Variable selection in Poisson HGLMs using h-likelihoood

Abstract

Selecting relevant variables for a statistical model is very important in regression analysis. Recently, variable selection methods using a penalized likelihood have been widely studied in various regression models. The main advantage of these methods is that they select important variables and estimate the regression coefficients of the covariates, simultaneously. In this paper, we propose a simple procedure based on a penalized h-likelihood (HL) for variable selection in Poisson hierarchical generalized linear models (HGLMs) for correlated count data. For this we consider three penalty functions (LASSO, SCAD and HL), and derive the corresponding variable-selection procedures. The proposed method is illustrated using a practical example.

ML estimation using Poisson HGLM approach in semi-parametric frailty models

“…For this purpose, we propose a Laplace approximation (LA) method based on h-likelihood (Lee and Nelder, 1996). Here, the h-likelihood obviates the integration itself and gives a statistically efficient procedure for various random-effect models such as HGLMs (Lee et al, 2006;Ha and Noh, 2013;Ha and Cho, 2015). In Poisson HGLMs and frailty models, the use of gamma random-effect distribution gives an explicit marginal likelihood, but other distributions such as normal random-effect distribution do not.…”