Differential item functioning (DIF) occurs when an item on a test, questionnaire, or interview has different measurement properties for one group of people versus another. One way to test items with ordinal response scales for DIF is likelihood ratio (LR) testing using item response theory (IRT), or IRT-LR-DIF. Despite the various advantages of…

DETECT is a nonparametric methodology to identify the dimensional structure underlying test data. The associated DETECT index, "D[subscript max]," denotes the degree of multidimensionality in data. Conditional covariances (CCOV) are the building blocks of this index. In specifying population CCOVs, the latent test composite [theta][subscript TT]…

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…

The examination of measurement invariance in polytomous items is complicated by the possibility that the magnitude and sign of lack of invariance may vary across the steps underlying the set of polytomous response options, a concept referred to as differential step functioning (DSF). This article describes three classes of nonparametric DSF effect…

This article considers two methods of estimating standard errors of equipercentile equating: the parametric bootstrap method and the nonparametric bootstrap method. Using a simulation study, these two methods are compared under three sample sizes (300, 1,000, and 3,000), for two test content areas (the Iowa Tests of Basic Skills Maps and Diagrams…

The nonparametric Mokken model of test data was compared with parametric models using simulated data through latent class analysis. It is demonstrated that latent class analysis provides a consistent comparison of item response models. (SLD)

Discusses the use of the nonparametric item response theory (IRT) Mokken models of monotone homogeneity and double monotonicity and the parametric Rasch and Verhelst models for the analysis of binary test data. Concludes that the simultaneous use of several IRT models for practical data analysis provides more insight into the structure of tests…

Questions are raised concerning differences between traditional metric multiple regression, which assumes all variables to be measured on interval scales, and nonmetric multiple regression. The ordinal model is generally superior in fitting derivation samples but the metric technique fits better than the nonmetric in cross-validation samples.…

In this article, an overview of nonparametric item response theory methods for determining the dimensionality of item response data is provided. Four methods were considered: MSP, DETECT, HCA/CCPROX, and DIMTEST. First, the methods were compared theoretically. Second, a simulation study was done to compare the effectiveness of MSP, DETECT, and…

A class of naive estimators of correlation was tested for robustness, accuracy, and efficiency against Pearson's r, Tukey's r, and Spearman's r. It was found that this class of estimators seems to be superior, being less affected by outliers, reasonably efficient, and frequently more easily calculated. (Author/CTM)