Variable Selection in Joint Mean and Dispersion Models via Double Penalized Likelihood

In this paper, we propose to jointly model the conditional mean and variance components associated with the response in multilevel data. We set a generalized linear mixed model (GLMM) for the mean and a generalized linear model (GLM) for the variance components. The variable selection method of our choice is the smoothly clipped absolute deviation (SCAD) penalty, a penalized likelihood variable selection procedure, which shrinks the coefficients of redundant variables to 0 while simultaneously estimating the coefficients of the remaining important covariates. To assess the performance of the proposed procedures, we carry out real data analysis as well as extensive simulation studies, and compare to a similar process which excludes variable selection. We conclude that our method outperforms a simple joint mean-variance modelling approach, in both identifying the important components in the joint models and also producing more efficient estimation.