Recent research reflects a growing awareness of the value of using structural equation models to analyze repeated measures data. However, such data, particularly in the presence of covariates, often lead to models that either fit the data poorly, are exceedingly general and hard to interpret, or are specified in a manner that is highly data dependent. This article introduces methods for developing parsimonious models for such data. The underlying technology uses reduced-rank representations of the variances, covariances and means of observed and latent variables. The value of this approach, which may be implemented using standard structural equation modeling software, is illustrated in an application study aimed at understanding heterogeneous consumer preferences. In this application, the parsimonious representations characterize systematic relationships among consumer demographics, attitudes and preferences that would otherwise be undetected. The result is a model that is parsimonious, illuminating, and fits the data well, while keeping data dependence to a minimum.