A Latent Class Bayesian Model for Multivariate Longitudinal Outcomes with Excess Zeros

2025-09-05

AI Summary

Multivariate longitudinal data—common in physiological and financial health research—frequently exhibit zero inflation, posing challenges for conventional modeling. To address this, we propose a Bayesian latent class mixture model that unifies Tobit, two-part, and zero-inflated Poisson (ZIP) structures, enabling flexible characterization of distinct zero-generating mechanisms. Innovatively, we couple an adaptive Lasso-type shrinkage prior to simultaneously perform variable selection and latent class identification, thereby capturing complex dependencies among multivariate trajectories and heterogeneous population substructures. Applied to the Health and Retirement Study (HRS) data, the model successfully identifies clinically meaningful subtypes exhibiting coupled physiological–financial decline. Simulation studies demonstrate that our approach significantly outperforms existing methods in both parameter estimation accuracy and latent class assignment precision.

Technology Category

Machine Learning: Multi-instance/Multi-view LearningReasoning under Uncertainty: Relational Probabilistic ModelsCognitive Modeling & Cognitive Systems: Adaptive Behavior

Application Category

User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systemsGraph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Latent class models have been successfully used to handle complex datasets in different disciplines. For longitudinal outcomes, we often get a trajectory of the outcome for each individual, and on that basis, we cluster them for a powerful statistical inference. Latent class models have been used to handle multivariate longitudinal outcomes coming from biology, health sciences, and economics. In this paper, we propose a Bayesian latent class model for multivariate outcomes with excess zeros. We consider a Tobit model for zero-inflated continuous outcomes such as out-of-pocket medical expenses (OOPME), a two-part model for financial debt, and a ZIP model for counting outcomes with excess zeros. We develop a Bayesian mixture model and employ an adaptive Lasso-type shrinkage method for variable selection. We analyze data from the Health and Retirement Study conducted by the University of Michigan and consider modeling four important outcomes measuring the physical and financial health of the aged individuals. Our analysis detects several latent clusters for different outcomes. Practical usefulness of the proposed model is validated through a simulation study.

Problem

• Modeling multivariate longitudinal outcomes with excess zeros
• Clustering individuals based on trajectory patterns
• Variable selection for zero-inflated financial and health data

Innovation

• Bayesian latent class model for multivariate outcomes
• Tobit and ZIP models for zero-inflated data
• Adaptive Lasso shrinkage for variable selection