -12.72       .004
+diet:drug_2                            -17.00      -37.94      +3.936       .104
+diet:feedback_1                        -16.00      -35.17      +3.172       .095
+drug:feedback_1                        -24.00      -42.08      -5.922       .011
+drug:feedback_2                        -7.061e-14  -19.93      +19.93      1.000
+diet:drug:feedback_1                   +35.00      +7.926      +62.07       .013
+diet:drug:feedback_2                   +5.000      -24.39      +34.39       .737
+
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+Y ~ 1 + diet + drug + feedback + diet:drug + diet:feedback + drug:feedback + diet:drug:feedback
+
+MODEL POSTHOC COMPARISONS
+
+name                                   mean        CI_lower    CI_upper    p-adj
+--------------------------------------------------------------------------------
+1, X, 1 - 0, X, 1                      +1.000      -15.45      +17.45      1.000
+0, Y, 1 - 0, X, 1                      +36.00      +21.52      +50.48       .002
+1, Y, 1 - 0, X, 1                      +4.000      -8.896      +16.90      1.000
+0, Z, 1 - 0, X, 1                      +21.00      +6.775      +35.22       .057
+1, Z, 1 - 0, X, 1                      +5.000      -8.547      +18.55      1.000
+0, X, 0 - 0, X, 1                      +20.00      +7.164      +32.84       .057
+1, X, 0 - 0, X, 1                      +5.000      -6.615      +16.62      1.000
+0, Y, 0 - 0, X, 1                      +32.00      +20.00      +44.00       .002
+1, Y, 0 - 0, X, 1                      +19.00      +2.687      +35.31       .190
+0, Z, 0 - 0, X, 1                      +41.00      +25.53      +56.47       .001
+1, Z, 0 - 0, X, 1                      +14.00      -4.969      +32.97       .603
+
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+Y ~ 1 + diet + drug + feedback + diet:drug + diet:feedback + drug:feedback + diet:drug:feedback
+
+MODEL ESTIMATED MARGINAL MEANS
+
+name                                   mean        CI_lower    CI_upper        N
+--------------------------------------------------------------------------------
+0, X, 1                                +168.0      +161.3      +174.6          6
+1, X, 1                                +169.0      +158.0      +181.0          6
+0, Y, 1                                +204.0      +193.6      +213.5          6
+1, Y, 1                                +172.0      +163.9      +180.9          6
+0, Z, 1                                +189.0      +178.8      +198.8          6
+1, Z, 1                                +173.0      +163.5      +181.1          6
+0, X, 0                                +188.0      +179.6      +196.0          6
+1, X, 0                                +173.0      +165.7      +181.0          6
+0, Y, 0                                +200.0      +192.6      +208.4          6
+1, Y, 0                                +187.0      +176.1      +197.4          6
+0, Z, 0                                +209.0      +198.1      +220.9          6
+1, Z, 0                                +182.0      +169.3      +196.4          6
+

and the following figure

+

+ + + + +
Figure 1
+

+
+

Demonstration 8

+
+

The following code

+
+
+ ## One-way design with continuous covariate. The data is from a study of the
+ ## additive effects of species and temperature on chirpy pulses of crickets,
+ ## from Stitch, The Worst Stats Text eveR
+
+ pulse = [67.9 65.1 77.3 78.7 79.4 80.4 85.8 86.6 87.5 89.1 ...
+          98.6 100.8 99.3 101.7 44.3 47.2 47.6 49.6 50.3 51.8 ...
+          60 58.5 58.9 60.7 69.8 70.9 76.2 76.1 77 77.7 84.7]';
+ temp = [20.8 20.8 24 24 24 24 26.2 26.2 26.2 26.2 28.4 ...
+         29 30.4 30.4 17.2 18.3 18.3 18.3 18.9 18.9 20.4 ...
+         21 21 22.1 23.5 24.2 25.9 26.5 26.5 26.5 28.6]';
+ species = {'ex' 'ex' 'ex' 'ex' 'ex' 'ex' 'ex' 'ex' 'ex' 'ex' 'ex' ...
+            'ex' 'ex' 'ex' 'niv' 'niv' 'niv' 'niv' 'niv' 'niv' 'niv' ...
+            'niv' 'niv' 'niv' 'niv' 'niv' 'niv' 'niv' 'niv' 'niv' 'niv'};
+
+ ## Perform ANCOVA 
+ ## Use 'anova' contrasts so that the continuous covariate is centered
+ [STATS, BOOTSTAT, AOVSTAT] = bootlm (pulse, {temp, species}, 'model', ...
+                           'linear', 'continuous', 1, 'display', 'off', ...
+                           'varnames', {'temp', 'species'}, ...
+                           'contrasts', 'anova');
+
+ fprintf ('ANCOVA SUMMARY\n')
+ for i = 1:numel(AOVSTAT.F)
+   fprintf ('F(%u,%u) = %.2f, p = %.3g for the model: %s\n', ...
+            AOVSTAT.DF(i), AOVSTAT.DFE, AOVSTAT.F(i), ...
+            AOVSTAT.PVAL(i), AOVSTAT.MODEL{i});
+ end
+
+ ## Estimate regression coefficients using 'anova' contrast coding 
+ STATS = bootlm (pulse, {temp, species}, 'model', 'linear', ...
+                           'continuous', 1, 'display', 'on', ...
+                           'varnames', {'temp', 'species'}, ...
+                           'contrasts', 'anova');
+
+ ## 95% confidence intervals and p-values for the differences in the mean of
+ ## chirpy pulses of ex ad niv species (computed by wild bootstrap).
+ STATS = bootlm (pulse, {temp, species}, 'model', 'linear', ...
+                           'continuous', 1, 'display', 'on', ...
+                           'varnames', {'temp', 'species'}, 'dim', 2, ...
+                           'posthoc', 'trt_vs_ctrl', 'contrasts', 'anova');
+
+ ## 95% credible intervals for the estimated marginal means of chirpy pulses
+ ## of ex and niv species (computed by Bayesian bootstrap).
+ STATS = bootlm (pulse, {temp, species}, 'model', 'linear', ...
+                           'continuous', 1, 'display', 'on', ...
+                           'varnames', {'temp', 'species'}, 'dim', 2, ...
+                           'method', 'bayesian', 'prior', 'auto', ...
+                           'contrasts', 'anova');
+

