examples/tutorials/MEPS.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Medical Expenditure Tutorial\n",
    "This tutorial illustrates the use of the AIX360 toolkit to obtain directly interpretable models for predicting medical expenditure of individuals. The two algorithms considered are [Linear Rule Regression (LinRR)](#LinRR), which is a version of Generalized Linear Rule Models (GLRM) for predicting real-valued outcomes, and [Boolean Rule Column Generation (BRCG)](#BRCG). LinRR yields weighted combinations of AND rules that are accurate and have the interpretability of linear models and [generalized additive models](https://en.wikipedia.org/wiki/Generalized_additive_model). It is featured for the task of [expenditure prediction](#expenditure). BRCG gives very simple OR-of-ANDs classification rules and is featured for the task of [high-cost patient identification](#high-cost). The data used is taken from the [Medical Expenditure Panel Survey (MEPS)](https://meps.ahrq.gov/mepsweb/) and is processed as described in the [Data](#data) section.\n",
    "\n",
    "1. [Use Case](#use-case)\n",
    "2. [Data](#data)\n",
    "3. [Expenditure prediction](#expenditure)\n",
    "4. [High-cost patient identification](#high-cost)\n",
    "5. [Conclusion](#conclusion)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"use-case\"></a>\n",
    "## 1. Use Case\n",
    "The task is to predict the annual healthcare expenditure of individuals based on demographic and socio-economic variables as well as self-reported medical conditions. These predictions are of interest to healthcare \"payers\", for example insurance companies, employers, governments, or individuals, who are financially responsible for the cost. The input data does not include actual healthcare experience (i.e. claims for services incurred), so the situation is similar to that of enrollment when an individual joins a healthcare plan.\n",
    "\n",
    "Directly interpretable models have a sufficiently simple and transparent form to allow understanding of the behavior of the model as a whole, not just in specific instances (specific individuals). They can identify not only which features are most predictive of the output but also the nature of the dependence (e.g. its direction and shape). This is most directly illustrated in the [Visualization](#visualize) section. For the present use case, these insights could be compared to a healthcare expert's domain knowledge and/or reviewed by managers before deploying the model, to increase confidence that it will perform as expected. Moreover, the insights could inform interventions to mitigate cost, for example as part of care management. While the models considered here are not causal models and the dependences identified are not necessarily causal, they could be interpreted causally with the help of expert knowledge, or they could suggest causal hypotheses to be tested in future studies."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"data\"></a>\n",
    "## 2. Data\n",
    "The specific data used is the [2015 Full Year Consolidated Data File](https://meps.ahrq.gov/data_stats/download_data_files_detail.jsp?cboPufNumber=HC-181), containing data from rounds 3, 4, 5 of panel 19 (2014) and rounds 1, 2, 3 of panel 20 (2015).\n",
    "\n",
    "We use AIX360's `MEPSDataset` class to load and pre-process the data. The more notable steps in this processing are 1) restricting race to white and black and ethnicity to non-Hispanic, and 2) removing records with special values (negative integers) for some variables. The selected variables include demographics (e.g. age, gender, marital status), socio-economic factors (education, income, insurance coverage), self-reported health statuses, diagnoses (e.g. heart disease, stroke, diabetes), and health limitations (e.g. cognitive, activity, sensory)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load MEPS data\n",
    "from aix360.datasets import MEPSDataset\n",
    "data = MEPSDataset().data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this tutorial, we also drop the panel number (19 or 20, not meant to be predictive) and sample weights, and reset the row index to consecutive integers for simplicity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>REGION</th>\n",
       "      <th>AGE31X</th>\n",
       "      <th>GENDER</th>\n",
       "      <th>RACE3</th>\n",
       "      <th>MARRY31X</th>\n",
       "      <th>EDRECODE</th>\n",
       "      <th>FTSTU31X</th>\n",
       "      <th>ACTDTY31</th>\n",
       "      <th>HONRDC31</th>\n",
       "      <th>RTHLTH31</th>\n",
       "      <th>...</th>\n",
       "      <th>ADSMOK42</th>\n",
       "      <th>PCS42</th>\n",
       "      <th>MCS42</th>\n",
       "      <th>K6SUM42</th>\n",
       "      <th>PHQ242</th>\n",
       "      <th>EMPST31</th>\n",
       "      <th>POVCAT15</th>\n",
       "      <th>INSCOV15</th>\n",
       "      <th>INCOME_M</th>\n",
       "      <th>HEALTHEXP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2</td>\n",
       "      <td>52</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5</td>\n",
       "      <td>13</td>\n",
       "      <td>-1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>...</td>\n",
       "      <td>2</td>\n",
       "      <td>25.93</td>\n",
       "      <td>58.47</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>11390.0</td>\n",
       "      <td>46612</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>55</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3</td>\n",
       "      <td>14</td>\n",
       "      <td>-1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>...</td>\n",
       "      <td>2</td>\n",
       "      <td>20.42</td>\n",
       "      <td>26.57</td>\n",
       "      <td>17</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>11390.0</td>\n",
       "      <td>9207</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>22</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5</td>\n",
       "      <td>13</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>2</td>\n",
       "      <td>53.12</td>\n",
       "      <td>50.33</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>18000.0</td>\n",
       "      <td>808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1.00</td>\n",
       "      <td>-1.00</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>385.0</td>\n",
       "      <td>2721</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3</td>\n",
       "      <td>25</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>14</td>\n",
       "      <td>-1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>2</td>\n",
       "      <td>59.89</td>\n",
       "      <td>45.91</td>\n",
       "      <td>9</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>3700.0</td>\n",
       "      <td>1573</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 44 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   REGION  AGE31X  GENDER  RACE3  MARRY31X  EDRECODE  FTSTU31X  ACTDTY31  \\\n",
       "0       2      52     0.0    0.0         5        13        -1         2   \n",
       "1       2      55     1.0    0.0         3        14        -1         2   \n",
       "2       2      22     1.0    0.0         5        13         3         2   \n",
       "3       2       2     0.0    0.0         6        -1        -1         3   \n",
       "4       3      25     1.0    0.0         1        14        -1         2   \n",
       "\n",
       "   HONRDC31  RTHLTH31    ...      ADSMOK42  PCS42  MCS42  K6SUM42  PHQ242  \\\n",
       "0         2         4    ...             2  25.93  58.47        3       0   \n",
       "1         2         4    ...             2  20.42  26.57       17       6   \n",
       "2         2         1    ...             2  53.12  50.33        7       0   \n",
       "3         3         1    ...            -1  -1.00  -1.00       -1      -1   \n",
       "4         2         1    ...             2  59.89  45.91        9       2   \n",
       "\n",
       "   EMPST31  POVCAT15  INSCOV15  INCOME_M  HEALTHEXP  \n",
       "0        4         1         2   11390.0      46612  \n",
       "1        4         3         2   11390.0       9207  \n",
       "2        1         2         2   18000.0        808  \n",
       "3       -1         2         2     385.0       2721  \n",
       "4        1         3         1    3700.0       1573  \n",
       "\n",
       "[5 rows x 44 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Reset index to consecutive integers\n",
    "data.reset_index(drop=True, inplace=True)\n",
    "# Drop panel number (not meant to be predictive) and sample weights\n",
    "data.drop(columns = ['PANEL', 'PERSONWT'], inplace=True)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"expenditure\"></a>\n",
    "## 3. Expenditure prediction\n",
    "\n",
    "<a name=\"process-data\"></a>\n",
