🤖 AI Summary
本文提出了一种基于采样-重要性重采样的随机EM算法(SIR-StEM)，用于解决非线性预测变量回归模型中缺失数据的问题，该方法适用于任意形式的非线性变换。
📝 Abstract
Estimating regression models with nonlinear predictor transformations is challenging when data are missing, because nonlinearity typically renders the conditional distribution of the missing values intractable. Previous methods require specific nonlinear forms, such as polynomials or interactions, or rely on approximations that can induce bias. We propose a stochastic EM algorithm that uses sampling-importance resampling (SIR-StEM) to handle missing data under arbitrary nonlinear transformations of predictors, either substantively motivated or incidental, such as spline basis expansions. Unlike approaches that require linearity or closed-form conditionals, SIR-StEM only requires evaluating the complete-data likelihood up to proportionality, making it applicable across a broad class of nonlinear regression models. We construct an algorithm that makes use of missing data pattern information for computational efficiency, and establish asymptotic normality of the estimator. We demonstrate the method in two simulation studies, one with parametric nonlinear transformations and another with a spline basis expansion based on real behavioral measures. Results show that SIR-StEM yields low bias and near-nominal confidence interval coverage, outperforming other common approaches. We conclude with limitations and directions for future research.