A multilevel thresholds of change model for analysis of stages of change data

In this article we describe a model for multilevel ordinal response data that allows for non-proportional odds for a subset of explanatory variables. As applied to stages of change data, which are commonly encountered in health promotion research, this model is termed the multilevel thresholds of change model since it focuses on modeling the K-1 thresholds that delineate membership in the K ordered stages. Explanatory variables can have the same effect across thresholds (i.e., proportional odds) or varying effects across thresholds (i.e., non-proportional odds). In addition to the explanatory variables of the model, random effects are included to account for the multilevel structure of the data (e.g., repeated observations within subjects, or subjects observed within clusters). A maximum marginal likelihood (MML) solution is described using Gauss-Hermite quadrature to numerically integrate over the distribution of normally-distributed random effects. Data from a skin cancer prevention study, in which subjects were repeatedly measured across time and clustered within schools, are used to illustrate the multilevel thresholds of change model.