State mastery learning: Dynamic models for longitudinal data

Abstract

Macready & Dayton (1980) showed that state mastery models are handled optimally within the general latent class framework for data from a single time point. An extension of this idea is presented here for longitudinal data obtained from repeated measurements across time. The static approach is extended using multiple-indicator Markov chain models. The approach presented here emphasizes the dynamic aspects of the process of change, such as growth, decay, and stability. The general approach is presented, and models with purely categorical and ordered categorical states and several extensions of these models are discussed. Problems of estimation, identification, assessment of model fit, and hypothesis testing associated with these models also are discussed. The applicability of these models is demonstrated using data from a longitudinal study on solving arithmetic word problems. The advantages and disadvantages of using the approach presented here are discussed. Index terms: arithmetic word problems, dynamic latent class models, latent class models, longitudinal categorical data, Markov models, state mastery models.