    "### 3.1. Process data for modelling\n",
    "In this section, the task is to predict healthcare expenditure (HEALTHEXP). We separate the target variable from the data and split it into training and test sets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Separate target variable\n",
    "y = data.pop('HEALTHEXP')\n",
    "# Split data into training and test sets\n",
    "from sklearn.model_selection import train_test_split\n",
    "dfTrain, dfTest, yTrain, yTest = train_test_split(data, y, random_state=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two algorithms LinRR and BRCG require non-binary features to be binarized using the provided `FeatureBinarizer` class. We list features that are to be considered as categorical, use the default of 9 quantile thresholds (i.e. 10 bins) to binarize ordinal (including continuous-valued) features, include all negations (e.g. '>' comparisons as well as '<='), and also return standardized versions of the original unbinarized ordinal features, which are used by LinRR but not BRCG."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Categorical features\n",
    "colCateg = ['REGION','MARRY31X','EDRECODE','FTSTU31X','ACTDTY31','HONRDC31',\n",
    "            'RTHLTH31','MNHLTH31','HIBPDX','CHDDX','ANGIDX','MIDX','OHRTDX','STRKDX',\n",
    "            'EMPHDX','CHBRON31','CHOLDX','CANCERDX','DIABDX','JTPAIN31','ARTHDX',\n",
    "            'ARTHTYPE','ASTHDX','ADHDADDX','PREGNT31','WLKLIM31','ACTLIM31','SOCLIM31',\n",
    "            'COGLIM31','DFHEAR42','DFSEE42','ADSMOK42','PHQ242','EMPST31','POVCAT15','INSCOV15']\n",
    "# Binarize data and also return standardized ordinal features\n",
    "from aix360.algorithms.rbm import FeatureBinarizer\n",
    "fb = FeatureBinarizer(colCateg=colCateg, negations=True, returnOrd=True)\n",
    "dfTrain, dfTrainStd = fb.fit_transform(dfTrain)\n",
    "dfTest, dfTestStd = fb.transform(dfTest)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below are the results of binarizing the REGION (US census region) and AGE31X features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th>operation</th>\n",
       "      <th colspan=\"4\" halign=\"left\">==</th>\n",
       "      <th colspan=\"4\" halign=\"left\">!=</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>value</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1955</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5122</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16933</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9837</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2865</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "operation ==          !=         \n",
       "value      1  2  3  4  1  2  3  4\n",
       "1955       0  0  1  0  1  1  0  1\n",
       "5122       0  1  0  0  1  0  1  1\n",
       "16933      0  0  1  0  1  1  0  1\n",
       "9837       0  1  0  0  1  0  1  1\n",
       "2865       0  1  0  0  1  0  1  1"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfTrain['REGION'].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th>operation</th>\n",
       "      <th colspan=\"9\" halign=\"left\">&lt;=</th>\n",
       "      <th colspan=\"9\" halign=\"left\">&gt;</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>value</th>\n",
       "      <th>7.0</th>\n",
       "      <th>14.0</th>\n",
       "      <th>23.0</th>\n",
       "      <th>31.0</th>\n",
       "      <th>38.0</th>\n",
       "      <th>47.0</th>\n",
       "      <th>54.0</th>\n",
       "      <th>61.0</th>\n",
       "      <th>70.0</th>\n",
       "      <th>7.0</th>\n",
       "      <th>14.0</th>\n",
       "      <th>23.0</th>\n",
       "      <th>31.0</th>\n",
       "      <th>38.0</th>\n",
       "      <th>47.0</th>\n",
       "      <th>54.0</th>\n",
       "      <th>61.0</th>\n",
       "      <th>70.0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1955</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5122</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16933</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9837</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2865</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "operation   <=                                            >                 \\\n",
       "value     7.0  14.0 23.0 31.0 38.0 47.0 54.0 61.0 70.0 7.0  14.0 23.0 31.0   \n",
       "1955         0    0    0    0    0    0    1    1    1    1    1    1    1   \n",
       "5122         0    0    0    0    1    1    1    1    1    1    1    1    1   \n",
       "16933        1    1    1    1    1    1    1    1    1    0    0    0    0   \n",
       "9837         0    0    0    0    1    1    1    1    1    1    1    1    1   \n",
       "2865         0    1    1    1    1    1    1    1    1    1    0    0    0   \n",
       "\n",
       "operation                           \n",
       "value     38.0 47.0 54.0 61.0 70.0  \n",
       "1955         1    1    0    0    0  \n",
       "5122         0    0    0    0    0  \n",
       "16933        0    0    0    0    0  \n",
       "9837         0    0    0    0    0  \n",
       "2865         0    0    0    0    0  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfTrain['AGE31X'].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"baseline\"></a>\n",
    "### 3.2. Establish baseline\n",
    "Predicting individual healthcare expenditure is inherently a difficult problem (particularly in the US healthcare system), especially given the limited input data considered here, which does not include past claims. The statistics of expenditure hint at this difficulty:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count     18350.000000\n",
       "mean       5184.511608\n",
       "std       15126.748532\n",
       "min           0.000000\n",
       "10%           0.000000\n",
       "20%         114.000000\n",
       "30.0%       302.000000\n",
       "40%         585.000000\n",
       "50%        1034.000000\n",
       "60%        1784.800000\n",
       "70%        3099.000000\n",
       "80%        5619.800000\n",
       "90%       12591.100000\n",
       "max      659952.000000\n",
       "Name: HEALTHEXP, dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "y.describe(percentiles=np.linspace(0.1, 0.9, 9))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The distribution has a long and heavy tail consisting of high-cost individuals. This manifests itself in the mean being 5 times the median, the standard deviation being 3 times the mean, and the most costly individuals running into the hundreds of thousands of dollars.\n",
    "\n",
    "Next we train and test a standard model, Gradient Boosted Regression Trees (GBRT), to establish a baseline. We use the same binarized/discretized data as [above](#process-data) to obtain a fair comparison. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training R^2: 0.5150817111907599\n",
      "Test R^2: 0.14069941876567726\n"
     ]
    }
   ],
   "source": [
    "# Train and evaluate GBRT\n",
    "from sklearn.ensemble import GradientBoostingRegressor\n",
    "gbr = GradientBoostingRegressor(n_estimators=500, random_state=0)\n",
    "gbr.fit(dfTrain, yTrain)\n",
    "from sklearn.metrics import r2_score\n",
    "print('Training R^2:', r2_score(yTrain, gbr.predict(dfTrain)))\n",
    "print('Test R^2:', r2_score(yTest, gbr.predict(dfTest)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The test R^2 of 14.1% (100% means perfect prediction) confirms that the problem is difficult. (The training R^2 of 51.5% also suggests overfitting.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"LinRR\"></a>\n",
    "### 3.3. Run Linear Rule Regression (LinRR)\n",
    "We now train and test a LinRR model. As seen below, LinRR produces a linear regression model that uses rule-based features. Here we are also including unbinarized ordinal features (`useOrd=True`) in addition to rules. The complexity parameters `lambda0`, `lambda1` penalize the number of rules included in the model and the number of conditions in each rule. The values for `lambda0`, `lambda1` below strike a good balance between accuracy and model complexity, based on our published experience with this MEPS dataset [[1]](http://proceedings.mlr.press/v97/wei19a.html). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training R^2: 0.16681096135277274\n",
      "Test R^2: 0.1439870705684898\n"
     ]
    }
   ],
   "source": [
    "# Instantiate LinRR with good complexity penalties and numerical features\n",
    "from aix360.algorithms.rbm import LinearRuleRegression\n",
    "lrr = LinearRuleRegression(lambda0=0.03, lambda1=0.006, useOrd=True)\n",
    "# Train and evaluate model\n",
    "lrr.fit(dfTrain, yTrain, dfTrainStd)\n",
    "print('Training R^2:', r2_score(yTrain, lrr.predict(dfTrain, dfTrainStd)))\n",
