Feedback Models for Discrete and Continuous Time Series

In public health research, it is common to follow a cohort of subjects over time, observing a vector of health indicators and a set of covariates at each of many visits. An objective of analysis is to characterize the inter-dependencies, in particular, the feedback of one response upon another while accounting for the covariates. With Gaussian responses, multivariate autoregressive models that incorporate feedback are commonly used. This paper discusses analogous Markov models for multivariate discrete and mixed discrete/continuous response variables. One special case is an extension of seemingly unrelated regressions to discrete and continuous outcomes. A generalized estimating equations approach that requires correct specification of only conditional means and variances is discussed. The methods are illustrated by a study of infectious diseases and vitamin A deficiency in Indonesian children.