Analysis from Adams, G.D., Leaf, R.T., Ballenger, J.C., Arnott, S.A., Mcdonough, C.J., 2018. Spatial variability in the growth of Sheepshead (Archosargus probatocephalus) in the Southeast US : Implications for assessment and management. Fish. Res. 206, 35–43. doi:10.1016/j.fishres.2018.04.023
We analyzed fishery-dependent and –independent length-at-age and weight-at-length data from Texas, Louisiana, Mississippi, Alabama, Florida, South Carolina, North Carolina, and Virginia to investigate the geographic variation in growth of Sheepshead. We constructed a three parameterizations of non-linear mixed-effects models for length-at-age (von Bertalanffy growth function: VBGF) and weight-at-length (WAL) data using a Bayesian framework in Stan that included sex, latitudinal, and regional effects.
Parameterization 1 is a fixed-effects model that assumes no small-scale spatial structure; parameterization 2 assumes small-scale spatial structure via normally distributed random effects with a mean of zero and parameter-specific variance; and parameterization 3 assumes small scale-spatial structure via random effects assuming a mean zero normally distributed conditionally conditionally autoregressive (CAR) model. The CAR model allows neighboring regions to be more informative of region-specific random effects by including spatial correlation parameters, weights matrix W where wi,j = 1 when regions i and j are neighbors. All random effects were parameterized using a non-centered approach to improve MCMC efficiency.