Latent variable regression for multiple discrete outcomes

Quantifying human health and functioning poses significant challenges in many research areas. Commonly in the social and behavioral sciences and increasingly in epidemiologic research, multiple indicators are utilized as responses in lieu of an obvious single measure for an outcome of interest. In this article we study the concomitant latent class model for analyzing such multivariate categorical outcome data. We develop practical theory for reducing and identifying such models. We detail parameter and standard error fitting that parallels standard latent class methodology, thus supplementing the approach proposed by Dayton and Macready. We propose and study diagnostic strategies, exemplifying our methods using physical disability data from an ongoing gerontologic study. Throughout, the focus of our work is on applications for which a primary goal is to study the association between health or functioning and covariates.