    "print('Test R^2:', r2_score(yTest, lrr.predict(dfTest, dfTestStd)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The test R-squared of 14.4% is slightly higher than that of GBRT. More importantly, the LinRR model is directly interpretable (provided that the feature names and values are explained, which we will do in the [Visualization](#visualize) section, see e.g. [[2]](https://meps.ahrq.gov/data_stats/download_data_files_codebook.jsp?PUFId=H181)[[3]](https://meps.ipums.org/meps/index.shtml) for more information on the features). The rule-based and ordinal features included in the linear regression model are shown below. Being a linear model, feature importance is naturally given by the model coefficients and thus the list is sorted in order of decreasing coefficient magnitude. The list can be truncated if the user wishes to display fewer features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rule</th>\n",
       "      <th>coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(intercept)</td>\n",
       "      <td>13998.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>PCS42 &lt;= -1.00</td>\n",
       "      <td>-8058</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>PCS42 &lt;= 31.52</td>\n",
       "      <td>6827.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>RTHLTH31 != 5 AND PREGNT31 != 1</td>\n",
       "      <td>-6614.27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>STRKDX == 1</td>\n",
       "      <td>4842.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>ADHDADDX != 1 AND PREGNT31 != 1 AND COGLIM31 !...</td>\n",
       "      <td>-3974.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>AGE31X</td>\n",
       "      <td>-3937.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>DIABDX == 1</td>\n",
       "      <td>3812.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>PREGNT31 != 1 AND ACTLIM31 != 1</td>\n",
       "      <td>-3778.59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>CANCERDX == 1</td>\n",
       "      <td>3624.82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>REGION != 1 AND DFSEE42 != -1</td>\n",
       "      <td>-2677.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>CHDDX == 1</td>\n",
       "      <td>2585.89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>OHRTDX == 1</td>\n",
       "      <td>2418.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>AGE31X &gt; 7.00 AND MARRY31X != 8 AND MARRY31X !...</td>\n",
       "      <td>2211.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>AGE31X &lt;= 38.00</td>\n",
       "      <td>-1847.94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>RTHLTH31 != 1 AND INSCOV15 != 3</td>\n",
       "      <td>1640.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>ADSMOK42 == 2</td>\n",
       "      <td>1567.41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>SOCLIM31 != -1 AND PHQ242 != 5 AND POVCAT15 != 5</td>\n",
       "      <td>-1565.76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>ACTDTY31 == 4</td>\n",
       "      <td>1396.76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>PCS42 &lt;= 53.99 AND INSCOV15 != 3</td>\n",
       "      <td>1277.63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>K6SUM42</td>\n",
       "      <td>1198.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>PCS42 &lt;= 43.05</td>\n",
       "      <td>1152.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>RTHLTH31 == 4</td>\n",
       "      <td>1116.37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>INCOME_M &lt;= 0.00</td>\n",
       "      <td>-1044.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>RTHLTH31 == 2</td>\n",
       "      <td>-1026.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>INCOME_M &lt;= 10000.00</td>\n",
       "      <td>-1006.56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>INSCOV15 == 1</td>\n",
       "      <td>955.713</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>EDRECODE == 13</td>\n",
       "      <td>-913.841</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>RACE3</td>\n",
       "      <td>-891.149</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>AGE31X &lt;= 54.00</td>\n",
       "      <td>-746.625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>HIBPDX == 1</td>\n",
       "      <td>678.576</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>REGION == 3</td>\n",
       "      <td>-587.263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>WLKLIM31 == 2</td>\n",
       "      <td>-565.434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>EMPST31 == 4</td>\n",
       "      <td>492.563</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>JTPAIN31 == 1</td>\n",
       "      <td>433.648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>ARTHDX == 1</td>\n",
       "      <td>321.778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>ARTHTYPE == -1</td>\n",
       "      <td>-321.775</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>PCS42 &lt;= 50.22</td>\n",
       "      <td>298.13</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                 rule coefficient\n",
       "0                                         (intercept)     13998.7\n",
       "1                                      PCS42 <= -1.00       -8058\n",
       "2                                      PCS42 <= 31.52     6827.75\n",
       "3                     RTHLTH31 != 5 AND PREGNT31 != 1    -6614.27\n",
       "4                                         STRKDX == 1     4842.36\n",
       "5   ADHDADDX != 1 AND PREGNT31 != 1 AND COGLIM31 !...    -3974.52\n",
       "6                                              AGE31X    -3937.74\n",
       "7                                         DIABDX == 1     3812.48\n",
       "8                     PREGNT31 != 1 AND ACTLIM31 != 1    -3778.59\n",
       "9                                       CANCERDX == 1     3624.82\n",
       "10                      REGION != 1 AND DFSEE42 != -1    -2677.43\n",
       "11                                         CHDDX == 1     2585.89\n",
       "12                                        OHRTDX == 1     2418.97\n",
       "13  AGE31X > 7.00 AND MARRY31X != 8 AND MARRY31X !...     2211.48\n",
       "14                                    AGE31X <= 38.00    -1847.94\n",
       "15                    RTHLTH31 != 1 AND INSCOV15 != 3     1640.62\n",
       "16                                      ADSMOK42 == 2     1567.41\n",
       "17   SOCLIM31 != -1 AND PHQ242 != 5 AND POVCAT15 != 5    -1565.76\n",
       "18                                      ACTDTY31 == 4     1396.76\n",
       "19                   PCS42 <= 53.99 AND INSCOV15 != 3     1277.63\n",
       "20                                            K6SUM42     1198.05\n",
       "21                                     PCS42 <= 43.05     1152.09\n",
       "22                                      RTHLTH31 == 4     1116.37\n",
       "23                                   INCOME_M <= 0.00    -1044.02\n",
       "24                                      RTHLTH31 == 2    -1026.42\n",
       "25                               INCOME_M <= 10000.00    -1006.56\n",
       "26                                      INSCOV15 == 1     955.713\n",
       "27                                     EDRECODE == 13    -913.841\n",
       "28                                            RACE3      -891.149\n",
       "29                                    AGE31X <= 54.00    -746.625\n",
       "30                                        HIBPDX == 1     678.576\n",
       "31                                        REGION == 3    -587.263\n",
       "32                                      WLKLIM31 == 2    -565.434\n",
       "33                                       EMPST31 == 4     492.563\n",
       "34                                      JTPAIN31 == 1     433.648\n",
       "35                                        ARTHDX == 1     321.778\n",
       "36                                     ARTHTYPE == -1    -321.775\n",
       "37                                     PCS42 <= 50.22      298.13"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Print model\n",
    "lrr.explain()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"categories\"></a>\n",
    "The feature list above consists of:\n",
    "1. unbinarized ordinal features (marked by just the feature name without conditions on its values, e.g. AGE31X),\n",
    "2. rules with a single condition (e.g. PCS42 <= -1.00),  \n",
    "3. rules with two or more conditions (e.g. RTHLTH31 != 5 AND PREGNT31 != 1). \n",
    "\n",
    "Features in categories 1 and 2 involve only one of the original unbinarized features (e.g. AGE31X, PCS42) at a time, while interactions between original features are all in category 3. Categories 1 and 2 therefore form a kind of [generalized additive model (GAM)](https://en.wikipedia.org/wiki/Generalized_additive_model), i.e. a sum of functions of individual features, where these functions are themselves sums of step function components from category 2 and linear components from category 1. A better visual summary of categories 1 and 2 can be obtained by plotting the univariate functions that make up the GAM, as we do next. We return to the interaction terms in category 3 in the [higher-degree rules](#higher-degree) section."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"visualize\"></a>\n",
