[Paper Review] Covariance pattern mixture models for multivariate longitudinal data with application to the Health and Retirement Study

Laura Anderlucci, Cinzia Viroli|arXiv (Cornell University)|Jan 7, 2014

Bayesian Methods and Mixture Models3 citations

TL;DR

This paper introduces the Covariance Pattern Mixture Model (CPMM), a flexible multivariate longitudinal model that captures unobserved heterogeneity, within-subject correlations, and response associations without requiring local independence. Applied to the Health and Retirement Study, CPMM identifies three distinct cognitive functioning clusters linked to socio-economic factors, revealing group-specific response patterns and regressor effects.

ABSTRACT

We propose a novel approach for modeling multivariate longitudinal data in the presence of unobserved heterogeneity for the analysis of the Health and Retirement Study (HRS) data. Our proposal can be cast within the framework of linear mixed model with discrete individual random intercepts, but differently from the standard formulation, the proposed Covariance Pattern Mixture Model (CPMM) does not require the usual local independence assumption; therefore, it is able to simultaneously model the heterogeneity, the association among the responses and the temporal dependence structure. We focus on the investigation of temporal patterns related to the cognitive functioning in retired American respondents, aiming to understand whether its behaviour can be affected by some individual socio-economical characteristics and whether it is possible to identify some homogenous groups of respondents that share a similar cognitive profile, so that opportune policy interventions can be addressed. Results identify three homogenous clusters of individuals with specific cognitive functioning, consistent with the class conditional distribution of the covariates. The flexibility of CPMM allows for a different contribution of each regressor on the responses according to group membership. In so doing, the identified groups receive a global and punctual phenomenal characterization.

Motivation & Objective

• To model multivariate longitudinal data with unobserved heterogeneity, temporal dependence, and response associations without relying on the local independence assumption.
• To investigate how socio-economic characteristics influence cognitive functioning trajectories in retired Americans.
• To identify homogeneous subgroups of respondents with distinct cognitive profiles for targeted policy interventions.
• To allow regressor effects to vary across identified clusters, enabling nuanced interpretation of individual-level predictors.

Proposed method

• Proposes a linear mixed model framework with discrete individual random intercepts to represent unobserved heterogeneity.
• Introduces the Covariance Pattern Mixture Model (CPMM) that explicitly models the covariance structure across responses and time without assuming local independence.
• Uses a finite mixture of multivariate normal distributions to represent group-specific conditional response distributions.
• Estimates model parameters via maximum likelihood with an EM algorithm, allowing for group-specific regression coefficients.
• Incorporates covariates to predict group membership and model conditional response means within each cluster.
• Models temporal dependence through a structured covariance matrix that varies by latent group.

Experimental results

Research questions

• RQ1 What latent subgroups of retirees exhibit distinct cognitive functioning trajectories over time?
• RQ2 How do socio-economic characteristics influence cognitive functioning within each identified subgroup?
• RQ3 To what extent does the association among multiple cognitive responses vary across latent groups?
• RQ4 Can the temporal dependence structure of cognitive responses be better captured by allowing group-specific covariance patterns?

Key findings

• The CPMM identified three distinct clusters of retirees with homogeneous cognitive functioning profiles, each associated with specific socio-economic covariate distributions.
• Cognitive functioning trajectories varied significantly across the three clusters, indicating heterogeneous aging patterns.
• The contribution of each regressor to cognitive outcomes differed across clusters, demonstrating group-specific effects.
• The model's flexibility allowed for accurate representation of within-subject correlation and cross-response associations without imposing restrictive local independence assumptions.