A Latent-Change Scaling Model for Longitudinal Multiple Choice Data

A latent-change scaling model for the analysis of repeated-measures multiple-choice data is presented. The model extends previous work by combining latent class analysis and low dimensional scaling techniques in a longitudinal framework where subjects may change their preferences for the response categories over time. The latent structural component of the model characterizes both the cross-sectional heterogeneity of the population and an underlying change process over time; the measurement component of the model uses a scaling procedure to produce a joint representation of latent classes and response categories in a low dimensional space that represents individual differences in the utilities of the categories. An analysis of a national panel data set is used to illustrate both aspects of the model. A hypothetical example illustrates additional features of the model that can be tested when multiple indicators are collected at each time point.