Latent growth curve modeling for longitudinal ordinal responses with applications

In this paper, we consider the use of the latent growth curve model to analyze longitudinal ordinal categorical data that involve measurements at different time points. By operating on the assumption that the ordinal response variables at different time points are related to normally distributed underlying continuous variables, and by further modeling these underlying continuous variables for different time points with the latent growth curve model, we achieve a comprehensive and flexible model with straightforward interpretations and a variety of applications. We discuss the applications of the model in treatment comparisons and in the analysis of the covariate effects. Moreover, one prominent advantage of the model lies in its ability to address possible differences in the initial conditions for the subjects who take part in different treatments. Making use of this property, we also develop a new method to test the equivalence of two treatments that involve ordinal responses obtained at two different time points. A real data set is used to illustrate the applicability and practicality of the proposed approach.