Shrinkage Estimators for Latent Variable Models in the Presence of Measurement Model Misspecification

• Activity Number: 48
• Type: Invited
• Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Brisa N Sánchez*+
• Companies: University of Michigan School of Public Health
• Keywords: shrinkage ; instrumental variables ; structural

Abstract

Latent variable models are increasingly being used in health studies as a way to summarize hard to measure predictor or outcome variables. Classic assumptions of these models include conditional independence of observed items given the latent constructs, and, in the case of longitudinal latent variables, time invariance of the measurement model. Although these assumptions can be relaxed when fitting the model, choosing which re-specification is better is not always straightforward and repeated modifications of the model can result in inflated Type I error. We examine the biases of MLE and instrumental variable estimators. Given that MLE estimators are necessarily more efficient when the model is correct, we propose and evaluate shrinkage estimators that data-adaptively choose between an efficient (possibly biased) estimator and an unbiased (less efficient) estimator. We were motivated by a study of prenatal lead exposure and mental development, where assumptions of the measurement model for a time-changing longitudinal exposure have appreciable impact on the inferences about the health effects of lead exposure.