Variable Selection in General Frailty Models Using Penalized H-Likelihood

Abstract

Il Do HA, Jianxin PAN, Seungyoung OH, and Youngjo LEE Variable selection methods using a penalized likelihood have been widely studied in various statistical models. However, in semiparametric frailty models, these methods have been relatively less studied because the marginal likelihood function involves analytically intractable integrals, particularly when modeling multicomponent or correlated frailties. In this article, we propose a simple but unified procedure via a penalized h-likelihood (HL) for variable selection of fixed effects in a general class of semiparametric frailty models, in which random effects may be shared, nested, or correlated. We consider three penalty functions (least absolute shrinkage and selection operator [LASSO], smoothly clipped absolute deviation [SCAD], and HL) in our variable selection procedure. We show that the proposed method can be easily implemented via a slight modification to existing HL estimation approaches. Simulation studies also show that the procedure using the SCAD or HL penalty performs well. The usefulness of the new method is illustrated using three practical datasets too. Supplementary materials for the article are available online.

Variable selection in Poisson HGLMs using h-likelihoood

“…It is well known that shrinkage estimations would be preferred for prediction (Efron and Morris, 1975;. Ha et al (2014) have showed via simulations that the HL has higher probability of choosing the true model than the LASSO and SCAD methods without losing prediction accuracy.…”

“…Here they considered three penalty functions (LASSO, SCAD and HL). In this paper we propose a simple variable-selection procedure in Poisson HGLMs (Lee and Nelder, 1996) using Ha et al's (2014) method. Here, the Poisson HGLMs with random effects are very useful for analyzing correlated count data.…”

“…Very recently, Ha et al (2014) developed a penalized h-likelihood procedure for variable selection of fixed effects in semi-parametric frailty models. Here they considered three penalty functions (LASSO, SCAD and HL).…”

“…Here, the Poisson HGLMs with random effects are very useful for analyzing correlated count data. 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).…”

“…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.…”