This study investigates polytomous item explanatory item response theory models under the multivariate generalized linear mixed modeling framework, using the linear logistic test model approach. Building on the original ideas of the many-facet Rasch model and the linear partial credit model, a polytomous Rasch model is extended to the item…

This paper presents the Latent Class Level-PCM as a method for identifying and interpreting latent classes of respondents according to empirically estimated performance levels. The model, which combines elements from latent class models and reparameterized partial credit models for polytomous data, can simultaneously (a) identify empirical…

The Rasch rating (or partial credit) model is a widely applied item response model that is used to model ordinal observed variables that are assumed to collectively reflect a common latent variable. In the application of the model there is considerable controversy surrounding the assessment of fit. This controversy is most notable when the set of…

In teaching, representations are used as ways to illustrate the concepts underlying a specific topic. For example, use symbols (e.g., 1?+?2?=?3) to express the concept of addition. To compare students' abilities to interpret different representations in mathematics, the symbolic representation (SR) test and the pictorial representation (PR) test…

The relationship between differential item functioning (DIF) and item difficulty on the SAT is such that more difficult items tended to exhibit DIF in favor of the focal group (usually minority groups). These results were reported by Kulick and Hu, and Freedle and have been enthusiastically discussed by more recent literature. Examining the…

Current college admissions tests inadequately predict college success (Geiser & Studley, 2002) and provide insufficient information for students and teachers regarding college readiness at earlier stages of students' academic careers (Olson, 2006). This article reports on the creation and validation of a more informative test rooted in college…

This study investigated the relationship between students' actual performance (accuracy) and their subjective judgments of accuracy (confidence) on selected English language proficiency tests. The unidimensional and multidimensional IRT Rasch approaches were used to model the discrepancy between confidence and accuracy at the item and test level…

The application of a class of Rasch models is discussed for situations in which test items are grouped into subsets and the common attributes of items within the subsets bring into question the usual assumption of conditional independence. Models are expressed as particular cases of the random coefficients multinomial logit model. (SLD)

In this article we describe the development, analysis, and interpretation of a novel item format we call Ordered Multiple-Choice (OMC). A unique feature of OMC items is that they are linked to a model of student cognitive development for the construct being measured. Each of the possible answer choices in an OMC item is linked to developmental…

A method for detecting and interpreting disturbances of the local-independence assumption among items that share common stimulus material or other features is presented. Dichotomous and polytomous Rasch models are used to analyze structure of the learning outcome superitems. (SLD)

This study presents a procedure for detecting differential item functioning (DIF) for dichotomous and polytomous items in testlet-based tests, whereby DIF is taken into account by adding DIF parameters into the Rasch testlet model. Simulations were conducted to assess recovery of the DIF and other parameters. Two independent variables, test type…

Standard item response theory (IRT) models posit latent variables to account for regularities in students' performance 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…

A parallel design, in which items across different scales within an instrument share common stimuli and subjects respond to the common stimulus for each scale, is sometimes used in questionnaires or inventories. Because the items across scales share the same stimuli, the assumption of local item independence may not hold, thereby violating the…

A strategy is described for dealing with measurement situations in which certain categories of responses are null, that is, persons do not respond in certain categories to certain items. The method is described for the partial credit model while maintaining the integrity of the original response framework. (SLD)