MARGINAL MAXIMUM LIKELIHOOD ESTIMATION FOR A PSYCHOMETRIC MODEL OF DISCONTINUOUS DEVELOPMENT

Abstract

ABSTRACTStandard item response theory (IRT) models posit latent variables to account for regularities in students' performances on test items. They can accommodate learning only if the expected changes in performance are smooth and, in an appropriate metric, uniform over items. Wilson's “Saltus” model extends the ideas of IRT to development that occurs in stages, where expected changes can be discontinuous, show different patterns for different types of items, and even exhibit reversals in probabilities of success on certain tasks. Examples include Piagetian stages of psychological development and Siegler's rule‐based learning. This paper derives marginal maximum likelihood (MML) estimation ..