Explanatory item response models (EIRMs) have been applied to investigate the effects of person covariates, item covariates, and their interactions in the fields of reading education and psycholinguistics. In practice, it is often assumed that the relationships between the covariates and the logit transformation of item response probability are…

This study proposes a structured constructs model (SCM) to examine measurement in the context of a multidimensional learning progression (LP). The LP is assumed to have features that go beyond a typical multidimentional IRT model, in that there are hypothesized to be certain cross-dimensional linkages that correspond to requirements between the…

Analyzing examinees' responses using cognitive diagnostic models (CDMs) has the advantage of providing diagnostic information. To ensure the validity of the results from these models, differential item functioning (DIF) in CDMs needs to be investigated. In this article, the Wald test is proposed to examine DIF in the context of CDMs. This study…

Latent growth curve modeling provides a powerful and flexible tool for researchers to study individual differences in change as well as the correlates and predictors of change. Recent developments in estimation and hypothesis testing procedures are largely based on confirmatory structural equation approaches. In this article, an alternative…

The validity of the equipercentile hypothesis of the Title I Evaluation and Reporting System norm-referenced evaluation model was examined using 3,224 seventh- and ninth-grade students. Findings from confidence interval procedures contradicted the equipercentile hypothesis. There was a pattern of large gains for students not receiving any special…

The use of restricted item response models to test hypotheses regarding item difficulty ordering and slope uniformity was demonstrated in a study in which 597 algebra students were asked to solve word problems reflecting various types of cognitive processing. Benefits and limitations of the procedures are discussed. (SLD)