Produces the following output

+
ANCOVA SUMMARY
+F(1,28) = 2474.04, p = 0.0001 for the model: pulse ~ 1 + temp
+F(1,28) = 187.40, p = 0.0001 for the model: pulse ~ 1 + temp + species
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+pulse ~ 1 + temp + species
+
+MODEL COEFFICIENTS
+
+name                                   coeff       CI_lower    CI_upper    p-val
+--------------------------------------------------------------------------------
+(Intercept)                            +73.37      +72.70      +74.05      <.001
+temp                                   +3.603      +3.408      +3.797      <.001
+species_1                              -10.07      -11.41      -8.720      <.001
+
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+pulse ~ 1 + temp + species
+
+MODEL POSTHOC COMPARISONS
+
+name                                   mean        CI_lower    CI_upper    p-adj
+--------------------------------------------------------------------------------
+niv - ex                               -10.07      -11.43      -8.700      <.001
+
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+pulse ~ 1 + temp + species
+
+MODEL ESTIMATED MARGINAL MEANS
+
+name                                   mean        CI_lower    CI_upper        N
+--------------------------------------------------------------------------------
+ex                                     +78.41      +77.44      +79.41         14
+niv                                    +68.34      +67.58      +69.18         17
+

and the following figure

+

+ + + + +
Figure 1
+

+
+

Demonstration 9

+
+

The following code

+
+
+ ## Factorial design with continuous covariate. The data is from a study of
+ ## the effects of treatment and exercise on stress reduction score after
+ ## adjusting for age. Data from R datarium package).
+
+ score = [95.6 82.2 97.2 96.4 81.4 83.6 89.4 83.8 83.3 85.7 ...
+          97.2 78.2 78.9 91.8 86.9 84.1 88.6 89.8 87.3 85.4 ...
+          81.8 65.8 68.1 70.0 69.9 75.1 72.3 70.9 71.5 72.5 ...
+          84.9 96.1 94.6 82.5 90.7 87.0 86.8 93.3 87.6 92.4 ...
+          100. 80.5 92.9 84.0 88.4 91.1 85.7 91.3 92.3 87.9 ...
+          91.7 88.6 75.8 75.7 75.3 82.4 80.1 86.0 81.8 82.5]';
+ treatment = {'yes' 'yes' 'yes' 'yes' 'yes' 'yes' 'yes' 'yes' 'yes' 'yes' ...
+              'yes' 'yes' 'yes' 'yes' 'yes' 'yes' 'yes' 'yes' 'yes' 'yes' ...
+              'yes' 'yes' 'yes' 'yes' 'yes' 'yes' 'yes' 'yes' 'yes' 'yes' ...
+              'no'  'no'  'no'  'no'  'no'  'no'  'no'  'no'  'no'  'no'  ...
+              'no'  'no'  'no'  'no'  'no'  'no'  'no'  'no'  'no'  'no'  ...
+              'no'  'no'  'no'  'no'  'no'  'no'  'no'  'no'  'no'  'no'}';
+ exercise = {'lo'  'lo'  'lo'  'lo'  'lo'  'lo'  'lo'  'lo'  'lo'  'lo'  ...
+             'mid' 'mid' 'mid' 'mid' 'mid' 'mid' 'mid' 'mid' 'mid' 'mid' ...
+             'hi'  'hi'  'hi'  'hi'  'hi'  'hi'  'hi'  'hi'  'hi'  'hi'  ...
+             'lo'  'lo'  'lo'  'lo'  'lo'  'lo'  'lo'  'lo'  'lo'  'lo'  ...
+             'mid' 'mid' 'mid' 'mid' 'mid' 'mid' 'mid' 'mid' 'mid' 'mid' ...
+             'hi'  'hi'  'hi'  'hi'  'hi'  'hi'  'hi'  'hi'  'hi'  'hi'}';
+ age = [59 65 70 66 61 65 57 61 58 55 62 61 60 59 55 57 60 63 62 57 ...
+        58 56 57 59 59 60 55 53 55 58 68 62 61 54 59 63 60 67 60 67 ...
+        75 54 57 62 65 60 58 61 65 57 56 58 58 58 52 53 60 62 61 61]';
+
+ ## ANOVA/ANCOVA statistics
+ ## Use 'anova' contrasts so that the continuous covariate is centered
+ [STATS, BOOTSTAT, AOVSTAT] = bootlm (score, {age, exercise, treatment}, ...
+                            'model', [1 0 0; 0 1 0; 0 0 1; 0 1 1], ...
+                            'continuous', 1, 'display', 'off', ...
+                            'varnames', {'age', 'exercise', 'treatment'},...
+                            'contrasts', 'anova');
+
+ fprintf ('ANOVA / ANCOVA SUMMARY\n')
+ for i = 1:numel(AOVSTAT.F)
+   fprintf ('F(%u,%u) = %.2f, p = %.3g for the model: %s\n', ...
+            AOVSTAT.DF(i), AOVSTAT.DFE, AOVSTAT.F(i), ...
+            AOVSTAT.PVAL(i), AOVSTAT.MODEL{i});
+ end
+
+ ## Estimate regression coefficients
+ STATS = bootlm (score, {age, exercise, treatment}, ...
+                            'model', [1 0 0; 0 1 0; 0 0 1; 0 1 1], ...
+                            'continuous', 1, 'display', 'on', ...
+                            'varnames', {'age', 'exercise', 'treatment'}, ...
+                            'contrasts', 'anova');
+
+ ## 95% confidence intervals and p-values for the differences in mean score
+ ## across different treatments and amounts of exercise after adjusting for
+ STATS = bootlm (score, {age, exercise, treatment}, ...
+                            'model', [1 0 0; 0 1 0; 0 0 1; 0 1 1], ...
+                            'continuous', 1, 'display', 'on', ...
+                            'varnames', {'age', 'exercise', 'treatment'}, ...
+                            'dim', [2, 3], 'posthoc', 'trt_vs_ctrl', ...
+                            'contrasts', 'anova');
+
+ ## 95% credible intervals for the estimated marginal means of scores across
+ ## different treatments and amounts of exercise after adjusting for age
+ ## (computed by Bayesian bootstrap).
+ STATS = bootlm (score, {age, exercise, treatment}, 'dim', [2, 3], ...
+                            'model', [1 0 0; 0 1 0; 0 0 1; 0 1 1], ...
+                            'continuous', 1, 'display', 'on', ...
+                            'varnames', {'age', 'exercise', 'treatment'}, ...
+                            'method', 'bayesian', 'prior', 'auto', ...
+                            'contrasts', 'anova');
+