    "### 3.4. Visualize Generalized Additive Model (GAM) part of LinRR model\n",
    "The `visualize()` method of LinRR is used to plot the GAM part of a LinRR model. To ease interpretation, we plot the component functions of the GAM in groups based on the semantics of the features. We can then examine the sizes and shapes of the dependences on individual features. These can be compared to a domain expert's knowledge to identify behaviors that are expected as well as those that may be surprising. We will attempt to provide such interpretation in this section, although we are not healthcare experts."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Health status summaries\n",
    "The first three plots show the contributions of features that summarize an individual's health status. \n",
    "\n",
    "PCS42 stands for Physical Component Summary and measures physical health status over the 4-week period before the MEPS survey date. It is a score computed from 12 responses that assigns higher weights to items such as limitations in activities, pain interfering with work, and difficulty climbing stairs. Lower values indicate poorer health. The plot shows corresponding increases in healthcare cost and especially high cost associated with values under 31."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lrr.visualize(data, fb, ['PCS42']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"RTHLTH31\"></a>\n",
    "RTHLTH31 represents self-reported health status, with values 1-5 corresponding to \"excellent\", \"very good\", \"good\", \"fair\", and \"poor\". The algorithm has given non-zero coefficients only to \"very good\" and \"fair\", even though one might think that individuals in \"excellent\" health should see a reduction in cost at least as great as those in \"very good\" health. On the other hand, since the statuses are self-reported, \"excellent\" may not necessarily be better than \"very good\". The absence of a non-zero coefficient for \"poor\" health may be explained by its low frequency in the data. The non-smooth dependence on RTHLTH31 is due in part to treating RTHLTH31 as a categorical variable (see the definition of `colCateg` [above](#process-data)). If smoother behavior is desired, one may try treating values 1-5 of RTHLTH31 as an ordinal variable and handling the value RTHLTH31 == -1 (\"inapplicable\") separately."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lrr.visualize(data, fb, ['RTHLTH31']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "K6SUM42 is a score known as the Kessler 6 Scale measuring non-specific psychological distress over the 30-day period prior to the survey. Higher values indicate higher stress and the LinRR algorithm finds a positive correlation with expenditure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lrr.visualize(data, fb, ['K6SUM42']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Medical diagnoses and conditions\n",
    "The next 10 plots show the effects of having various medical diagnoses and conditions on the predicted cost. In order of importance and as shown below, these are diabetes, cancer, stroke, other heart disease, coronary heart disease, high blood pressure, joint pain in last 12 months, limitation in physical functioning (walking), arthritis, and type of arthritis. Except for WLKLIM31 and ARTHTYPE, a value of 1 means that the condition is present and contributes positively to the prediction as shown. A value of 2 means that the condition is absent, which in the case of WLKLIM31 contributes negatively. The increases in predicted cost due to these conditions (or decrease in the case of WLKLIM31) are all expected and the sizes of the coefficients indicate relative importance. Lastly, ARTHTYPE == -1 means \"inapplicable\", covering both those without arthritis as well as those under age 17 to whom the arthritis question is not applicable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZEAAAEKCAYAAADTgGjXAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAFy5JREFUeJzt3Xu0JlV55/Hvz/aOII72DJemBWOrAWIaOEGMk5uitOiAGmSBElCS6SGDCVlmzRKCiTEZZkhUJsFrOgm3BCUOiBBAkV4DioMEmgEamos2KHKkNQgKbUCShmf+eOvgS3MuZZ3znve8nO9nrVpdtWtX1fPSrH7W3rtq71QVkiR18bRhByBJGl0mEUlSZyYRSVJnJhFJUmcmEUlSZyYRSVJnI5dEkqxKcnuSjUmOH3Y8krSYZZS+E0myBPg68HpgHLgWOLyqbhlqYJK0SI1aS2RfYGNV3VlV/wqcAxw85JgkadF6+rAD+CntDNzddzwOvGrrSklWA6sBttlmm31e8YpXdHrYTd95oNN1C9HP7fz8YYcgaURcd91136+qpW3qjloSySRlT+qPq6o1wBqAsbGxWrduXaeH7Xr8xZ2uW4jWnfymYYcgaUQkuatt3VHrzhoHduk7XgbcM6RYJGnRG7Ukci2wIsluSZ4JHAZcOOSYJGnRGqnurKrakuQ9wKXAEuC0qtow5LAkadEaqSQCUFWXAJcMOw5J0uh1Z0mSFhCTiCSpM5OIJKkzk4gkqTOTiCSpM5OIJKkzk4gkqTOTiCSpM5OIJKkzk4gkqTOTiCSpM5OIJKkzk4gkqTOTiCSpM5OIJKkzk4gkqTOTiCSpM5OIJKkzk4gkqTOTiCSpM5OIJKkzk4gkqTOTiCSpswWXRJL8cZLvJLmh2Q7sO3dCko1Jbk9ywDDjlCTB04cdwBT+V1V9uL8gye7AYcAewE7A2iQvq6pHhxGgJGkBtkSmcTBwTlU9UlXfBDYC+w45Jkla1BZqEnlPkvVJTkvygqZsZ+DuvjrjTZkkaUiGkkSSrE1y8yTbwcAngZ8BVgKbgI9MXDbJrWqK+69Osi7JunvvvXcgv0GSNKQxkarav029JH8NXNQcjgO79J1eBtwzxf3XAGsAxsbGJk00kqTZW3DdWUl27Dt8K3Bzs38hcFiSZyXZDVgBXDPf8UmSfmIhvp3150lW0uuq+hbwXwCqakOSzwK3AFuAY30zS5KGa8Elkar6jWnOnQScNI/hSJKmseC6syRJo8MkIknqzCQiSerMJCJJ6swkIknqzCQiSerMJCJJ6swkIknqzCQiSeqs1RfrSZYA/6G/flV9e1BBSZJGw4xJJMnvAB8Avgc81hQX8MoBxiVJGgFtWiLHAS+vqvsGHYwkabS0GRO5G3hg0IFIkkZPm5bIncAVSS4GHpkorKpTBhaVJGkktEki3262ZzabJElAiyRSVR8ESLJt77B+NPCoJEkjYcYxkSR7Jrme3jK1G5Jcl2SPwYcmSVro2gysrwHeW1UvrqoXA78P/PVgw5IkjYI2SWSbqrp84qCqrgC2GVhEkqSR0ertrCR/CPxdc3wE8M3BhSRJGhVtWiJHA0uBzwHnN/vvHmRQkqTR0ObtrB8AvzsPsUiSRsyUSSTJX1TV7yX5R3pzZT1BVR000MgkSQvedC2RiTGQD89HIJKk0TPlmEhVXdfsrqyqL/dvwMrZPDTJ25NsSPJYkrGtzp2QZGOS25Mc0Fe+qinbmOT42TxfkjQ32gysHzVJ2btm+dybgbcBX+kvTLI7cBiwB7AK+ESSJc16Jh8H3gjsDhze1JUkDdF0YyKHA+8AdktyYd+pbYFZTQtfVbc2z9j61MHAOVX1CPDNJBuBfZtzG6vqzua6c5q6t8wmDknS7Ew3JnIVsAl4EfCRvvLNwPoBxbMzcHXf8XhTBr0p6fvLXzXVTZKsBlYDLF++fI5DlCRNmDKJVNVdwF1J3gncU1U/BkjyHGAZ8K3pbpxkLbDDJKdOrKoLprpsslCYvNvtSW+MPX6iag296VoYGxubsp4kaXbafLH+WeAX+44fBf438AvTXVRV+3eIZxzYpe94GXBPsz9VuSRpSNoMrD+9qv514qDZH9S6IhcChyV5VpLdgBXANcC1wIokuyV5Jr3B9wunuY8kaR60SSL3Jnn8w8IkBwPfn81Dk7w1yTjwauDiJJcCVNUGei2fW4AvAsdW1aNVtQV4D3ApcCvw2aauJGmI2nRnHQOcneRj9MYs7gaOnM1Dq+p8evNwTXbuJOCkScovAS6ZzXMlSXOrzdxZdwD7JXkekKraPPiwJEmjYLrvRI6oqr9P8t6tygGoqlMGHJskaYGbriUysfDUtvMRiCRp9Ez3nchfNX9+cP7CkSSNkum6s06d7sKqco0RSVrkpnvF97pmezawN/CNZltJ74NDSdIiN1131pkASd4F/FpV/Vtz/CngS/MSnSRpQWvzseFOPHFw/XlNmSRpkWvzseHJwPVJLm+OfwX444FFJEkaGW0+Njw9yRf4ydTrx1fVdwcbliRpFMzYnZXe14X7Az/fTOH+zCT7znCZJGkRaDMm8gl6EyUe3hxvprdUrSRpkWszJvKqqto7yfUAVfWDZjp2SdIi16Yl8m9JltCsJJhkKfDYQKOSJI2ENknkVHrTtv/7JCcBXwX+x0CjkiSNhDZvZ52d5DrgdfTWE3lLVd068MgkSQvetEkkydOA9VW1J3Db/IQkSRoV03ZnVdVjwI1Jls9TPJKkEdLm7awdgQ1JrgH+ZaKwqg6a+hJJ0mLQJom4nogkaVJtBta/nGQHYF96r/le67QnkiRoN+3JbwHXAG8DDgGuTnL0oAOTJC18bbqz/huwV1XdB5DkhcBVwGmDDEyStPC1+dhwnN58WRM2A3fP5qFJ3p5kQ5LHkoz1le+a5OEkNzTbp/rO7ZPkpiQbk5zaTAwpSRqiNi2R7wD/lOQCemMiBwPXJHkvQFWd0uG5N9PrHvurSc7dUVUrJyn/JLAauBq4BFgFfKHDsyVJc6RNErmj2SZc0Py57SR1W5n44r1tYyLJjsB2VfW15vgs4C2YRCRpqNq8nTXfr/ju1swY/CDw/qq6EtiZXrfahPGmbFJJVtNrtbB8ud9JStKgtGmJdJJkLbDDJKdObBa3mswmYHlV3ZdkH+DzSfagN2fX1mqqZ1fVGmANwNjY2JT1JEmzM7AkUlX7d7jmEeCRZv+6JHcAL6PX8ljWV3UZcM9cxClJ6q7N21nzJsnSZu0SkrwEWAHcWVWbgM1J9mveyjqSn4zNSJKGpM3HhsuSnJ/k3iTfS3JekmUzXTfDPd+aZJzesrsXJ7m0OfXLwPokNwLnAsdU1f3Nud8G/gbYSG+g30F1SRqyNt1ZpwOfBt7eHB/RlL2+60Or6nx6C11tXX4ecN4U16wD9uz6TEnS3GvTnbW0qk6vqi3NdgawdMBxSZJGQJsk8v0kRyRZ0mxHAPcNOjBJ0sLXJokcDRwKfJfeK7iHAO8eZFCSpNHQZkxkl60XoEryGuDbgwlJkjQq2rREPtqyTJK0yEzZEknyauAXgaUTky02tgOWDDowSdLCN1131jOB5zV1+idbfJDeuIgkaZGbMolU1ZeBLyc5o6rumseYJEkjYsYxEROIJGkqC2ruLEnSaDGJSJI6m/E7kSRLgf8M7Npfv6qOHlxYkqRR0OZjwwuAK4G1wKODDUeSNEraJJHnVtX7Bh6JJGnktBkTuSjJgQOPRJI0ctokkePoJZIfJ9ncbA8OOjBJ0sI3Y3dWVW07Ux1J0uLUZkyEJAfRW7oW4IqqumhwIUmSRkWbNdZPpteldUuzHdeUSZIWuTYtkQOBlVX1GECSM4HrgeMHGZgkaeFr+8X69n37zx9EIJKk0dOmJfI/geuTXA6E3tjICQONSpI0Etq8nfWZJFcAv0Avibyvqr476MAkSQvflN1ZSV7R/Lk3sCMwDtwN7NSUdZbkQ0luS7I+yflJtu87d0KSjUluT3JAX/mqpmxjEsdjJGkBmK4l8l5gNfCRSc4V8NpZPPcy4ISq2pLkz+h1j70vye7AYcAewE7A2iQva675OPB6esns2iQXVtUts4hBkjRL061suLrZfWNV/bj/XJJnz+ahVfWlvsOr+clyuwcD51TVI8A3k2wE9m3ObayqO5vnn9PUNYlI0hC1eTvrqpZlXR0NfKHZ35lel9mE8aZsqvJJJVmdZF2Sdffee+8chipJ6jdlSyTJDvT+oX5Okr3oDaoDbAc8d6YbJ1kL7DDJqROr6oKmzonAFuDsicsmqV9MnuxqqmdX1RpgDcDY2NiU9SRJszPdmMgBwLuAZcApfeWbgT+Y6cZVtf9055McBbwZeF1VTfxDPw7s0ldtGXBPsz9VuSRpSKYbEzkTODPJr1fVeXP50CSrgPcBv1JVD/WduhD4dJJT6A2srwCuoddCWZFkN+A79Abf3zGXMUmSfnptPjbcM8keWxdW1Z/M4rkfA54FXJYE4OqqOqaqNiT5LL0B8y3AsVX1KECS9wCXAkuA06pqwyyeL0maA22SyI/69p9Nrwvq1tk8tKpeOs25k4CTJim/BLhkNs+VJM2tNl+sP+E7kSQfptftJEla5NpOwNjvucBL5joQSdLombElkuQmfvI67RJgKTCb8RBJ0lNEmzGRN/ftbwG+V1VbBhSPJGmEtBkTuauZcPE/0muRfJXeolSSpEWuzfK4fwScCbwQeBFwRpL3DzowSdLC16Y763Bgr4lJGJv11f8f8N8HGZgkaeFr83bWt+h9HzLhWcAdA4lGkjRSppuA8aP0xkAeATYkuaw5fj29cRFJ0iI3XXfWuubP64Dz+8qvGFg0kqSRMtMEjJIkTWm67qzPVtWhW31s+LiqeuVAI5MkLXjTdWcd1/z55mnqSJIWsem6szYlWQL87UwLTEmSFqdpX/Ft1vJ4KMnz5ykeSdIIafOx4Y+Bm5pXfP9lorCqfndgUUmSRkKbJHJxs/V70kC7JGnxaZNEtq+qv+wvSHLcVJUlSYtHm2lPjpqk7F1zHIckaQRN953I4cA7gN2S9C+Huy1w36ADkyQtfNN1Z10FbKI3/Xv/OuubgfWDDEqSNBqm+07kLuAu4NXzF44kaZS0WZTqbUm+keSBJA8m2ZzkwfkITpK0sLUZWP9z4KCqen5VbVdV21bVdrN5aJIPJbktyfok5yfZvinfNcnDSW5otk/1XbNPkpuSbExyapLMJgZJ0uy1SSLfq6pb5/i5lwF7NpM4fh04oe/cHVW1stmO6Sv/JLAaWNFsq+Y4JknST6nNdyLrkvwD8Hl6C1QBUFWf6/rQqvpS3+HVwCHT1U+yI7BdVX2tOT4LeAvwha4xSJJmr00S2Q54CHhDX1kBnZPIVo4G/qHveLck1wMPAu+vqiuBnYHxvjrjTdmkkqym12ph+fLlcxSmJGlrMyaRqnp3lxsnWQvsMMmpE6vqgqbOicAW4Ozm3CZgeVXdl2Qf4PNJ9gAmG/+YcuqVqloDrAEYGxtzihZJGpAZk0iSZcBHgdfQ+4f7q8BxVTU+3XUzTR+f5Ch6a5W8rqqqueYRmi6zqrouyR3Ay+i1PJb1Xb4MuGem2CVJg9VmYP104EJgJ3pdSP/YlHWWZBXwPnpvfT3UV760WcOEJC+hN4B+Z1VtAjYn2a95K+tI4ILZxCBJmr02SWRpVZ1eVVua7Qxg6Syf+zF606dcttWrvL8MrE9yI3AucExV3d+c+23gb4CNwB04qC5JQ9dmYP37SY4APtMcH84s586qqpdOUX4ecN4U59YBe87muZKkudWmJXI0cCjwXXoD34c0ZZKkRa7N21nfBg6ah1gkSSOmzdxZZ05MS9IcvyDJaYMNS5I0Ctp0Z72yqn44cVBVPwD2GlxIkqRR0SaJPC3JCyYOkvw72g3IS5Ke4tokg48AVyU5l97HhocCJw00KknSSGgzsH5WknXAa+lNP/K2qrpl4JFJkha8Vt1STdIwcUiSnqDNmIgkSZMyiUiSOjOJSJI6M4lIkjoziUiSOjOJSJI6M4lIkjoziUiSOjOJSJI6M4lIkjoziUiSOjOJSJI6M4lIkjoziUiSOjOJSJI6G1oSSfKnSdYnuSHJl5Ls1JQnyalJNjbn9+675qgk32i2o4YVuySpZ5gtkQ9V1SuraiVwEfBHTfkbgRXNthr4JDy+tvsHgFcB+wIf6F/7XZI0/4aWRKrqwb7Dbeit3w5wMHBW9VwNbJ9kR+AA4LKqur+qfgBcBqya16AlSU/QanncQUlyEnAk8ADwa03xzsDdfdXGm7Kpyie772p6rRiWL18+t0FLkh430JZIkrVJbp5kOxigqk6sql2As4H3TFw2ya1qmvInF1atqaqxqhpbunTpXPwUSdIkBtoSqar9W1b9NHAxvTGPcWCXvnPLgHua8l/dqvyKWQcpSepsmG9nreg7PAi4rdm/EDiyeUtrP+CBqtoEXAq8IckLmgH1NzRlkqQhGeaYyMlJXg48BtwFHNOUXwIcCGwEHgLeDVBV9yf5U+Dapt6fVNX98xuyJKnf0JJIVf36FOUFHDvFudOA0wYZlySpPb9YlyR1ZhKRJHVmEpEkdWYSkSR1ZhKRJHVmEpEkdWYSkSR1ZhKRJHU21Fl8F7pvnfymYYcgSQuaLRFJUmcmEUlSZyYRSVJnJhFJUmcmEUlSZyYRSVJnJhFJUmcmEUlSZyYRSVJnJhFJUmfpLWn+1JXkXuCuYccxjRcB3x92EBqKxfx3v5h/Oyz83//iqlrapuJTPoksdEnWVdXYsOPQ/FvMf/eL+bfDU+v3250lSerMJCJJ6swkMnxrhh2AhmYx/90v5t8OT6Hf75iIJKkzWyKSpM5MIpKkzkwiC0CStyfZkOSxJE+J1/40tSSnJfnnJDcPO5b5lmSXJJcnubX5f/64Ycc0X5I8O8k1SW5sfvsHhx3TXDCJLAw3A28DvjLsQDQvzgBWDTuIIdkC/H5V/SywH3Bskt2HHNN8eQR4bVX9PLASWJVkvyHHNGtPH3YAgqq6FSDJsEPRPKiqryTZddhxDENVbQI2Nfubk9wK7AzcMtTA5kH13mL6UXP4jGYb+TebbIlIGoomke4F/NNwI5k/SZYkuQH4Z+Cyqhr5325LZJ4kWQvsMMmpE6vqgvmORxqmJM8DzgN+r6oeHHY886WqHgVWJtkeOD/JnlU10mNjJpF5UlX7DzsGaSFI8gx6CeTsqvrcsOMZhqr6YZIr6I2NjXQSsTtL0rxJb+Dvb4Fbq+qUYcczn5IsbVogJHkOsD9w23Cjmj2TyAKQ5K1JxoFXAxcnuXTYMWlwknwG+Brw8iTjSX5z2DHNo9cAvwG8NskNzXbgsIOaJzsClydZD1xLb0zkoiHHNGtOeyJJ6syWiCSpM5OIJKkzk4gkqTOTiCSpM5OIJKkzk4g0hebV60ryiuZ41yQPN6+l3pLkrCTPSHJA3+uqP0pye7N/VpJfTXLRVvc9I8khSc5v6m1M8kDfPf5Pkj/rq//iJHcm2T7JFc39b0zyf5O8vKlzRd9zb0hy7vz+19JiZRKRpnY48FXgsL6yO6pqJfBzwDLg0Kq6tKpWNuXrgHc2x0dOd/OqemtzzW8BV/bd403AwUl+tqn6l8AfVtUPm+N3NjPBngl8qO+WE89dWVWHzO6nS+2YRKRJNHM7vQb4TZ6YRIDH50C6ht4MtHOqqh4G3gt8IskbgW2r6uxJqn4FeOlcP1/6aZhEpMm9BfhiVX0duD/J3v0nkzwbeBXwxRb3+qW+bqYbgINmuqCqLgHuB84C/usU1f4TcFPf8dl9z/nQFNdIc8oJGKXJHQ78RbN/TnP8ceBnmkSwAji3qta3uNeVVfXmiYMkZ7SM4ePAc6rq9q3Kz07yMPAt4Hf6yt9ZVeta3luaEyYRaStJXgi8FtgzSQFL6C0e9AmaMZEkOwJXJDmoqi4cUCiPNdvWTBZaMOzOkp7sEOCsqnpxVe1aVbsA36Q3kA48vkLf8cAJQ4pRWhBMItKTHQ6cv1XZecAfbFX2eeC5SX5pXqKaWf+YyNphB6PFwVl8JUmd2RKRJHVmEpEkdWYSkSR1ZhKRJHVmEpEkdWYSkSR1ZhKRJHX2/wEIq2RUQ+8p/QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lrr.visualize(data, fb, ['DIABDX','CANCERDX','STRKDX','OHRTDX','CHDDX','HIBPDX','JTPAIN31','WLKLIM31','ARTHDX','ARTHTYPE']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Current smoking status\n",
    "The effect of current smoking status (ADSMOK42) is one example of a counter-intuitive finding that may warrant further investigation. A value of 2 indicates that the individual does not currently smoke, to which the model assigns a positive contribution to predicted cost. There may be confounding at work behind this association. For example, the average age of smokers (ADSMOK42 == 1) is 44 while the average age of non-smokers is 49, and older individuals are generally more costly. Furthermore, some individuals who currently do not smoke may have stopped due to poor health."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEKCAYAAAAFJbKyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAGplJREFUeJzt3XuYXVWd5vHva2hQFA2SQkMSLLTT2sioYIk4djs2KBcbCeOIJoqGS0+mZ1Dx0jZ4mcFL24OOghcUJy2B4NBEFGgi0iIiyPgglwQUCNEmRi5lIgkGIYhcAm//sVfBSVGXfarqXCr1fp5nP2fv317n7B88kF/WXnuvJdtERETU9bROJxAREZNLCkdERDQlhSMiIpqSwhEREU1J4YiIiKakcERERFNSOCIioikpHBER0ZQUjoiIaMp2nU6gFWbMmOHe3t5OpxERMamsXLnyHts9o7XbJgtHb28vK1as6HQaERGTiqQ76rTLraqIiGhKywqHpCWSNki6ZVD8vZJ+KWmVpM81xD8iaU05d1BD/OASWyPpxFblGxER9bTyVtVZwGnA2QMBSX8FzANeZvthSbuW+J7AfOClwG7ADyX9WfnaV4E3Av3A9ZKW2761hXlHRMQIWlY4bF8lqXdQ+L8DJ9t+uLTZUOLzgGUl/mtJa4B9y7k1ttcCSFpW2qZwRER0SLvHOP4M+EtJ10r6saRXlfgs4K6Gdv0lNlz8KSQtkrRC0oqNGze2IPWIiID2F47tgJ2B/YAPA+dJEqAh2nqE+FOD9mLbfbb7enpGfZosIiLGqN2P4/YDF7hadvA6SY8DM0p8TkO72cC6sj9cPCIiOqDdPY5/AfYHKIPf2wP3AMuB+ZJ2kLQHMBe4DrgemCtpD0nbUw2gL29zzhER0aBlPQ5J5wKvB2ZI6gdOApYAS8ojuo8AC0vvY5Wk86gGvbcAx9l+rPzOe4BLgWnAEturWpVzRESMTtWf29uWvr4+583xiKmp98TvdTqFjrr95L8e83clrbTdN1q7vDkeERFNSeGIiIimpHBERERTUjgiIqIpKRwREdGUFI6IiGhKCkdERDQlhSMiIpqSwhEREU1J4YiIiKakcERERFNSOCIioikpHBER0ZQUjoiIaEoKR0RENCWFIyIimpLCERERTWlZ4ZC0RNKGskzs4HN/J8mSZpRjSfqypDWSbpK0T0PbhZJuK9vCVuUbERH1tLLHcRZw8OCgpDnAG4E7G8KHAHPLtgg4vbR9LtVa5a8G9gVOkrRzC3OOiIhRtKxw2L4K2DTEqVOBvwcaFzufB5ztyjXAdEkzgYOAy2xvsn0vcBlDFKOIiGifto5xSDoM+I3tnw86NQu4q+G4v8SGi0dERIds164LSdoR+Bhw4FCnh4h5hPhQv7+I6jYXu++++xizjIiI0bSzx/EiYA/g55JuB2YDN0h6PlVPYk5D29nAuhHiT2F7se0+2309PT0tSD8iIqCNhcP2zbZ3td1ru5eqKOxj+7fAcuDd5emq/YD7bK8HLgUOlLRzGRQ/sMQiIqJDWvk47rnAT4EXS+qXdOwIzS8B1gJrgH8C/geA7U3Ap4Hry/apEouIiA5p2RiH7QWjnO9t2Ddw3DDtlgBLJjS5iIgYs7w5HhERTUnhiIiIpqRwREREU1I4IiKiKSkcERHRlBSOiIhoSgpHREQ0JYUjIiKaksIRERFNqfXmuKRpwPMa29u+c/hvRETEtmrUwiHpvVSr8N0NPF7CBl7WwrwiIqJL1elxHA+82PbvWp1MRER0vzpjHHcB97U6kYiImBzq9DjWAldK+h7w8EDQ9iktyyoiIrpWncJxZ9m2L1tERExhoxYO258EkLRTdegHWp5VRER0rVHHOCTtJelG4BZglaSVkl7a+tQiIqIb1RkcXwx80PYLbL8A+BDV8q4RETEF1Skcz7R9xcCB7SuBZ472JUlLJG2QdEtD7P9I+oWkmyRdKGl6w7mPSFoj6ZeSDmqIH1xiaySdWPufLCIiWqJO4Vgr6X9K6i3bx4Ff1/jeWcDBg2KXAXvZfhnwb8BHACTtCcwHXlq+8zVJ08ob618FDgH2BBaUthER0SF1CscxQA9wAXBh2T96tC/ZvgrYNCj2A9tbyuE1wOyyPw9YZvth278G1gD7lm2N7bW2HwGWlbYREdEhdZ6quhd4XwuufQzwrbI/i6qQDOgvMaheQGyMv3qoH5O0CFgEsPvuu09oohER8aRhC4ekL9p+v6TvUs1NtRXbh431opI+BmwBzhkIDdHMDN0jekouJZ/FVAP59PX1DdkmIiLGb6QexzfL5+cn8oKSFgKHAgfYHvgDvh+Y09BsNrCu7A8Xj4iIDhh2jMP2yrL7Cts/btyAV4zlYpIOBk4ADrP9YMOp5cB8STtI2gOYC1wHXA/MlbSHpO2pBtCXj+XaERExMeoMji8cInbUaF+SdC7wU+DFkvolHQucBuwEXCbpZ5K+DmB7FXAecCvwfeA424+VgfT3AJcCq4HzStuIiOiQkcY4FgDvAPaQ1Pi3/J2AUadYt71giPAZI7T/DPCZIeKXAJeMdr2IiGiPkcY4rgbWAzOALzTENwM3tTKpiIjoXsMWDtt3AHdIeiewzvZDAJKeQTVIfXtbMoyIiK5SZ4zjPJ5cMhbgMeDbrUknIiK6XZ3CsV15axuAsp91OSIipqg6hWOjpCde9pM0D7indSlFREQ3q7MC4N8C50g6jeoN77uAd7c0q4iI6Fp15qr6FbCfpGcBsr259WlFRES3Guk9jiNt/z9JHxwUB8D2KS3OLSIiutBIPY6BxZp2akciERExOYz0Hsf/LZ+fbF86ERHR7Ua6VfXlkb5ouxVrdERERJcb6XHclWV7OrAPcFvZXkH1EmBERExBI92qWgog6Sjgr2w/Wo6/DvygLdlFRETXqfMC4G5sPUD+rBKLiIgpqM4LgCcDN0q6ohz/J+ATLcsoIiK6Wp0XAM+U9K/Aq0voRNu/bW1aERHRrUa9VaXqjb83AC+3fRGwvaR9W55ZRER0pTpjHF8DXgMMrOi3GfjqaF+StETSBkm3NMSeK+kySbeVz51LXJK+LGmNpJsk7dPwnYWl/W2ShlrGNiIi2qhO4Xi17eOAhwBs30u9adXPAg4eFDsRuNz2XODycgxwCDC3bIuA06EqNMBJVLfJ9gVOGig2ERHRGXUKx6OSpgEGkNTD1gs7Dcn2VcCmQeF5wNKyvxQ4vCF+tivXANMlzQQOAi6zvakUrMt4ajGKiIg2qlM4vgxcCOwq6TPAT4B/HOP1nmd7PUD53LXEZ1FN1z6gv8SGi0dERIfUearqHEkrgQOo1uM43PbqCc5DQ116hPhTf0BaRHWbi913333iMouIiK2MWDgkPQ24yfZewC8m4Hp3S5ppe325FbWhxPuBOQ3tZgPrSvz1g+JXDvXDthcDiwH6+vqGLC4RETF+I96qsv048HNJE/VX+OXAwJNRC4GLGuLvLk9X7QfcV25lXQocKGnnMih+YIlFRESH1HlzfCawStJ1wB8GgrYPG/4rIOlcqt7CDEn9VE9HnQycJ+lY4E7giNL8EuBNwBrgQeDoco1Nkj4NXF/afcr24AH3iIhoozqFY0zrcdheMMypA4Zoa+C4YX5nCbBkLDlERMTEqzM4/mNJz6d6j8LA9ZlyJCJi6qoz5cjfANcBbwHeClwj6ZhWJxYREd2pzq2qDwN72/4dgKRdgKvJ7aOIiCmpzguA/VTzUw3YzNYv5UVExBRSp8fxG+BaSRdRjXHMA66T9EEA26e0ML+IiOgydQrHr8o2YODdi52GaBsREdu4Ok9Vjelx3IiI2DbVGeOIiIh4QgpHREQ0JYUjIiKaUucFwNmSLpS0UdLdks6XNLsdyUVERPep0+M4k2r22plUiyh9t8QiImIKqlM4emyfaXtL2c4CelqcV0REdKk6heMeSUdKmla2I4HftTqxiIjoTnUKxzHA24DfAuupJjo8upVJRURE96rz5vicwYs2SXot1UJMERExxdTpcXylZiwiIqaAYXsckl4D/EegZ2BCw+LZwLTxXFTSB4C/oZo08WaqW18zgWXAc4EbgHfZfkTSDsDZwCupxlbebvv28Vw/IiLGbqQex/bAs6iKy04N2/1U4xxjImkW8D6gz/ZeVEVoPvBZ4FTbc4F7gWPLV44F7rX9p8CppV1ERHTIsD0O2z8GfizpLNt3tOC6z5D0KLAj1aD7/sA7yvmlwCeA06mmcf9EiX8HOE2SyjrlERHRZqOOcUx00bD9G+DzVIPr64H7gJXA721vKc36qV42pHzeVb67pbTfZSJzioiI+to+V5Wknal6EXsAuwHPBA4ZoulAj0IjnGv83UWSVkhasXHjxolKNyIiBunEJIdvAH5te6PtR4ELqAbhp0sauHU2G1hX9vuBOQDl/HOATYN/1PZi2322+3p68mJ7RESrjPoeh6Qe4L8CvY3tbR8zxmveCewnaUfgj8ABwArgCqpB92XAQp5caXB5Of5pOf+jjG9ERHROnRcALwL+P/BD4LHxXtD2tZK+Q/XI7RbgRmAx8D1gmaR/KLEzylfOAL4paQ1VT2P+eHOIiIixq1M4drR9wkRe1PZJwEmDwmuBfYdo+xBwxERePyIixq7OGMfFkt7U8kwiImJSqFM4jqcqHg9J2ly2+1udWEREdKdRb1XZ3qkdiURExORQZ4wDSYcBryuHV9q+uHUpRUREN6uz5vjJVLerbi3b8SUWERFTUJ0ex5uAV9h+HEDSUqrHZU9sZWIREdGd6r45Pr1h/zmtSCQiIiaHOj2O/w3cKOkKqnmjXgd8pKVZRURE16rzVNW5kq4EXkVVOE6w/dtWJxYREd1p2FtVkl5SPvehWp2vn2p6891KLCIipqCRehwfBBYBXxjinKkWXoqIiClmpBUAF5XdQ8p8UU+Q9PSWZhUREV2rzlNVV9eMRUTEFDBsj0PS86mWbX2GpL15ciW+Z1OtEx4REVPQSGMcBwFHUa3Gd0pDfDPw0RbmFBERXWykMY6lwFJJ/8X2+W3MKSIiulidFwD3kvTSwUHbn2pBPhER0eXqFI4HGvafDhwKrG5NOhER0e3qvDm+1Xsckj4PLB/PRSVNB74B7EX1TsgxwC+BbwG9wO3A22zfK0nAl6gmW3wQOMr2DeO5fkREjF3dSQ4b7Qi8cJzX/RLwfdsvAV5O1YM5Ebjc9lzgcp6cffcQYG7ZFgGnj/PaERExDqP2OCTdTNUrAJgG9ABjHt+Q9GyqiRKPArD9CPCIpHnA60uzpcCVwAnAPOBs2waukTRd0kzb68eaQ0REjF2dMY5DG/a3AHfb3jKOa74Q2AicKenlwEqqhaKeN1AMbK+XtGtpP4tqjqwB/SWWwhER0QGj3qqyfQewC9Xf/N8C/IdxXnM7YB/gdNt7A39g5EWhNETMT2kkLZK0QtKKjRs3jjPFiIgYTp2lY/8X1a2jXYAZwFmSPj6Oa/YD/bavLcffoSokd0uaWa45E9jQ0H5Ow/dnA+sG/6jtxbb7bPf19PSMI72IiBhJncHxBcCrbJ9k+yRgP+CdY71gWcvjLkkvLqEDqNYyXw4sLLGFwEVlfznwblX2A+7L+EZEROfUGeO4ner9jYEZcncAfjXO674XOEfS9sBa4GiqInaepGOBO4EjSttLqB7FXUP1OO7R47x2RESMw0iTHH6FaizhYWCVpMvK8RuBn4znorZ/BvQNceqAIdoaOG4814uIiIkzUo9jRflcCVzYEL+yZdlERETXG22Sw4iIiK2MdKvqPNtvG/QC4BNsv6ylmUVERFca6VbV8eXz0BHaRETEFDPSrar1kqYBZ9h+QxtzioiILjbiexy2HwMelPScNuUTERFdrs57HA8BN5fHcf8wELT9vpZlFRERXatO4fhe2Ro9ZbA8IiKmhjqFY7rtLzUGJB0/XOOIiNi21ZmrauEQsaMmOI+IiJgkRnqPYwHwDmAPSY1Lxe4E/K7ViUVERHca6VbV1VSLJc0AGtcd3wzc1MqkIiKie430HscdwB3Aa9qXTkREdLs6Czm9RdJtku6TdL+kzZLub0dyERHRfeo8VfU54M22V7c6mYiI6H51nqq6O0UjIiIG1OlxrJD0LeBfqBZ1AsD2BS3LKiIiuladHsezqZZsPRB4c9nGPWOupGmSbpR0cTneQ9K1ZTzlW2VZWSTtUI7XlPO94712RESM3ag9DtutWuP7eGA1VWEC+Cxwqu1lkr4OHAucXj7vtf2nkuaXdm9vUU4RETGKOk9VzZZ0oaQNku6WdL6k2eO5aPn+XwPfKMcC9ge+U5osBQ4v+/PKMeX8AaV9RER0QJ1bVWcCy4HdgFnAd0tsPL4I/D3weDneBfi97S3luL9ci/J5F0A5f19pHxERHVCncPTYPtP2lrKdBfSM9YKSDgU22F7ZGB6iqWuca/zdRZJWSFqxcePGsaYXERGjqFM47pF0ZBnMnibpSMY3V9VrgcMk3Q4so7pF9UVguqSBMZfZwLqy3w/MASjnnwNsGvyjthfb7rPd19Mz5roWERGjqFM4jgHeBvyWau6qt5bYmNj+iO3ZtnuB+cCPbL8TuKL8NlQz8l5U9pfz5Ay9by3tsx5IRESH1Hmq6k7gsDbkcgKwTNI/ADcCZ5T4GcA3Ja2h6mnMb0MuERExjFELh6SlwPG2f1+Odwa+YHvMvY4Btq8Eriz7a4F9h2jzEHDEeK8VERETo86tqpcNFA0A2/cCe7cupYiI6GZ1CsfTSi8DAEnPpd5UJRERsQ2qUwC+AFwt6TtUj8G+DfhMS7OKiIiuVWdw/GxJK6gemxXwFtu3tjyziIjoSrVuOZVCkWIRERG1xjgiIiKekMIRERFNSeGIiIimpHBERERTUjgiIqIpKRwREdGUFI6IiGhKCkdERDQlhSMiIpqSwhEREU1J4YiIiKakcERERFNSOCIioiltLxyS5ki6QtJqSaskHV/iz5V0maTbyufOJS5JX5a0RtJNkvZpd84REfGkTvQ4tgAfsv3nwH7AcZL2BE4ELrc9F7i8HAMcAswt2yLg9PanHBERA9peOGyvt31D2d8MrAZmAfOApaXZUuDwsj8PONuVa4Dpkma2Oe2IiCg6OsYhqRfYG7gWeJ7t9VAVF2DX0mwWcFfD1/pLbPBvLZK0QtKKjRs3tjLtiIgprWOFQ9KzgPOB99u+f6SmQ8T8lIC92Haf7b6enp6JSjMiIgbpSOGQ9CdUReMc2xeU8N0Dt6DK54YS7wfmNHx9NrCuXblGRMTWOvFUlYAzgNW2T2k4tRxYWPYXAhc1xN9dnq7aD7hv4JZWRES033YduOZrgXcBN0v6WYl9FDgZOE/SscCdwBHl3CXAm4A1wIPA0e1NNyIiGrW9cNj+CUOPWwAcMER7A8e1NKmIiKgtb45HRERTUjgiIqIpKRwREdGUFI6IiGhKCkdERDQlhSMiIpqSwhEREU1J4YiIiKakcERERFNSOCIioikpHBER0ZQUjoiIaEoKR0RENCWFIyIimpLCERERTUnhiIiIpqRwREREUyZN4ZB0sKRfSloj6cRO5xMRMVVNisIhaRrwVeAQYE9ggaQ9O5tVRMTUNCkKB7AvsMb2WtuPAMuAeR3OKSJiSposhWMWcFfDcX+JRUREm23X6QRq0hAxb9VAWgQsKocPSPply7NqnRnAPZ1OIqas/Pc3Ph3996fPjuvrL6jTaLIUjn5gTsPxbGBdYwPbi4HF7UyqVSStsN3X6Txiasp/f+MzFf79TZZbVdcDcyXtIWl7YD6wvMM5RURMSZOix2F7i6T3AJcC04Altld1OK2IiClpUhQOANuXAJd0Oo822SZuucWklf/+xmeb//cn26O3ioiIKCbLGEdERHSJFI4uJOkISaskPS5pm346I7qHpCWSNki6pdO5TEaS5ki6QtLq8v/v8Z3OqVVSOLrTLcBbgKs6nUhMKWcBB3c6iUlsC/Ah238O7Acct61OjTRpBsenEturAaSh3nuMaA3bV0nq7XQek5Xt9cD6sr9Z0mqqGS5u7WhiLZAeR0TEBCsFeG/g2s5m0hrpcXSIpB8Czx/i1MdsX9TufCJiYkh6FnA+8H7b93c6n1ZI4egQ22/odA4RMbEk/QlV0TjH9gWdzqdVcqsqImICqBqUPANYbfuUTufTSikcXUjSf5bUD7wG+J6kSzudU2z7JJ0L/BR4saR+Scd2OqdJ5rXAu4D9Jf2sbG/qdFKtkDfHIyKiKelxREREU1I4IiKiKSkcERHRlBSOiIhoSgpHREQ0JYUjoiiPQVvSS8pxr6Q/SrqxzHh6naSFDe2fJ+liST+XdKukSxq+Z0mfbmg7Q9Kjkk5riC2S9IuyXSfpLxrOXTkwM3L5vdskHdRwfndJD0j6u3I8ZWZmjc5L4Yh40gLgJ1Rr2g/4le29y4yn84EPSDq6nPsUcJntl9veEzix4XtrgUMbjo8AnljuWNKhwH8D/sL2S4C/Bf5Z0lbT0EiaTbVk8odsN77Pcyrwrw3HU2Zm1ui8FI4Inphf6LXAsWxdOJ5gey3wQeB9JTQT6G84f1ND8z8CqxvWU3k7cF7D+ROAD9u+p3z3BmApcFxDm+cDPwA+bnt5Q66HUxWmJwqR7fXlN7C9GRiYmTViwqVwRFQOB75v+9+ATZL2GabdDcBLyv5XgTPKLaKPSdptUNtlwPzSa3gMWNdw7qXAykHtV5T4gLOB02x/eyAg6ZlUReeTw/2DbOszs0bnpXBEVBZQ/UFP+VwwTLsnFkkpt45eCPwTVTG5UVJPQ9vvA28sv/WtGjkIaJzK4YfAuyTt2BD7JHCq7QeG/IEpMDNrdF5mx40pT9IuwP7AXpIMTKP6A/xrQzTfm+o2EAC2NwH/TDU+cTHwOkpPwvYjklYCH6LqSby54XduBV4J/Kghtg9bL/rzOeBI4NuS5tneArwaeKukzwHTgcclPWT7tKkyM2t0XnocEfBW4GzbL7Dda3sO8GtgdmOjcgvo88BXyvH+A70BSTsBLwLuHPTbXwBOsP27QfHPAZ8tRQtJrwCO4qnF6gPA/VS3xGT7L0uOvcAXgX8sRWPKzMwanZceR0R1K+nkQbHzgY8CL5J0I/B0YDPwFdtnljavBE6TtIXqL2HfsH194/KrtlfRMIjdEF8uaRZwdenlbAaOLMuPNrZzeQT4Yqpi8+Fh/hkGZma9WdLPSuyjti+p8y8gohmZHTciIpqSW1UREdGUFI6IiGhKCkdERDQlhSMiIpqSwhEREU1J4YiIiKakcERERFNSOCIioin/DlPBsgNmJoWuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lrr.visualize(data, fb, ['ADSMOK42']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Socio-economic factors\n",
    "The following four plots examine the effects of socio-economic variables: income, insurance coverage, education, and employment status. \n",
    "\n",
    "The first plot shows that individuals with incomes less than $10,000 have lower cost while those with zero income have even lower cost. This is likely due to these individuals seeking less care because of inability to pay for their portion of the cost."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lrr.visualize(data, fb, ['INCOME_M']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second plot shows that individuals covered by any kind of private health insurance (INSCOV15 == 1) have higher costs. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lrr.visualize(data, fb, ['INSCOV15']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the third plot, EDRECODE is a re-coded version of education. A value of 13 means high school graduate or GED, to which the model assigns a relatively small reduction in predicted cost. Values of 1 and 2 mean education less than a high school diploma, while values greater than 13 mean at least some college education."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lrr.visualize(data, fb, ['EDRECODE']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The last plot on employment status shows that the predicted cost for unemployed individuals (EMPST31 == 4) is slightly higher."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lrr.visualize(data, fb, ['EMPST31']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Other demographic factors\n",
    "The last four plots show the effects of other demographic variables such as age, race, and geography. \n",
    "\n",
    "The first plot with respect to age (in years) is non-smooth and points to a limitation of the LinRR model. Specifically, since the dependence on age is limited to a linear function (category 1 discussed [above](#categories)) plus step functions corresponding to threshold rules (category 2, not including interaction terms in category 3), the curve is constrained to be piecewise linear with all segments having the same slope and step discontinuities in between. The plot shows that predicted cost first decreases with age until the late 30s, roughly levels off in middle age, and then decreases further after the late 50s. While the first two stages of this behavior are reasonable, the last stage runs counter to the expectation that older individuals (say 60+) experience increasing healthcare costs. This unexpected dependence is mitigated by the second ACTDTY31 plot. While the ACTDTY31 feature is ostensibly about active military duty, a value of 4 actually means that the individual is over age 59 and the question is not applicable. ACTDTY31 == 4 is therefore a proxy for older age and does have a significant positive effect on cost. The non-smooth dependence on AGE31X may also be improved by allowing more general functions in the GAM, for example piecewise linear functions with arbitrary slopes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lrr.visualize(data, fb, ['AGE31X', 'ACTDTY31']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The last two plots show that the predicted cost is lower for black individuals (RACE3 == 1) as well as residents in the South US Census region (REGION == 