H-likelihood approach for variable selection in gamma frailty models

Abstract

Recently, variable selection methods using penalized likelihood with a shrink penalty function have been widely studied in various statistical models including generalized linear models and survival models. In particular, they select important variables and estimate coefficients of covariates simultaneously. In this paper, we develop a penalized h-likelihood method for variable selection in gamma frailty models. For this we use the smoothly clipped absolute deviation (SCAD) penalty function, which satisfies a good property in variable selection. The proposed method is illustrated using simulation study and a practical data set.

Variable selection in Poisson HGLMs using h-likelihoood

“…For the distribution of random effects we use a normal distribution, which is useful for modeling of multi-component or correlated random effects (Ha et al, 2014). For the variable selection we use the hierarchical likelihood (h-likelihood; Lee and Nelder, 1996) as in Ha and Cho (2012) and Ha et al (2014). The h-likelihood avoids the need for the marginalization over the random-effect distribution and provides a statistically efficient procedure in various random-effect models such as HGLMs and frailty models (Rondeau et al, 2008;Ha et al, 2011), but the marginal likelihood often requires the computation of intractable integrals when eliminating the random effects, particularly for normally distributed random effects.…”

A visualizing method for investigating individual frailties using frailtyHL R-package

“…For the inference, the marginal likelihood often involves analytically intractable integrals, particularly when modelling multilevel or correlated frailties. However, the hierarchicallikelihood (h-likelihood; Nelder, 1996, 2001) obviates the need for intractable integration over the frailty terms (Ha et al, 2001Ha and Cho, 2012). It is also important to investigate the potential heterogeneity in event times among clusters (e.g.…”