Produces the following output

+
ANOVA / ANCOVA SUMMARY
+F(1,53) = 44.02, p = 0.0001 for the model: score ~ 1 + age
+F(2,53) = 19.74, p = 0.0001 for the model: score ~ 1 + age + exercise
+F(1,53) = 11.10, p = 0.00196 for the model: score ~ 1 + age + exercise + treatment
+F(2,53) = 4.45, p = 0.0159 for the model: score ~ 1 + age + exercise + treatment + exercise:treatment
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+score ~ 1 + age + exercise + treatment + exercise:treatment
+
+MODEL COEFFICIENTS
+
+name                                   coeff       CI_lower    CI_upper    p-val
+--------------------------------------------------------------------------------
+(Intercept)                            +84.58      +83.32      +85.84      <.001
+age                                    +0.5036     +0.1828     +0.8243      .003
+exercise_1                             +0.09497    -3.106      +3.296       .950
+exercise_2                             -9.594      -12.82      -6.373      <.001
+treatment_1                            +4.320      +1.611      +7.028       .002
+exercise:treatment_1                   +0.1550     -6.443      +6.753       .961
+exercise:treatment_2                   +8.218      +1.763      +14.67       .015
+
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+score ~ 1 + age + exercise + treatment + exercise:treatment
+
+MODEL POSTHOC COMPARISONS
+
+name                                   mean        CI_lower    CI_upper    p-adj
+--------------------------------------------------------------------------------
+mid, yes - lo, yes                     +0.01746    -5.361      +5.396      1.000
+hi, yes - lo, yes                      -13.70      -18.49      -8.915      <.001
+lo, no - lo, yes                       +1.529      -3.283      +6.341      1.000
+mid, no - lo, yes                      +1.701      -3.118      +6.520      1.000
+hi, no - lo, yes                       -3.957      -9.147      +1.234       .514
+
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+score ~ 1 + age + exercise + treatment + exercise:treatment
+
+MODEL ESTIMATED MARGINAL MEANS
+
+name                                   mean        CI_lower    CI_upper        N
+--------------------------------------------------------------------------------
+lo, yes                                +86.98      +83.34      +90.47         10
+mid, yes                               +87.00      +83.33      +90.39         10
+hi, yes                                +73.28      +70.56      +76.23         10
+lo, no                                 +88.51      +86.09      +91.32         10
+mid, no                                +88.68      +86.31      +91.15         10
+hi, no                                 +83.02      +79.71      +86.50         10
+

and the following figure

+

+ + + + +
Figure 1
+

+
+

Demonstration 10

+
+

The following code

+
+
+ ## Unbalanced one-way design with custom, orthogonal contrasts. Data from
+ ## www.uvm.edu/~statdhtx/StatPages/Unequal-ns/Unequal_n%27s_contrasts.html
+
+ dv =  [ 8.706 10.362 11.552  6.941 10.983 10.092  6.421 14.943 15.931 ...
+        22.968 18.590 16.567 15.944 21.637 14.492 17.965 18.851 22.891 ...
+        22.028 16.884 17.252 18.325 25.435 19.141 21.238 22.196 18.038 ...
+        22.628 31.163 26.053 24.419 32.145 28.966 30.207 29.142 33.212 ...
+        25.694 ]';
+ g = [1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 3 3 3 ...
+      4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5]';
+ C = [ 0.4001601  0.3333333  0.5  0.0
+       0.4001601  0.3333333 -0.5  0.0
+       0.4001601 -0.6666667  0.0  0.0
+      -0.6002401  0.0000000  0.0  0.5
+      -0.6002401  0.0000000  0.0 -0.5];
+
+ ## 95% confidence intervals and p-values for linear contrasts 
+ STATS = bootlm (dv, g, 'contrasts', C, 'varnames', 'score', ...
+                          'alpha', 0.05, 'display', true);
+
+ ## 95% credible intervals for estimated marginal means 
+ STATS = bootlm (dv, g, 'contrasts', C, 'varnames', 'score', ...
+                          'alpha', 0.05, 'display', true, 'dim', 1, ...
+                          'method', 'Bayesian', 'prior', 'auto');
+

Produces the following output

+
MODEL FORMULA (based on Wilkinson's notation):
+
+dv ~ 1 + score
+
+MODEL COEFFICIENTS
+
+name                                   coeff       CI_lower    CI_upper    p-val
+--------------------------------------------------------------------------------
+(Intercept)                            +19.40      +18.43      +20.37      <.001
+score_1                                -9.330      -11.32      -7.340      <.001
+score_2                                -5.000      -7.791      -2.209       .001
+score_3                                -8.000      -11.48      -4.524      <.001
+score_4                                -8.000      -11.05      -4.953      <.001
+
+
+MODEL FORMULA (based on Wilkinson's notation):
+
+dv ~ 1 + score
+
+MODEL ESTIMATED MARGINAL MEANS
+
+name                                   mean        CI_lower    CI_upper        N
+--------------------------------------------------------------------------------
+1                                      +10.00      +8.137      +12.00          8
+2                                      +18.00      +16.01      +20.68          5
+3                                      +19.00      +16.99      +21.01          8
+4                                      +21.00      +19.08      +23.02          7
+5                                      +29.00      +26.95      +30.94          9
+

and the following figure

+

+ + + + +
Figure 1
+

+
+

Demonstration 11

+
+

The following code

+
+
+ ## Comparing analysis of nested design using ANOVA with clustered resampling.
+ ## Two factor nested model example from:
+ ## https://www.southampton.ac.uk/~cpd/anovas/datasets/#Chapter2
+
+ data = [4.5924 7.3809 21.322; -0.5488 9.2085 25.0426; ...
+         6.1605 13.1147 22.66; 2.3374 15.2654 24.1283; ...
+         5.1873 12.4188 16.5927; 3.3579 14.3951 10.2129; ...
+         6.3092 8.5986 9.8934; 3.2831 3.4945 10.0203];
+
+ clustid = [1 3 5; 1 3 5; 1 3 5; 1 3 5; ...
+            2 4 6; 2 4 6; 2 4 6; 2 4 6];
+
+ group = {'A' 'B' 'C'; 'A' 'B' 'C'; 'A' 'B' 'C'; 'A' 'B' 'C'; ...
+          'A' 'B' 'C'; 'A' 'B' 'C'; 'A' 'B' 'C'; 'A' 'B' 'C'};
+
+ [STATS, BOOTSTAT, AOVSTAT] = bootlm (data(:), group(:), 'seed', 1, ...
+                                      'clustid', clustid(:));
+ 
+ fprintf ('ANOVA SUMMARY\n')
+ fprintf ('F(%u,%u) = %.2f, p = %.3g for the model: %s\n', ...
+            AOVSTAT.DF(1), AOVSTAT.DFE, AOVSTAT.F(1), ...
+            AOVSTAT.PVAL(1), AOVSTAT.MODEL{1});
+

Produces the following output

+
MODEL FORMULA (based on Wilkinson's notation):
+
+Y ~ 1 + X1
+
+MODEL COEFFICIENTS
+
+name                                   coeff       CI_lower    CI_upper    p-val
+--------------------------------------------------------------------------------
+(Intercept)                            +3.835      -1.793e+14  +1.793e+14   .406
+X1_1                                   +6.650      -7.776      +21.08       .121
+X1_2                                   +13.65      -349.5      +376.8       .512
+
+ANOVA SUMMARY
+F(2,21) = 17.08, p = 0.018 for the model: Y ~ 1 + X1
+

and the following figure

+

+ + + + +
Figure 1
+

+
+

Demonstration 12

+
+

The following code

+
+
+ ## Prediction errors of linear models. Data from Table 9.1, on page 107 of
+ ## Efron and Tibshirani (1993) An Introduction to the Bootstrap.
+
+ amount = [25.8; 20.5; 14.3; 23.2; 20.6; 31.1; 20.9; 20.9; 30.4; ...
+          16.3; 11.6; 11.8; 32.5; 32.0; 18.0; 24.1; 26.5; 25.8; ...
+          28.8; 22.0; 29.7; 28.9; 32.8; 32.5; 25.4; 31.7; 28.5];
+
+ hrs = [99; 152; 293; 155; 196; 53; 184; 171; 52; ...
+        376; 385; 402; 29; 76; 296; 151; 177; 209; ...
+        119; 188; 115; 88; 58; 49; 150; 107; 125];
+
+ lot = {'A'; 'A'; 'A'; 'A'; 'A'; 'A'; 'A'; 'A'; 'A'; ...
+        'B'; 'B'; 'B'; 'B'; 'B'; 'B'; 'B'; 'B'; 'B'; ...
+        'C'; 'C'; 'C'; 'C'; 'C'; 'C'; 'C'; 'C'; 'C'};
+
+ [STATS, BOOTSTAT, AOVSTAT, PRED_ERR] = bootlm (amount, {hrs, lot}, ...
+                                    'continuous', 1, 'seed', 1, ...
+                                    'model', 'linear', 'display', 'on', ...
+                                    'varnames', {'hrs', 'lot'}, ...
+                                    'contrasts', 'treatment');
+
+ fprintf ('PREDICTION ERROR of the FULL MODEL = %.2f\n', PRED_ERR.PE(3))
+
+ ## Note: The value of prediction error is lower than the 3.00 calculated by
+ ## Efron and Tibhirani (1993) using the same refined bootstrap procedure,
+ ## because they have used case resampling whereas we have used wild bootstrap
+ ## resampling. The equivalent value of Cp (eq. to AIC) statistic is 2.96.
+

Produces the following output

+
MODEL FORMULA (based on Wilkinson's notation):
+
+amount ~ 1 + hrs + lot
+
+MODEL COEFFICIENTS
+
+name                                   coeff       CI_lower    CI_upper    p-val
+--------------------------------------------------------------------------------
+(Intercept)                            +32.13      +30.27      +34.00      <.001
+hrs                                    -0.06014    -0.06841    -0.05186    <.001
+lot_1                                  +3.973      +2.172      +5.775      <.001
+lot_2                                  +3.466      +1.962      +4.970      <.001
+
+PREDICTION ERROR of the FULL MODEL = 2.86
+

and the following figure

+

+ + + + +
Figure 1
+

+
+

Demonstration 13

+
+

The following code

+
+
+ ## Stepwise regression
+
+ sr = [11.43;12.07;13.17;05.75;12.88;08.79;00.60;11.90; ...
+       04.98;10.78;16.85;03.59;11.24;12.64;12.55;10.67; ...
+       03.01;07.70;01.27;09.00;11.34;14.28;21.10;03.98; ...
+       10.35;15.48;10.25;14.65;10.67;07.30;04.44;02.02; ...
+       12.70;12.78;12.49;11.14;13.30;11.77;06.86;14.13; ...
+       05.13;02.81;07.81;07.56;09.22;18.56;07.72;09.24; ...
+       08.89;4.71];
+
+ pop15 = [29.35;23.32;23.80;41.89;42.19;31.72;39.74;44.75;
+          46.64;47.64;24.42;46.31;27.84;25.06;23.31;25.62;
+          46.05;47.32;34.03;41.31;31.16;24.52;27.01;41.74;
+          21.80;32.54;25.95;24.71;32.61;45.04;43.56;41.18;
+          44.19;46.26;28.96;31.94;31.92;27.74;21.44;23.49;
+          43.42;46.12;23.27;29.81;46.40;45.25;41.12;28.13;
+         43.69;47.20];
+
+ pop75 = [2.87;4.41;4.43;1.67;0.83;2.85;1.34;0.67; ...
+          1.06;1.14;3.93;1.19;2.37;4.70;3.35;3.10; ...
+          0.87;0.58;3.08;0.96;4.19;3.48;1.91;0.91; ...
+          3.73;2.47;3.67;3.25;3.17;1.21;1.20;1.05; ...
+          1.28;1.12;2.85;2.28;1.52;2.87;4.54;3.73; ...
+          1.08;1.21;4.46;3.43;0.90;0.56;1.73;2.72; ...
+          2.07;0.66];
+
+ dpi = [2329.68;1507.99;2108.47;0189.13;0728.47;2982.88;0662.86;0289.52; ...
+        0276.65;0471.24;2496.53;0287.77;1681.25;2213.82;2457.12;0870.85; ...
+        0289.71;0232.44;1900.10;0088.94;1139.95;1390.00;1257.28;0207.68; ...
+        2449.39;0601.05;2231.03;1740.70;1487.52;0325.54;0568.56;0220.56; ...
+        0400.06;0152.01;0579.51;0651.11;0250.96;0768.79;3299.49;2630.96; ...
+        0389.66;0249.87;1813.93;4001.89;0813.39;0138.33;0380.47;0766.54; ...
+        0123.58;0242.69];
+
+ ddpi = [02.87;03.93;03.82;00.22;04.56;02.43;02.67;06.51;
+         03.08;02.80;03.99;02.19;04.32;04.52;03.44;06.28;
+         01.48;03.19;01.12;01.54;02.99;03.54;08.21;05.81;
+         01.57;08.12;03.62;07.66;01.76;02.48;03.61;01.03;
+         00.67;02.00;07.48;02.19;02.00;04.35;03.01;02.70;
+         02.96;01.13;02.01;02.45;00.53;05.14;10.23;01.88;
+         16.71;05.08];
+
+  [STATS, BOOTSTAT, AOVSTAT, PRED_ERR] = bootlm (sr, {pop15, pop75, ...
+                                     dpi, ddpi}, 'seed', 1, 'continuous', [1:4], ...
+                                     'model', 'linear', 'display', 'off', ...
+                                     'varnames', {'pop15','pop75','dpi','ddpi'},
+                                     'contrasts', 'treatment');
+
+ PRED_ERR
+ 
+ ## The results from the bootstrap are broadly consistent to the results
+ ## obtained for PE, PRESS and RSQ_pred using cross-validation:
+ ##
+ ##     MODEL                                  PE-CV    PRESS-CV  RSQ_pred-CV
+ ##     Y ~ 1                                  20.48    1024.186       -0.041
+ ##     Y ~ 1 + pop15                          16.88     843.910       +0.142
+ ##     Y ~ 1 + pop15 + pop75                  16.62     830.879       +0.155
+ ##     Y ~ 1 + pop15 + pop75 + dpi            16.54     827.168       +0.159
+ ##     Y ~ 1 + pop15 + pop75 + dpi + ddpi     15.98     798.939       +0.188
+

