State mastery learning: Dynamic models for longitudinal data

Macready & Dayton (1980) showed that state masterymodels are handled optimally within the generallatent class framework for data from a single timepoint. An extension of this idea is presented here forlongitudinal data obtained from repeated measurementsacross time. The static approach is extendedusing multiple-indicator Markov chain models. Theapproach presented here emphasizes the dynamic aspectsof the process of change, such as growth, decay,and stability. The general approach is presented, andmodels with purely categorical and ordered categoricalstates and several extensions of these models are discussed.Problems of estimation, identification, assessmentof model fit, and hypothesis testing associatedwith these models also are discussed. The applicabilityof these models is demonstrated using data from a longitudinalstudy on solving arithmetic word problems.The advantages and disadvantages of using the approachpresented here are discussed. Index terms:arithmetic word problems, dynamic latent class models,latent class models, longitudinal categorical data,Markov models, state mastery models.