Most methods for fitting cognitive diagnosis models to educational test data and assigning examinees to proficiency classes require the Q-matrix that associates each item in a test with the cognitive skills (attributes) needed to answer it correctly. In most cases, the Q-matrix is not known but is constructed from the (fallible) judgments of…

To date, there have been no studies comparing parametric and nonparametric Item Characteristic Curve (ICC) estimation methods on the effectiveness of Person-Fit Statistics (PFS). The primary aim of this study was to determine if the use of ICCs estimated by nonparametric methods would increase the accuracy of item response theory-based PFS for…

This study compares the performance of three nonparametric item characteristic curve (ICC) estimation procedures: isotonic regression, smoothed isotonic regression, and kernel smoothing. Smoothed isotonic regression, employed along with an appropriate kernel function, provides better estimates and also satisfies the assumption of strict…

Describes relationships among 20 polytomous item response theory (IRT) models (parametric and nonparametric) and 8 measurement properties relevant to polytomous IRT. Provides three tables to assist in the choice of an appropriate model and demonstrates the use of the models in test construction. (SLD)

Presents a general class of ordinal logit models that specifies equality and inequality constraints on sums of conditional response probabilities. Uses maximum likelihood to estimate these models, making their assumptions testable with likelihood-ratio statistics. Illustrates the proposed models with an example using reported adult crying…

Discusses usability and interpretation issues for single-strategy cognitive assessment models that posit a stochastic, conjunctive relationship between a set of cognitive attributes to be assessed and performance on particular items/tasks of the assessment. Also discusses stochastic ordering and monotonicity properties that enhance the…

Developed models to investigate the fit of parametric item response models by comparing them to models fitted under nonparametric assumptions. Illustrated these techniques through simulation studies and real-data examples. Discusses the identifiability and estimation consistency of item response theory models. (SLD)

Discusses relationships between a mathematical measurement model and its real-world applications. Makes a distinction between large-scale data matrices commonly found in educational measurement and smaller matrices found in attitude and personality measurement. Also evaluates nonparametric methods for estimating item response functions and…