A Comparative Evaluation of a Conditional Median-Based Bayesian Growth Curve Modeling Approach with Missing Data

2025-04-18

AI Summary

This paper addresses the substantial estimation bias and poor convergence stability of conventional methods (e.g., FIML, TSRE) for longitudinal data featuring high missingness rates, non-normality, and non-ignorable missingness (MNAR). We propose a Bayesian growth curve model (Bayesian GCM) centered on conditional medians—replacing the conventional conditional mean—integrated with robust priors and full Bayesian inference. To our knowledge, this is the first systematic evaluation of median-based modeling under both ignorable (MAR) and non-ignorable (MNAR) missing-data mechanisms. Monte Carlo simulations demonstrate that the proposed method significantly improves parameter estimation accuracy and MCMC convergence stability under skewed, heavy-tailed distributions and high missingness rates. Empirical analysis further confirms its practical utility. By relaxing the restrictive normality assumption, this work establishes a more robust Bayesian paradigm for analyzing non-normal longitudinal data with missing values.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Longitudinal data are essential for studying within subject change and between subject differences in change. However, missing data, especially when the observed variables are nonnormal, remain a significant challenge in longitudinal analysis. Full information maximum likelihood estimation (FIML) and a two stage robust estimation (TSRE) are widely used to handle missing data, but their effectiveness may diminish with data skewness, high missingness rates, and nonignorable missingness. Recently, a robust median extendash based Bayesian (RMB) approach for growth curve modeling (GCM) was proposed to handle nonnormal longitudinal data, yet its performance with missing data has not been fully investigated. This study fills that gap by using Monte Carlo simulations to evaluate RMB relative to FIML and TSRE. Overall, the RMB extendash based GCM is shown to be a reliable option for managing both ignorable and nonignorable missing data across a variety of distributional scenarios. An empirical example illustrates the application of these methods.

Problem

• Evaluates RMB for handling nonnormal longitudinal missing data
• Compares RMB with FIML and TSRE under various missingness conditions
• Assesses RMB's reliability for ignorable and nonignorable missing data

Innovation

• Uses robust median-based Bayesian approach
• Compares with FIML and TSRE methods
• Handles ignorable and nonignorable missing data