Regularization in dynamic random‐intercepts models for analysis of longitudinal data
研究了纵向数据动态随机截距模型中同时进行变量选择和估计的问题，发现忽略相关性的条件似然方法会导致有偏估计，而联合建模初始响应和后续观测可实现一致性和Oracle性质。
Abstract This paper addresses the problem of simultaneous variable selection and estimation in the random‐intercepts model with the first‐order lag response. This type of model is commonly used for analyzing longitudinal data obtained through repeated measurements on individuals over time. This model uses random effects to cover the intra‐class correlation, and the first lagged response to address the serial correlation, which are two common sources of dependency in longitudinal data. We demonstrate that the conditional likelihood approach by ignoring correlation among random effects and initial responses can lead to biased regularized estimates. Furthermore, we demonstrate that joint modeling of initial responses and subsequent observations in the structure of dynamic random‐intercepts models leads to both consistency and Oracle properties of regularized estimators. We present theoretical results in both low‐ and high‐dimensional settings and evaluate regularized estimators' performances by conducting simulation studies and analyzing a real dataset. Supporting information is available online.