3)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZAAAAEKCAYAAAA8QgPpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAFHpJREFUeJzt3X+wJWV95/H3x2HHH4CAcQwwM/zIhmghIYg3jJpkkyjyKy6zZQyZSShBdjNlFiKJm10xuGs0IUsMsqvRZHc2DuCuK5IoYYykCFQJxkICM6LAoOiIIiOI/HARQ4AA3/3j9IXDcO+5Td977jmH+35VdU330923v1M1M5/p5+l+OlWFJEnP1HNGXYAkaTIZIJKkTgwQSVInBogkqRMDRJLUiQEiSepk4gIkyTFJbkmyPckZo65HkpaqTNJ7IEmWAV8DXg/sAK4D1lfVzSMtTJKWoEm7AzkC2F5Vt1bVI8CFwNoR1yRJS9Iuoy7gGVoJ3N63vQNY039Akg3ABoBdd931lS972csWrzppkd34nftHXYLG1E+u3KPzuVu3br2nqlbMddykBUhmaHtKH1xVbQQ2AkxNTdWWLVsWoy5pJA444zOjLkFjasvZv9T53CS3tTlu0rqwdgCr+7ZXAXeMqBZJWtImLUCuAw5KcmCS5cA6YPOIa5KkJWmiurCq6tEkpwGXAcuATVW1bcRlSdKSNFEBAlBVlwKXjroOSVrqJq0LS5I0JgwQSVInBogkqRMDRJLUiQEiSerEAJEkdWKASJI6MUAkSZ0YIJKkTgwQSVInBogkqRMDRJLUiQEiSerEAJEkdWKASJI6MUAkSZ0YIJKkTgwQSVInBogkqRMDRJLUiQEiSerEAJEkdWKASJI6MUAkSZ0YIJKkTgwQSVInBogkqRMDRJLUiQEiSerEAJEkdWKASJI6MUAkSZ0YIJKkTgwQSVInBogkqRMDRJLUiQEiSerEAJEkdTKSAEnyJ0m+muSGJBcn2bNv3zuTbE9yS5Kj+9qPadq2JzljFHVLkp40qjuQy4FDqupQ4GvAOwGSHAysA14OHAP8WZJlSZYBHwaOBQ4G1jfHSpJGZCQBUlV/V1WPNpvXAKua9bXAhVX1cFV9E9gOHNEs26vq1qp6BLiwOVaSNCK7tDmouQP40f7jq+rbC1TDKcAnmvWV9AJl2o6mDeD2ndrXzFLrBmADwH777bdAJUqSdjZngCT5LeDdwF3A401zAYfOcd4VwN4z7Dqzqi5pjjkTeBT42PRpMxxfzHynVDNdt6o2AhsBpqamZjxGkjR/be5ATgdeWlX3PpMfXFVHDtqf5CTgDcDrqmr6H/odwOq+w1YBdzTrs7VLkkagzRjI7cD9C3nRJMcA7wCOr6oH+3ZtBtYleW6SA4GDgGuB64CDkhyYZDm9gfbNC1mTJOmZaXMHcitwZZLPAA9PN1bVufO47oeA5wKXJwG4pqreWlXbklwE3Eyva+vUqnoMIMlpwGXAMmBTVW2bx/UlSfPUJkC+3SzLm2XequrHB+w7CzhrhvZLgUsX4vqSpPmbM0Cq6j0ASXbvbdYPh16VJGnszTkGkuSQJNcDNwHbkmxN8vLhlyZJGmdtBtE3Am+vqv2ran/gPwD/a7hlSZLGXZsA2bWqPju9UVVXArsOrSJJ0kRo9RRWkv8M/O9m+0Tgm8MrSZI0CdrcgZwCrAA+BVzcrL9lmEVJksZfm6ewvg+8bRFqkSRNkFkDJMl/r6rfTvJpZph3qqqOH2plkqSxNugOZHrM45zFKESSNFlmDZCq2tqsHlZVH+jfl+R04KphFiZJGm9tBtFPmqHt5AWuQ5I0YQaNgawHfg04MEn/zLe7A89oandJ0rPPoDGQq4E7gRcD7+9rfwC4YZhFSZLG36AxkNuA25L8OnBHVT0EkOT59D7o9K1FqVCSNJbajIFcxJOfsgV4DPjL4ZQjSZoUbQJkl6p6ZHqjWV+Q74JIkiZXmwC5O8kTLw0mWQvcM7ySJEmToM1kim8FPpbkQ0DofSP9zUOtSpI09trMhfUN4FVJdgNSVQ8MvyxJ0rgb9B7IiVX1f5K8fad2AKrq3CHXJkkaY4PuQKY/GrX7YhQiSZosg94D+Z/Nr+9ZvHIkSZNiUBfWBwedWFV+I0SSlrBBj/FubZbnAYcDX2+Ww+i9TChJWsIGdWFdAJDkZOAXq+qfm+3/AfzdolQnSRpbbV4k3JenDqTv1rRJkpawNi8Sng1cn+SzzfbPA78/tIokSROhzYuE5yX5W2BN03RGVX13uGVJksbdnF1Y6b05eCTwU1V1CbA8yRFDr0ySNNbajIH8GfBqYH2z/QDw4aFVJEmaCG3GQNZU1eFJrgeoqu8ncTp3SVri2tyB/HOSZUABJFnBUz8wJUlagtoEyAeBi4GXJDkL+DzwR0OtSpI09to8hfWxJFuB19H7Hsi/qaqvDL0ySdJYGxggSZ4D3FBVhwBfXZySJEmTYGAXVlU9Dnw5yX6LVI8kaUK0eQprH2BbkmuBf5xurKrjZz9FkvRs1yZAhvY9kCS/C/wJsKKq7mleWvwAcBzwIHByVX2xOfYk4F3NqX84PdmjJGk02gyiX5Vkb+AIeo/yXrcQU5kkWQ28Hvh2X/OxwEHNsgb4c2BNkhcB7wammhq2JtlcVd+fbx2SpG7aTGXy74BrgTcCbwKuSXLKAlz7vwH/ieb9ksZa4KPVcw2wZ5J9gKOBy6vqviY0LgeOWYAaJEkdtenC+o/AK6rqXoAkPwJcDWzqetEkxwPfqaov93qtnrASuL1ve0fTNlv7TD97A7ABYL/9HPuXpGFpEyA76M1/Ne0BnvqP+YySXAHsPcOuM4HfA46a6bQZ2mpA+9MbqzYCGwGmpqZmPEaSNH9tAuQ7wD8kuYTeP9prgWuTvB2gqs6d6aSqOnKm9iQ/CRxI7/FggFXAF5sZfncAq/sOXwXc0bT/wk7tV7aoXZI0JG2mMvkG8Nc8+T/+S4A76X2lcPfZTppNVd1YVS+pqgOq6gB64XB4MzC/GXhzel4F3F9VdwKXAUcl2SvJXvTuXi57pteWJC2cNk9hDe0x3hlcSu8R3u30HuN9S1PDfUn+ALiuOe69VXXfItYlSdpJmy6soWruQqbXCzh1luM2MY+Be0nSwmrThSVJ0tMYIJKkTtq8SLgqycVJ7k5yV5JPJlm1GMVJksZXmzuQ8+g9HbUPvZf3Pt20SZKWsDYBsqKqzquqR5vlfGDFkOuSJI25NgFyT5ITkyxrlhOBe4ddmCRpvLUJkFOAE4Dv0nuB8E0072dIkpauNu+BrN7541FJfoanTsMuSVpi2tyB/GnLNknSEjLrHUiSVwOvAVZMT5zYeCGwbNiFSZLG26AurOXAbs0x/ZMm/oDeOIgkaQmbNUCq6irgqiTnV9Vti1iTJGkCzDkGYnhIkmbiXFiSpE4MEElSJ3O+B5JkBfAbwAH9x1fVKcMrS5I07tq8SHgJ8PfAFcBjwy1HkjQp2gTIC6rqHUOvRJI0UdqMgfxNkuOGXokkaaK0CZDT6YXIQ0keaJYfDLswSdJ4m7MLq6p2n+sYSdLS02YMhCTHA/+q2byyqv5meCVJkiZBm2+in02vG+vmZjm9aZMkLWFt7kCOAw6rqscBklwAXA+cMczCJEnjre2b6Hv2re8xjEIkSZOlzR3IfwWuT/JZIPTGQt451KokSWOvzVNYH09yJfDT9ALkHVX13WEXJkkab7N2YSV5WfPr4cA+wA7gdmDfpk2StIQNugN5O7ABeP8M+wp47VAqkiRNhEFfJNzQrB5bVQ/170vyvKFWJUkae22ewrq6ZZskaQmZ9Q4kyd7ASuD5SV5BbwAd4IXACxahNknSGBs0BnI0cDKwCji3r/0B4PeGWJMkaQIMGgO5ALggyS9X1ScXsSZJ0gRo8yLhIUlevnNjVb13CPVIkiZEmwD5Yd/684A3AF8ZTjmSpEnR5k30p7wHkuQcYPPQKpIkTYS2kyn2ewHwYwtdiCRpsrT5HsiNSW5olm3ALcAH5nvhJL+V5JYk25K8r6/9nUm2N/uO7ms/pmnbnsSp5CVpxNqMgbyhb/1R4K6qenQ+F03yi8Ba4NCqejjJS5r2g4F1wMuBfYErkvxEc9qHgdfTm5PruiSbq+rm+dQhSequzRjIbc3kiT9Lbw6sz9P7oNR8/CZwdlU93Fzje037WuDCpv2bSbYDRzT7tlfVrQBJLmyONUAkaUTadGH9F+AC4EeAFwPnJ3nXPK/7E8DPJfmHJFcl+emmfSW9GX+n7WjaZmufqd4NSbYk2XL33XfPs0xJ0mzadGGtB14xPaFi8z30LwJ/OOikJFcAe8+w68zmunsBr6L3nZGLkvwYT06X0q+YOehqputW1UZgI8DU1NSMx0iS5q9NgHyL3vsf0zPyPhf4xlwnVdWRs+1L8pvAp6qqgGuTPE7v7mYHsLrv0FXAHc36bO2SpBEYNJnin9L7X/7DwLYklzfbr6c3DjIff03veyJXNoPky4F76L1f8n+TnEtvEP0g4Fp6dyYHJTkQ+A69gfZfm2cNkqR5GHQHsqX5dStwcV/7lQtw3U3ApiQ3AY8AJzV3I9uSXERvcPxR4NSqegwgyWnAZcAyYFNVbVuAOiRJHc01meJQVNUjwImz7DsLOGuG9kuBS4dVkyTpmRnUhXVRVZ2Q5EZmGLCuqkOHWpkkaawN6sI6vfn1DQOOkSQtUYO6sO5Msgz4yKAnqiRJS9PAFwmbAewHk+yxSPVIkiZEm/dAHgJubB7j/cfpxqp629CqkiSNvTYB8plm6ecb3pK0xLUJkD2r6inTtyc5fbaDJUlLQ5sPSp00Q9vJC1yHJGnCDHoPZD296UIOTNL/CdvdgXuHXZgkabwN6sK6GriT3iSH/d9FfwC4YZhFSZLG36D3QG4DbgNevXjlSJImRZsPSr0xydeT3J/kB0keSPKDxShOkjS+2jyF9T7gX1fVV4ZdjCRpcrR5Cusuw0OStLM2dyBbknyC3kegHp5urKpPDa0qSdLYaxMgLwQeBI7qayvAAJGkJWzOAKmqtyxGIZKkydLmKaxVSS5O8r0kdyX5ZJJVi1GcJGl8tRlEPw/YDOwLrAQ+3bRJkpawNgGyoqrOq6pHm+V8YMWQ65Ikjbk2AXJPkhOTLGuWE3EuLEla8toEyCnACcB36c2N9aamTZK0hLV5CuvbwPGLUIskaYK0eQrrgiR79m3vlWTTcMuSJI27Nl1Yh1bV/5veqKrvA68YXkmSpEnQJkCek2Sv6Y0kL6LdG+ySpGexNkHwfuDqJH9FbwqTE4CzhlqVJGnstRlE/2iSLcBrgQBvrKqbh16ZJGmsteqKagLD0JAkPaHNGIgkSU9jgEiSOjFAJEmdGCCSpE4MEElSJwaIJKkTA0SS1IkBIknqZCQBkuSwJNck+VKSLUmOaNqT5INJtie5IcnhfeeclOTrzXLSKOqWJD1pVJMivg94T1X9bZLjmu1fAI4FDmqWNcCfA2uaCRzfDUzRm49ra5LNzczAkqQRGFUXVgEvbNb3AO5o1tcCH62ea4A9k+wDHA1cXlX3NaFxOXDMYhctSXrSqO5Afhu4LMk59ELsNU37SuD2vuN2NG2ztT9Nkg3ABoD99ttvYauWJD1haAGS5Apg7xl2nQm8DvidqvpkkhOAjwBH0pvtd2c1oP3pjVUbgY0AU1NTMx4jSZq/oQVIVR05274kHwVObzb/EviLZn0HsLrv0FX0urd20Bsj6W+/coFKlSR1MKoxkDuAn2/WXwt8vVnfDLy5eRrrVcD9VXUncBlwVPM99r2Ao5o2SdKIjGoM5DeADyTZBXiIZswCuBQ4DtgOPAi8BaCq7kvyB8B1zXHvrar7FrdkSVK/kQRIVX0eeOUM7QWcOss5m4BNQy5NktSSb6JLkjoxQCRJnRggkqRODBBJUicGiCSpEwNEktSJASJJ6sQAkSR1YoBIkjoxQCRJnRggkqRODBBJUicGiCSpEwNEktSJASJJ6mRUH5SStAC+dfYvjboELWHegUiSOjFAJEmdGCCSpE4MEElSJwaIJKkTA0SS1IkBIknqxACRJHVigEiSOjFAJEmdpKpGXcPQJLkbuG3UdTxLvBi4Z9RFSAP4Z3Th7F9VK+Y66FkdIFo4SbZU1dSo65Bm45/RxWcXliSpEwNEktSJAaK2No66AGkO/hldZI6BSJI68Q5EktSJASJJ6sQA0ZySHJPkliTbk5wx6nqkfkk2JflekptGXctSY4BooCTLgA8DxwIHA+uTHDzaqqSnOB84ZtRFLEUGiOZyBLC9qm6tqkeAC4G1I65JekJVfQ64b9R1LEUGiOayEri9b3tH0yZpiTNANJfM0Oaz35IMEM1pB7C6b3sVcMeIapE0RgwQzeU64KAkByZZDqwDNo+4JkljwADRQFX1KHAacBnwFeCiqto22qqkJyX5OPAF4KVJdiT5t6OuaalwKhNJUifegUiSOjFAJEmdGCCSpE4MEElSJwaIJKkTA0TqKMljSb6U5KYkn06y5077fyfJQ0n22Kn9iCSfa2Y4/mqSv0jygiQnJ7m7+ZnTy8FJ9k+ytdneluSti/s7lWbmY7xSR0l+WFW7NesXAF+rqrP69l8LPAx8pKrOb9p+FLgWWFdVX0gS4JeBv6c34/FUVZ2203WW0/u7+nCS3YCbgNdUlTMCaKS8A5EWxhfom2Qyyb8EdgPeBazvO+5U4IKq+gJA9fxVVd012w+uqkeq6uFm87n491Zjwj+I0jw130x5HU+d4mU98HF6dxYvTfKSpv0QYOuAH/erO3VhPb+5xuokN9CbGfmPvfvQODBApO6en+RLwL3Ai4DL+/atAy6sqseBTwG/0vJnfqKqDutb/gmgqm6vqkOBHwdOarrCpJEyQKTu/qmqDgP2B5bT654iyaHAQcDlSb5FL0ymu7G2Aa/sesHmzmMb8HPdy5YWhgEizVNV3Q+8DfjdJP+CXlj8flUd0Cz7AiuT7A98iN4dxJrp85OcmGTv2X5+klV9XVl7AT8D3DLE35LUyi6jLkB6Nqiq65N8md7dxjp6T1T1u5jek1d/nGQdcE4zLvI48Dl63VzQGwP52b7z/j2wK/D+JEXvA1/nVNWNQ/ztSK34GK8kqRO7sCRJnRggkqRODBBJUicGiCSpEwNEktSJASJJ6sQAkSR18v8BCnZUGAIhMiwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lrr.visualize(data, fb, ['RACE3', 'REGION']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"higher-degree\"></a>\n",
    "### 3.5. Examine higher-degree rules\n",
    "Now that the linear terms (feature category 1 [above](#categories)) and first-degree rules (category 2) in the model have been summarized in the [Visualization](#visualize) section, we consider the higher-degree rules that remain (category 3). The `explain()` method of LinRR can print just the higher-degree rules:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rule</th>\n",
       "      <th>coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(intercept)</td>\n",
       "      <td>13998.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>RTHLTH31 != 5 AND PREGNT31 != 1</td>\n",
       "      <td>-6614.27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>ADHDADDX != 1 AND PREGNT31 != 1 AND COGLIM31 != 1 AND DFSEE42 != -1</td>\n",
       "      <td>-3974.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>PREGNT31 != 1 AND ACTLIM31 != 1</td>\n",
       "      <td>-3778.59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>REGION != 1 AND DFSEE42 != -1</td>\n",
       "      <td>-2677.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>AGE31X &gt; 7.00 AND MARRY31X != 8 AND MARRY31X != 10 AND PCS42 &lt;= 50.22</td>\n",
       "      <td>2211.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>RTHLTH31 != 1 AND INSCOV15 != 3</td>\n",
       "      <td>1640.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>SOCLIM31 != -1 AND PHQ242 != 5 AND POVCAT15 != 5</td>\n",
       "      <td>-1565.76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>PCS42 &lt;= 53.99 AND INSCOV15 != 3</td>\n",
       "      <td>1277.63</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                                    rule coefficient\n",
       "0                                                            (intercept)     13998.7\n",
       "1                                        RTHLTH31 != 5 AND PREGNT31 != 1    -6614.27\n",
       "2    ADHDADDX != 1 AND PREGNT31 != 1 AND COGLIM31 != 1 AND DFSEE42 != -1    -3974.52\n",
       "3                                        PREGNT31 != 1 AND ACTLIM31 != 1    -3778.59\n",
       "4                                          REGION != 1 AND DFSEE42 != -1    -2677.43\n",
       "5  AGE31X > 7.00 AND MARRY31X != 8 AND MARRY31X != 10 AND PCS42 <= 50.22     2211.48\n",
       "6                                        RTHLTH31 != 1 AND INSCOV15 != 3     1640.62\n",
       "7                       SOCLIM31 != -1 AND PHQ242 != 5 AND POVCAT15 != 5    -1565.76\n",
