Squeezing interval change from ordinal panel data: latent growth curves with ordinal outcomes

A didactic on latent growth curve modeling for ordinal outcomes is presented. The conceptual aspects of modeling growth with ordinal variables and the notion of threshold invariance are illustrated graphically using a hypothetical example. The ordinal growth model is described in terms of 3 nested models: (a) multivariate normality of the underlying continuous latent variables (yt) and its relationship with the observed ordinal response pattern (Yt), (b) threshold invariance over time, and (c) growth model for the continuous latent variable on a common scale. Algebraic implications of the model restrictions are derived, and practical aspects of fitting ordinal growth models are discussed with the help of an empirical example and Mx script (M. C. Neale, S. M. Boker, G. Xie, & H. H. Maes, 1999). The necessary conditions for the identification of growth models with ordinal data and the methodological implications of the model of threshold invariance are discussed.