Xu Ronghui, Vaida Florin, Harrington David P
Stat Sin. 2009 Apr;19(2):819-842.
We consider selection of nested and non-nested semiparametric models. Using profile likelihood we can define both a likelihood ratio statistic and an Akaike information for models with nuisance parameters. Asymptotic quadratic expansion of the log profile likelihood allows derivation of the asymptotic null distribution of the likelihood ratio statistic including the boundary cases, as well as unbiased estimation of the Akaike information by an Akaike information criterion. Our work was motivated by the proportional hazards mixed effects model (PHMM), which incorporates general random effects of arbitrary covariates and includes the frailty model as a special case. The asymptotic properties of its parameter estimate has recently been established, which enables the quadratic expansion of the log profile likelihood. For computation of the (profile) likelihood under PHMM we apply three algorithms: Laplace approximation, reciprocal importance sampling, and bridge sampling. We compare the three algorithms under different data structures, and apply the methods to a multi-center lung cancer clinical trial.
我们考虑嵌套和非嵌套半参数模型的选择。利用轮廓似然，我们可以为带有干扰参数的模型定义似然比统计量和赤池信息准则。对数轮廓似然的渐近二次展开允许推导似然比统计量的渐近零分布，包括边界情况，以及通过赤池信息准则对赤池信息进行无偏估计。我们的工作受到比例风险混合效应模型（PHMM）的推动，该模型纳入了任意协变量的一般随机效应，并将脆弱模型作为一个特殊情况包含在内。最近已经建立了其参数估计的渐近性质，这使得对数轮廓似然的二次展开成为可能。为了计算PHMM下的（轮廓）似然，我们应用三种算法：拉普拉斯近似、倒数重要性抽样和桥抽样。我们在不同的数据结构下比较这三种算法，并将这些方法应用于一项多中心肺癌临床试验。
