Partial Replacement Imputation Estimation Method for Complex Missing Covariates in Additive Partially Linear Models

TL;DR

This paper introduces PRIME, a new imputation method for handling complex missing data in additive partially linear models, and demonstrates its superior performance through simulations and real data analysis.

Contribution

The paper proposes PRIME, a novel imputation method for complex missing data in semiparametric models, and extends it with model averaging (PRIME-MA) for unknown model structures.

Findings

PRIME outperforms existing methods in simulations across various scenarios.

PRIME-MA provides satisfactory prediction performance with unknown model structure.

The method shows improved results on the Pima Indians Diabetes dataset.

Abstract

Missing data is a common problem in clinical data collection, which causes difficulty in the statistical analysis of such data. In this article, we consider the problem under a framework of a semiparametric partially linear model when observations are subject to missingness with complex patterns. If the correct model structure of the additive partially linear model is available, we propose to use a new imputation method called Partial Replacement IMputation Estimation (PRIME), which can overcome problems caused by incomplete data in the partially linear model. Also, we use PRIME in conjunction with model averaging (PRIME-MA) to tackle the problem of unknown model structure in the partially linear model. In simulation studies, we use various error distributions, sample sizes, missing data rates, covariate correlations, and noise levels, and PRIME outperforms other methods in almost all cases. With an unknown correct model structure, PRIME-MA has satisfactory performance in terms of prediction, while slightly worse than PRIME. Moreover, we conduct a study of influential factors in Pima Indians Diabetes data, which shows that our method performs better than the other models.