A latent class model for repeated measurements experiments

Standard models for the analysis of repeated measurements assume a common response profile for all experimental units within a treatment group. However, in many applications this under-represents the nature of the response. There may be several distinct modes of response within a group (for example, responders versus non-responders to a given treatment), or there may be a set of distinct response profiles which are common to all the treatment groups. In these situations the effect of treatment can be characterized both by the shape of the fitted profiles and by estimating the proportion of cases who exhibit each particular response profile. This paper describes how such experiments may be analysed through the introduction of a latent variable into the standard model. Maximum likelihood estimation is straight-forward using the EM algorithm. Model choice requires some care, but good-fitting models can be identified via inspection of residuals and the use of empirical semi-variogram plots. Once the number of distinct profiles has been determined, treatment effects can be investigated using likelihood-ratio statistics. The approach is illustrated with a re-analysis of a dataset first described by Grizzle and Allen.