Produces the following output

+
PRED_ERR =
+
+  scalar structure containing the fields:
+
+    MODEL =
+    {
+      [1,1] = Y ~ 1
+      [2,1] = sr ~ 1 + pop15
+      [3,1] = sr ~ 1 + pop15 + pop75
+      [4,1] = sr ~ 1 + pop15 + pop75 + dpi
+      [5,1] = sr ~ 1 + pop15 + pop75 + dpi + ddpi
+    }
+
+    PE =
+
+       20.477
+       16.800
+       16.340
+       16.220
+       15.191
+
+    PRESS =
+
+       1023.83
+        840.00
+        817.01
+        811.02
+        759.53
+
+    RSQ_pred =
+
+      -0.040869
+       0.146016
+       0.169388
+       0.175483
+       0.227832
+

Package: statistics-resampling

diff --git a/docs/function/bootmode.html b/docs/function/bootmode.html index 4194c07b..d6cf0bc6 100644 --- a/docs/function/bootmode.html +++ b/docs/function/bootmode.html @@ -78,6 +78,78 @@ You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/ +

Demonstration 1

+
+

The following code

+
+
+ # Stamp data example used in reference [1] in bootstrap R package
+ x=[0.060;0.064;0.064;0.065;0.066;0.068;0.069;0.069;0.069;0.069;0.069; ...
+    0.069;0.069;0.070;0.070;0.070;0.070;0.070;0.070;0.070;0.070;0.070; ...
+    0.070;0.070;0.070;0.070;0.070;0.070;0.070;0.070;0.070;0.070;0.070; ...
+    0.070;0.070;0.070;0.070;0.070;0.070;0.071;0.071;0.071;0.071;0.071; ...
+    0.071;0.071;0.071;0.071;0.071;0.071;0.071;0.071;0.071;0.071;0.071; ...
+    0.071;0.071;0.071;0.071;0.072;0.072;0.072;0.072;0.072;0.072;0.072; ...
+    0.072;0.072;0.072;0.072;0.072;0.072;0.072;0.072;0.072;0.072;0.072; ...
+    0.072;0.072;0.072;0.072;0.072;0.072;0.072;0.072;0.072;0.072;0.072; ...
+    0.072;0.072;0.072;0.073;0.073;0.073;0.073;0.073;0.073;0.073;0.073; ...
+    0.073;0.073;0.073;0.074;0.074;0.074;0.074;0.074;0.074;0.074;0.074; ...
+    0.074;0.074;0.075;0.075;0.075;0.075;0.075;0.075;0.075;0.075;0.075; ...
+    0.075;0.075;0.075;0.075;0.075;0.075;0.075;0.075;0.075;0.075;0.075; ...
+    0.076;0.076;0.076;0.076;0.076;0.076;0.076;0.076;0.076;0.076;0.076; ...
+    0.076;0.076;0.076;0.076;0.076;0.076;0.076;0.077;0.077;0.077;0.077; ...
+    0.077;0.077;0.077;0.077;0.077;0.077;0.077;0.078;0.078;0.078;0.078; ...
+    0.078;0.078;0.078;0.078;0.078;0.078;0.078;0.078;0.078;0.078;0.078; ...
+    0.078;0.078;0.078;0.078;0.078;0.078;0.078;0.078;0.079;0.079;0.079; ...
+    0.079;0.079;0.079;0.079;0.079;0.079;0.079;0.079;0.079;0.079;0.079; ...
+    0.079;0.079;0.079;0.079;0.079;0.079;0.079;0.079;0.079;0.079;0.079; ...
+    0.079;0.079;0.079;0.079;0.079;0.079;0.079;0.079;0.079;0.079;0.079; ...
+    0.079;0.079;0.079;0.079;0.079;0.079;0.080;0.080;0.080;0.080;0.080; ...
+    0.080;0.080;0.080;0.080;0.080;0.080;0.080;0.080;0.080;0.080;0.080; ...
+    0.080;0.080;0.080;0.080;0.080;0.080;0.080;0.080;0.080;0.080;0.080; ...
+    0.080;0.080;0.080;0.080;0.080;0.080;0.080;0.080;0.080;0.080;0.081; ...
+    0.081;0.081;0.081;0.081;0.081;0.081;0.081;0.081;0.081;0.081;0.081; ...
+    0.081;0.081;0.081;0.082;0.082;0.082;0.082;0.082;0.082;0.082;0.082; ...
+    0.082;0.082;0.082;0.082;0.082;0.082;0.082;0.082;0.082;0.082;0.083; ...
+    0.083;0.083;0.083;0.083;0.083;0.083;0.084;0.084;0.084;0.085;0.085; ...
+    0.086;0.086;0.087;0.088;0.088;0.089;0.089;0.089;0.089;0.089;0.089; ...
+    0.089;0.089;0.089;0.089;0.090;0.090;0.090;0.090;0.090;0.090;0.090; ...
+    0.090;0.090;0.091;0.091;0.091;0.092;0.092;0.092;0.092;0.092;0.093; ...
+    0.093;0.093;0.093;0.093;0.093;0.094;0.094;0.094;0.095;0.095;0.096; ...
+    0.096;0.096;0.097;0.097;0.097;0.097;0.097;0.097;0.097;0.098;0.098; ...
+    0.098;0.098;0.098;0.099;0.099;0.099;0.099;0.099;0.100;0.100;0.100; ...
+    0.100;0.100;0.100;0.100;0.100;0.100;0.100;0.100;0.100;0.100;0.100; ...
+    0.100;0.101;0.101;0.101;0.101;0.101;0.101;0.101;0.101;0.101;0.102; ...
+    0.102;0.102;0.102;0.102;0.102;0.102;0.102;0.103;0.103;0.103;0.103; ...
+    0.103;0.103;0.103;0.104;0.104;0.105;0.105;0.105;0.105;0.105;0.106; ...
+    0.106;0.106;0.106;0.107;0.107;0.107;0.108;0.108;0.108;0.108;0.108; ...
+    0.108;0.108;0.109;0.109;0.109;0.109;0.109;0.109;0.109;0.110;0.110; ...
+    0.110;0.110;0.110;0.110;0.110;0.110;0.110;0.110;0.110;0.111;0.111; ...
+    0.111;0.111;0.112;0.112;0.112;0.112;0.112;0.114;0.114;0.114;0.115; ...
+    0.115;0.115;0.117;0.119;0.119;0.119;0.119;0.120;0.120;0.120;0.121; ...
+    0.122;0.122;0.123;0.123;0.125;0.125;0.128; 0.129;0.129;0.129;0.130;0.131];
+ 
+ [H1, P1, CRITVAL1] = bootmode(x,1,2000);
+
+ # Repeat function call systematically increasing the number of modes (M) by 
+ # 1, until the null hypothesis is accepted (i.e. H0 = 0)
+
+ [H2, P2, CRITVAL2] = bootmode(x,2,2000);
+ 
+ sprintf ('Summary of results:\n') 
+ sprintf (cat (2, 'H1 is %u with p = %.3g so reject the null hypothesis', ...
+                  'that there is 1 mode\n'), H1, P1)
+ sprintf (cat (2, 'H2 is %u with p = %.3g so accept the null hypothesis', ...
+                  ' that there are 2 modes\n'), H2, P2)
+ 
+ # Please be patient, these calculations take a while...
+

