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 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.

基于惩罚似然的变量选择方法已在各类统计模型中得到广泛研究。然而，在半参数脆弱模型（semiparametric frailty models）中，这类方法的研究相对较少，原因在于其边际似然函数包含解析上难以求解的积分，尤其是在构建多组分或相关脆弱性模型时。本文针对一类通用的半参数脆弱模型，提出了一种基于惩罚h似然（penalized h-likelihood, HL）的简洁统一的固定效应变量选择流程，该模型中的随机效应可具备共享、嵌套或相关结构。本文的变量选择流程共考虑了三类惩罚函数：最小绝对收缩和选择算子（least absolute shrinkage and selection operator, LASSO）、平滑截断绝对偏差（smoothly clipped absolute deviation, SCAD）以及HL惩罚。研究表明，仅需对现有的HL估计方法进行小幅修改，即可便捷地实现所提方法。仿真实验结果显示，采用SCAD或HL惩罚的变量选择流程性能优异。本文还通过三个实际数据集验证了所提新方法的实用价值。本文的补充材料可在线获取。