Longitudinal Confirmatory Factor Analysis for Polytomous Item Responses: Model Definition and Model Selection on the Basis of Stochastic Measurement Theory

Based on a distinction between four different models of longitudinal confirmatory factor analysis (LCFA) originally explained by Marsh and Grayson (1994) an analogous class of LCFA models for polytomous variables is described. Then, the probabilistic foundations of LCFA models for polytomous variables are explained and it is shown that only two models of the initially considered four LCFA models can be defined as stochastic measurement models on the basis of an explicated random experiment. For these two models the representation, uniqueness, and meaningfulness theorems are proven and it is shown how some implications of these models can be tested. The two stochastic measurement LCFA models are illustrated by a short empirical application. Finally, the results are discussed with respect to the role of stochastic measurement theory for the definition and selection of different LCFA models.