Produces the following output

+
ans = Summary of results:
+
+ans = H1 is 1 with p = 0.0005 so reject the null hypothesisthat there is 1 mode
+
+ans = H2 is 0 with p = 0.329 so accept the null hypothesis that there are 2 modes
+

Package: statistics-resampling

diff --git a/docs/function/bootstrp.html b/docs/function/bootstrp.html index 5de30225..16f5792b 100644 --- a/docs/function/bootstrp.html +++ b/docs/function/bootstrp.html @@ -86,6 +86,75 @@ You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/ +

Demonstration 1

+
+

The following code

+
+
+ # Input univariate dataset
+ data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+         0 33 28 34 4 32 24 47 41 24 26 30 41]';
+
+ # Compute 50 bootstrap statistics for the mean and calculate the bootstrap
+ # standard arror
+ bootstat = bootstrp (50, @mean, data)
+ std (bootstat)
+

Produces the following output

+
bootstat =
+
+   31.077
+   26.615
+   29.731
+   29.231
+   27.885
+   28.962
+   29.231
+   28.654
+   35.615
+   27.654
+   26.462
+   30.885
+   31.731
+   29.615
+   28.308
+   29.538
+   29.923
+   30.115
+   32.538
+   28.962
+   31.385
+   25.231
+   30.154
+   26.115
+   25.231
+   25.962
+   33.654
+   33.269
+   31.154
+   34.385
+   30.962
+   30.808
+   29.192
+   29.038
+   25.769
+   30.192
+   30.231
+   28.192
+   28.808
+   31.269
+   27.692
+   28.231
+   32.346
+   31.385
+   28.500
+   31.038
+   28.192
+   33.308
+   30.231
+   28.038
+
+ans = 2.3366
+

Package: statistics-resampling

diff --git a/docs/function/bootwild.html b/docs/function/bootwild.html index a0cf2f15..7fa7d0d2 100644 --- a/docs/function/bootwild.html +++ b/docs/function/bootwild.html @@ -145,6 +145,73 @@ You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/ +

Demonstration 1

+
+

The following code

+
+
+ ## Input univariate dataset
+ heights = [183, 192, 182, 183, 177, 185, 188, 188, 182, 185].';
+
+ ## Test statistics and p-values (H0 = 0)
+ bootwild(heights);
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
Summary of wild bootstrap null hypothesis significance tests for linear models
+*******************************************************************************
+
+Bootstrap settings: 
+ Function: X \ y
+ Resampling method: Wild bootstrap-t
+ Number of resamples: 1999 
+ Standard error calculations: Heteroscedasticity-Consistent (HC0)
+ Confidence interval (CI) type: Symmetric bootstrap-t interval
+ Nominal central coverage: 95%
+ Null value (H0) used for hypothesis testing (p-values): 0 
+
+Test Statistics: 
+ original     std_err      CI_lower     CI_upper     t-stat      p-val     FPR
+ +184.5       +1.243       +181.6       +187.4       +148.       <.001    .010
+
+

Demonstration 2

+
+

The following code

+
+
+ ## Input bivariate dataset
+ X = [ones(43,1),...
+     [01,02,03,04,05,06,07,08,09,10,11,...
+      12,13,14,15,16,17,18,19,20,21,22,...
+      23,25,26,27,28,29,30,31,32,33,34,...
+      35,36,37,38,39,40,41,42,43,44]'];
+ y = [188.0,170.0,189.0,163.0,183.0,171.0,185.0,168.0,173.0,183.0,173.0,...
+     173.0,175.0,178.0,183.0,192.4,178.0,173.0,174.0,183.0,188.0,180.0,...
+     168.0,170.0,178.0,182.0,180.0,183.0,178.0,182.0,188.0,175.0,179.0,...
+     183.0,192.0,182.0,183.0,177.0,185.0,188.0,188.0,182.0,185.0]';
+
+ ## Compute test statistics and p-values
+ bootwild(y,X);
+
+ ## Please be patient, the calculations will be completed soon...
+

Produces the following output

+
Summary of wild bootstrap null hypothesis significance tests for linear models
+*******************************************************************************
+
+Bootstrap settings: 
+ Function: X \ y
+ Resampling method: Wild bootstrap-t
+ Number of resamples: 1999 
+ Standard error calculations: Heteroscedasticity-Consistent (HC0)
+ Confidence interval (CI) type: Symmetric bootstrap-t interval
+ Nominal central coverage: 95%
+ Null value (H0) used for hypothesis testing (p-values): 0 
+
+Test Statistics: 
+ original     std_err      CI_lower     CI_upper     t-stat      p-val     FPR
+ +175.5       +2.502       +169.8       +181.2       +70.1       <.001    .010
+ +0.1904      +0.08261     +0.003534    +0.3773      +2.31        .047    .280
+

Package: statistics-resampling

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a/docs/function/randtest2.html b/docs/function/randtest2.html index b27416e6..219bf360 100644 --- a/docs/function/randtest2.html +++ b/docs/function/randtest2.html @@ -123,6 +123,110 @@ You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/ +

Demonstration 1

+
+

The following code

+
+
+ % Mouse data from Table 2 (page 11) of Efron and Tibshirani (1993)
+ treatment = [94 197 16 38 99 141 23]';
+ control = [52 104 146 10 51 30 40 27 46]';
+
+ % Randomization test comparing the distributions of observations from two
+ % independent samples (assuming i.i.d and exchangeability) using the
+ % Wasserstein metric
+ pval = randtest2 (control, treatment, false, 5000)
+
+ % Randomization test comparing the difference in means between two
+ % independent samples (assuming i.i.d and exchangeability) 
+ pval = randtest2 (control, treatment, false, 5000, ...
+                           @(x, y) mean (x) - mean (y))
+
+ % Randomization test comparing the ratio of variances between two
+ % independent samples (assuming i.i.d and exchangeability). (Note that
+ % the log transformation is necessary to make the p-value two-tailed)
+ pval = randtest2 (control, treatment, false, 5000, ...
+                           @(x, y) log (var (y) ./ var (x)))
+
+

