This article presents a new approach for analysis of multidimensional longitudinal data, motivated by studies using an item response battery to measure traits of an individual repeatedly over time. A general modeling framework is proposed that allows mixtures of count, categorical, and continuous response variables. Each response is related to age-specific latent traits through a generalized linear model that accommodates item-specific measurement errors. A transition model allows the latent traits at a given age to depend on observed predictors and on previous latent traits for that individual. Following a Bayesian approach to inference, a Markov chain Monte Carlo algorithm is proposed for posterior computation. The methods are applied to data from a neurotoxicity study of the pesticide methoxychlor, and evidence of a dose-dependent increase in motor activity is presented.