       "8                                       PCS42 <= 53.99 AND INSCOV15 != 3     1277.63"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "pd.set_option('display.max_colwidth', 70)\n",
    "pd.set_option('display.width', 100)\n",
    "lrr.explain(highDegOnly=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These higher-degree rules are naturally more difficult to interpret and require more domain expertise to do so. The first three rules are perhaps the simplest. They yield large reductions in predicted cost when certain conditions are absent, with the common element being lack of pregnancy (PREGNT31 != 1). As noted [above](#RTHLTH31), RTHLTH31 != 5 means the individual is not in self-reported \"poor\" health, while ADHDADDX, COGLIM31, and ACTLIM31 refer respectively to attention-deficit/hyperactivity disorder, cognitive limitations, and any activity limitations at work, in housework, or at school. \n",
    "\n",
    "In rule 4, REGION != 1 indicates that the individual does not live in the Northeast census region, while DFSEE42 != -1 (also present in rule 2) indicates that the question about \"serious difficulty seeing (even) with glasses\" is not inapplicable. More cannot be said without knowing what makes the \"serious difficulty seeing\" question inapplicable. In rule 5, values of 8 and 10 for MARRY31X indicate that the individual was widowed or separated during the survey round. Again it is not clear why the absence of these conditions contributes to higher predicted cost, but the last condition PCS42 <= 50.22 does make sense as it corresponds to poor physical health.\n",
    "\n",
    "In rules 6 and 8, INSCOV15 != 3 means that the individual has health insurance, whether public or private. Conditioned on this, self-reported health that is less than \"excellent\" (RTHLTH31 != 1) and poorer physical health (PCS42 <= 53.99) result in higher predicted cost. Lastly in rule 7, PHQ242 is a score for depression with higher values corresponding to greater tendency toward depression. PHQ242 != 5 thus indicates the absence of a high value, although not the highest value of 6. POVCAT15 != 5 means that the individual does not have high income (400% above the poverty level) while SOCLIM != -1 means that the question about social limitations is applicable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"high-cost\"></a>\n",
    "## 4. High-cost patient identification\n",
    "To demonstrate the Boolean Rule Column Generation (BRCG) algorithm, we require a binary classification task since that is what BRCG is designed for. Here we consider the identification of high-cost individuals, which is of interest for the care management use case. We define high cost as being above the mean (which is already high relative to the median) and create a binary-valued target variable accordingly. The input features are the same as used to predict expenditure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.21493188010899184"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Binarize target variable\n",
    "y2 = (y > y.mean()).astype(int)\n",
    "y2.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Only 21.5% of individuals have costs greater than the mean, which is consistent with the mean being close to the 80th percentile of expenditure as seen [earlier](#baseline)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1. Re-process data\n",
    "We re-split the data into training and test sets, this time stratifying on the target variable. The features are then binarized as before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Re-split data into training and test sets\n",
    "dfTrain, dfTest, yTrain, yTest = train_test_split(data, y2, random_state=0, stratify=y2)\n",
    "# Binarize data\n",
    "dfTrain, _ = fb.fit_transform(dfTrain)\n",
    "dfTest, _ = fb.transform(dfTest)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2. Establish baseline\n",
    "We again use gradient-boosted trees to establish a baseline for accuracy, specifically the classification variant (GBCT)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training accuracy: 0.8705856706874001\n",
      "Test accuracy: 0.8304272013949433\n"
     ]
    }
   ],
   "source": [
    "# Train and evaluate GBCT\n",
    "from sklearn.ensemble import GradientBoostingClassifier\n",
    "gbc = GradientBoostingClassifier(n_estimators=500)\n",
    "gbc.fit(dfTrain, yTrain)\n",
    "from sklearn.metrics import accuracy_score\n",
    "print('Training accuracy:', accuracy_score(yTrain, gbc.predict(dfTrain)))\n",
    "print('Test accuracy:', accuracy_score(yTest, gbc.predict(dfTest)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"BRCG\"></a>\n",
    "### 4.3. Run Boolean Rule Column Generation (BRCG) and interpret rules\n",
    "Now we use BRCG to perform the same classification task. BRCG produces a very simple set of rules (also known as an OR-of-ANDs or disjunctive normal form (DNF) rule) for predicting that an individual is high-cost. Similar to LinRR, the complexity parameters `lambda0`, `lambda1` penalize the number of rules in the rule set and the number of conditions in each rule. The values of `lambda0`, `lambda1` below provide a good trade-off between accuracy and rule set complexity. Lower values were observed to yield more complex rules but with no improvement in accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Learning DNF rule with complexity parameters lambda0=0.0001, lambda1=0.0001\n",
      "Initial LP solved\n",
      "Iteration: 1, Objective: 0.1903\n",
      "Iteration: 2, Objective: 0.1858\n",
      "Iteration: 3, Objective: 0.1858\n",
      "Iteration: 4, Objective: 0.1844\n",
      "Iteration: 5, Objective: 0.1830\n",
      "Iteration: 6, Objective: 0.1823\n",
      "Iteration: 7, Objective: 0.1820\n",
      "Iteration: 8, Objective: 0.1815\n",
      "Iteration: 9, Objective: 0.1815\n",
      "Iteration: 10, Objective: 0.1814\n",
      "Iteration: 11, Objective: 0.1814\n",
      "Training accuracy: 0.8129632320883593\n",
      "Test accuracy: 0.8092850915431561\n",
      "Predict Y=1 if ANY of the following rules are satisfied, otherwise Y=0:\n",
      "['EDRECODE == 15 AND ACTLIM31 == 1', 'ARTHTYPE != -1 AND WLKLIM31 != 2 AND PCS42 <= 50.22 AND INSCOV15 != 3']\n"
     ]
    }
   ],
   "source": [
    "# Instantiate BRCG\n",
    "from aix360.algorithms.rbm import BooleanRuleCG\n",
    "br = BooleanRuleCG(lambda0=1e-4, lambda1=1e-4)\n",
    "# Train, print, and evaluate model\n",
    "br.fit(dfTrain, yTrain)\n",
    "print('Training accuracy:', accuracy_score(yTrain, br.predict(dfTrain)))\n",
    "print('Test accuracy:', accuracy_score(yTest, br.predict(dfTest)))\n",
    "print('Predict Y=1 if ANY of the following rules are satisfied, otherwise Y=0:')\n",
    "print(br.explain()['rules'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, the test accuracy is lower than that of GBCT. The advantage of the BRCG model is its simplicity: It identifies two readily understood subgroups of individuals (not mutually exclusive) predicted to have high cost. The first subgroup consists of individuals with bachelor's degrees (EDRECODE == 15) who have activity limitations affecting work, housework, or school (ACTLIM31 == 1). The second subgroup has limitations in physical functioning (walking, WLKLIM31 != 2), lower physical health status (PCS42 <= 50.22), and some health insurance coverage (INSCOV15 != 3). The first condition, ARTHTYPE != -1, indicates that the question about arthritis type is not inapplicable, which presumably means that the individual does have arthritis and is also 18 years of age or older. One might infer that the common thread between the two subgroups is some sort of physical limitation or poor health coupled with a proxy for higher income (bachelor's degree) or ability to pay (insurance coverage)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a name=\"conclusion\"></a>\n",
    "## 5. Conclusion\n",
    "This tutorial has shown that the directly interpretable supervised learning algorithms included in AIX360, Generalized Linear Rule Models (GLRM) and Boolean Rule Column Generation (BRCG), are capable of producing accurate and interpretable models for predicting healthcare expenditure. In the case of GLRM (specifically the Linear Rule Regression version), the accuracy is higher than an uninterpretable gradient boosting benchmark while retaining the form of a linear model, the interpretation of which is enhanced by plotting the generalized additive model (GAM) part of the overall model. In the case of BRCG, the accuracy is lower but the model consists of just two rules that are readily understood. We believe that such directly interpretable predictive models (not reliant on post-hoc explanations of individual cases) can be particularly helpful in human-machine collaborations with domain experts and downstream decision-makers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}