Produces the following output

+
pval = 0.3562
+pval = 0.2770
+pval = 0.3058
+
+

Demonstration 2

+
+

The following code

+
+
+ % Example data from: 
+ % https://www.biostat.wisc.edu/~kbroman/teaching/labstat/third/notes18.pdf
+ A = [117.3 100.1 94.5 135.5 92.9 118.9 144.8 103.9 103.8 153.6 163.1]';
+ B = [145.9 94.8 108 122.6 130.2 143.9 149.9 138.5 91.7 162.6 202.5]';
+
+ % Randomization test comparing the distributions of observations from two
+ % paired or matching samples (assuming i.i.d and exchangeability) using the
+ % Wasserstein metric
+ pval = randtest2 (A, B, true, 5000)
+
+ % Randomization test comparing the difference in means between two
+ % independent samples (assuming i.i.d and exchangeability) 
+ pval = randtest2 (A, B, true, 5000, @(A, B) mean (A) - mean (B))
+
+ % Randomization test comparing the ratio of variances between two
+ % paired or matching samples (assuming i.i.d and exchangeability). (Note
+ % that the log transformation is necessary to make the p-value two-tailed)
+ pval = randtest2 (A, B,  true, 5000, @(A, B) log (var (A) ./ var (B)))
+                           
+
+

Produces the following output

+
pval = 0.1289
+pval = 0.037109
+pval = 0.5117
+
+

Demonstration 3

+
+

The following code

+
+
+ X = [21,26,33,22,18,25,26,24,21,25,35,28,32,36,38]';
+ GX = [1,1,1,1,2,2,2,2,2,2,3,3,3,3,3]';
+ Y = [26,34,27,38,44,34,45,38,31,41,34,35,38,46]';
+ GY = [4,4,4,5,5,5,5,5,6,6,6,6,6,6]';
+
+ % Randomization test comparing the distributions of observations from two
+ % independent samples (assuming i.i.d) using the Wasserstein metric
+ pval = randtest2 (X, Y, false, 5000)
+
+ % Randomization test comparing the distributions of clustered observations
+ % from two independent samples using the Wasserstein metric
+ pval = randtest2 ([X GX], [Y GY], false, 5000)
+
+

Produces the following output

+
pval = 8.0000e-04
+pval = 0.2000
+
+

Demonstration 4

+
+

The following code

+
+
+ X = [21,26,33,22,18,25,26,24,21,25,35,28,32,36,38]';
+ GX = [1,1,1,1,2,2,2,2,2,2,3,3,3,3,3]';
+ Y = [26,34,27,38,44,34,45,38,31,41,34,35,38,46,36]';
+ GY = [1,1,1,1,2,2,2,2,2,2,3,3,3,3,3]';
+
+ % Randomization test comparing the distributions of observations from two
+ % paired or matched samples (assuming i.i.d) using the Wasserstein metric
+ pval = randtest2 (X, Y, true, 5000)
+
+ % Randomization test comparing the distributions of clustered observations
+ % from two paired or matched using the Wasserstein metric
+ pval = randtest2 ([X GX], [Y GY], true, 5000)
+
+

Produces the following output

+
pval = 1.2000e-03
+pval = 0.2500
+

Package: statistics-resampling

diff --git a/docs/function/sampszcalc.html b/docs/function/sampszcalc.html index fc9409c3..b9f1466f 100644 --- a/docs/function/sampszcalc.html +++ b/docs/function/sampszcalc.html @@ -95,6 +95,68 @@ You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/ +

Demonstration 1

+
+

The following code

+
+
+ # The difference between a sample mean from a zero constant (one sample test)
+ # or the difference between two dependent means (matched pair). Sample size
+ # determined for Cohen's d = 0.8.
+ # d effect size
+
+ n = sampszcalc ('t', 0.8)
+

Produces the following output

+
n = 15
+
+

Demonstration 2

+
+

The following code

+
+
+ # The difference between two independent means (two groups). Sample size
+ # determined for Cohen's d = 0.8.
+
+ n = sampszcalc ('t2', 0.8)
+

Produces the following output

+
n = 26
+
+

Demonstration 3

+
+

The following code

+
+
+ # The difference between two independent means (two groups). Sample size
+ # determined for Cohen's d = 0.8 and a design effect of 1.5
+
+ n = sampszcalc ('t2', 0.8, [], [], [], 1.5)
+

Produces the following output

+
n = 39
+
+

Demonstration 4

+
+

The following code

+
+
+ # The difference between two independent proportions (two sample test). 
+ # Sample size determined for Cohen's h = 0.8 using Normal approximation.
+
+ n = sampszcalc ('z2', 0.8)
+

Produces the following output

+
n = 25
+
+

Demonstration 5

+
+

The following code

+
+
+ # The test for Pearson's correlation coefficient (r) equal to 0 (constant),
+ # Sample size determined for r effect size = 0.5.
+
+ n = sampszcalc ('r', 0.5)
+

Produces the following output

+
n = 30
+

Package: statistics-resampling

diff --git a/docs/index.html b/docs/index.html index f94385dc..ca8a824c 100644 --- a/docs/index.html +++ b/docs/index.html @@ -26,11 +26,11 @@

About this package

- - + + - +
Package Version:5.5.3
Last Release Date:2024-01-03
Package Version:5.5.4
Last Release Date:2024-01-04
Package Author:Andrew Penn <andy.c.penn@gmail.com>
Package Maintainer:Andrew Penn <andy.c.penn@gmail.com>
License:GPLv3+
License:GPLv3+
diff --git a/docs/readme.html b/docs/readme.html index e9e733c0..25112d4f 100644 --- a/docs/readme.html +++ b/docs/readme.html @@ -84,9 +84,11 @@

Installation

In Octave, you can find out basic information about the package by typing: pkg describe -verbose statistics-resampling

Usage

-

All help and demos are documented on the ‘Function Reference’ page in -the manual. For the best experience navigating the manual, please ensure -that javascript is enabled in your browser.

+

All help and demos are documented on the ‘Function Reference’ page in +the manual. +If you do not see the navigation pane on the manual web pages, please +enable javascript in your browser.

Function help can also be requested from the Octave/MATLAB command prompt, by typing help function-name.

