The Impact of Covariance Misspecification in Multivariate Gaussian Mixtures on Estimation and Inference: An Application to Trajectory Modeling

• Activity Number: 475
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Brianna Heggeseth*+ and Nicholas Jewell
• Companies: University of California at Berkeley and University of California at Berkeley
• Keywords: covariance ; model misspecification ; mixture models ; Kullback-Leibler divergence

Abstract

Multivariate Gaussian mixtures are a class of models that provide a flexible parametric approach for the representation of heterogeneous multivariate outcomes. When the outcome is a trajectory vector of observations taken over time, there is often inherent dependence between measurements. However, one of the most used covariance assumption is conditional independence, which assumes that given the mixture component label, the outcomes for an observation unit are independent of each other. In this paper, we study, through asymptotic bias calculations and simulation, the impact of covariance misspecification in multivariate Gaussian mixtures. Although maximum likelihood estimators of parameters are not consistent under misspecification, they have little asymptotic bias when mixture components are well-separated even when outcomes are wrongly assumed to be conditionally independent. We also present a robust standard error estimator and show that it outperforms conventional estimators in simulations when the model is misspecified. Body mass index data from a national longitudinal study is used to demonstrate the effects of misspecification on potential inferences made in practice.