Variable Selection in General Frailty Models using Penalized H-likelihood

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 modelling multi-component or correlated frailties. In this paper, 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 (LASSO, SCAD and HL) in our variable selection procedure. We show that the proposed method can be easily implemented via a slight modification to existing h-likelihood 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 data sets too. Supplemental materials for the paper are available online.