In Octave only, you can also request the demonstrations of function diff --git a/man/generate_manual_helper.sh b/man/generate_manual_helper.sh deleted file mode 100755 index 965b5458..00000000 --- a/man/generate_manual_helper.sh +++ /dev/null @@ -1,84 +0,0 @@ -#!/bin/bash - -# Delete files that are surplus to requirements -rm ./manual_docs/footer.js -rm ./manual_docs/news.png -rm ./manual_docs/manual.png -rm ./manual_docs/oct.png -rm ./manual_docs/favicon.ico - -# Move custom javascript and css documents to a subfolder in the dir containing index.html -mkdir ./manual_docs/statistics-resampling/site-files -cp ./templates/javascript.js ./manual_docs/statistics-resampling/site-files/javascript.js -cp ./templates/manual.css ./manual_docs/statistics-resampling/site-files/manual.css -cp ../doc/icon_48x48.png ./manual_docs/statistics-resampling/site-files/pkg_icon_48x48.png -rm ./manual_docs/javascript.js -rm ./manual_docs/octave-forge.css -mv ./manual_docs/fixed.js ./manual_docs/statistics-resampling/site-files/fixed.js -mv ./manual_docs/doc.png ./manual_docs/statistics-resampling/site-files/doc.png -mv ./manual_docs/homepage.png ./manual_docs/statistics-resampling/site-files/homepage.png -mv ./manual_docs/repository.png ./manual_docs/statistics-resampling/site-files/repository.png -mv ./manual_docs/download.png ./manual_docs/statistics-resampling/site-files/download.png -rm -Rf ./manual_docs/icons - -# Update file references -sed -i '' -e "s/write\_top\_menu \(\(.*\)\)\;/write\_top\_menu \(\'\.\'\)\;/g" ./manual_docs/statistics-resampling/*.html -sed -i '' -e "s/write\_top\_menu \(\(.*\)\)\;/write\_top\_menu \(\'\.\.\'\)\;/g" ./manual_docs/statistics-resampling/function/*.html -sed -i '' -e "s/write\_docs\_left\_menu \(\(.*\)\)\;/write\_docs\_left\_menu \(\'\.\'\)\;/g" ./manual_docs/statistics-resampling/*.html -sed -i '' -e "s/write\_docs\_left\_menu \(\(.*\)\)\;/write\_docs\_left\_menu \(\'\.\.\'\)\;/g" ./manual_docs/statistics-resampling/function/*.html -sed -i '' -e 's/\.\.\/octave\-forge\.css/\.\/site\-files\/manual\.css/g' ./manual_docs/statistics-resampling/*.html -sed -i '' -e 's/\.\.\/octave\-forge\.css/site\-files\/manual\.css/g' ./manual_docs/statistics-resampling/function/*.html -sed -i '' -e 's/\.\.\/fixed\.js/\.\/site\-files\/fixed\.js/g' ./manual_docs/statistics-resampling/*.html -sed -i '' -e 's/\.\.\/fixed\.js/site\-files\/fixed\.js/g' ./manual_docs/statistics-resampling/function/*.html -sed -i '' -e 's/\.\.\/javascript\.js/\.\/site\-files\/javascript\.js/g' ./manual_docs/statistics-resampling/*.html -sed -i '' -e 's/\.\.\/javascript\.js/site\-files\/javascript\.js/g' ./manual_docs/statistics-resampling/function/*.html -sed -i '' -e '/footer\.js/d' ./manual_docs/statistics-resampling/*.html -sed -i '' -e '/footer\.js/d' ./manual_docs/statistics-resampling/function/*.html -sed -i '' -e 's/\ write\_footer ()\; \<\/script\>//g' ./manual_docs/statistics-resampling/*.html -sed -i '' -e 's/\ write\_footer ()\; \<\/script\>//g' ./manual_docs/statistics-resampling/function/*.html -sed -i '' -e 's/\.\.\/download\.png/\.\/site\-files\/download\.png/g' ./manual_docs/statistics-resampling/index.html -sed -i '' -e 's/\.\.\/repository\.png/\.\/site\-files\/repository\.png/g' ./manual_docs/statistics-resampling/index.html -sed -i '' -e 's/\.\.\/doc\.png/\.\/site\-files\/doc\.png/g' ./manual_docs/statistics-resampling/index.html -sed -i '' -e 's/\.\.\/homepage\.png/\.\/site\-files\/homepage\.png/g' ./manual_docs/statistics-resampling/index.html - -# Change page headings of the index (package info) and function reference pages -sed -i '' -e 's/statistics\-resampling\<\/h2\>/About this package\<\/h2\>/g' ./manual_docs/statistics-resampling/index.html -sed -i '' -e 's/statistics\-resampling\<\/h2\>/Function Reference\<\/h2\>/g' ./manual_docs/statistics-resampling/function_reference.html - -# Change to main package directory -cd .. - -# Publish README markdown file as HTML and add header -pandoc README.md -o ./man/manual_docs/statistics-resampling/tmp.html -cat ./man/templates/header.html ./man/manual_docs/statistics-resampling/tmp.html > ./man/manual_docs/statistics-resampling/readme.html -printf "\n\n\n" >> ./man/manual_docs/statistics-resampling/readme.html -rm ./man/manual_docs/statistics-resampling/tmp.html - -# Add hyperlink to function reference directly in the HTML of the readme file (since the link in the markdown file would fail on the GitHub page) -#sed -i '' -e 's/Function Reference/\Function Reference\<\/a\>/g' ./man/manual_docs/statistics-resampling/readme.html - -# Update meta information in all html files -sed -i '' -e 's/\/\/' ./man/manual_docs/statistics-resampling/*.html -sed -i '' -e 's/\/\/' ./man/manual_docs/statistics-resampling/function/*.html -sed -i '' -e 's/\\(.*\)\<\/title\>/The statistics\-resampling package manual\<\/title\>/' ./man/manual_docs/statistics-resampling/*.html -sed -i '' -e 's/\\(.*\)\<\/title\>/The statistics\-resampling package manual\<\/title\>/' ./man/manual_docs/statistics-resampling/function/*.html -sed -i '' -e 's/\/\/' ./man/manual_docs/statistics-resampling/*.html -sed -i '' -e 's/\/\/' ./man/manual_docs/statistics-resampling/function/*.html -sed -i '' -e 's/\/\/' ./man/manual_docs/statistics-resampling/*.html -sed -i '' -e 's/\/\/' ./man/manual_docs/statistics-resampling/function/*.html -sed -i '' -e '/\/d' ./man/manual_docs/statistics-resampling/*.html -sed -i '' -e '/\/d' ./man/manual_docs/statistics-resampling/function/*.html - -# Fixes for validation of XHTML 1.0 Strict -sed -i '' -e 's/\/\