We discuss analysis of 5-grade Likert type data in the two-sample case. Analysis using two-sample "t" tests, nonparametric Wilcoxon tests, and ordinal regression methods, are compared using simulated data based on an ordinal regression paradigm. One thousand pairs of samples of size "n"=10 and "n"=30 were generated,…

This study analysed polytomous items' psychometric properties according to nonparametric item response theory (NIRT) models. Thus, simulated datasets--three different test lengths (10, 20 and 30 items), three sample distributions (normal, right and left skewed) and three samples sizes (100, 250 and 500)--were generated by conducting 20…

Structural equation modeling (SEM) has become widespread in educational and psychological research. Its flexibility in addressing complex theoretical models and the proper treatment of measurement error has made it the model of choice for many researchers in the social sciences. Nevertheless, the model imposes some daunting assumptions and…

As item response theory has been more widely applied, investigating the fit of a parametric model becomes an important part of the measurement process. There is a lack of promising solutions to the detection of model misfit in IRT. Douglas and Cohen introduced a general nonparametric approach, RISE (Root Integrated Squared Error), for detecting…

An automated item selection procedure in Mokken scale analysis partitions a set of items into one or more Mokken scales, if the data allow. Two algorithms are available that pursue the same goal of selecting Mokken scales of maximum length: Mokken's original automated item selection procedure (AISP) and a genetic algorithm (GA). Minimum…

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…

Investigating the fit of a parametric model is an important part of the measurement process when implementing item response theory (IRT), but research examining it is limited. A general nonparametric approach for detecting model misfit, introduced by J. Douglas and A. S. Cohen (2001), has exhibited promising results for the two-parameter logistic…

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…

The development of the DETECT procedure marked an important advancement in nonparametric dimensionality analysis. DETECT is the first nonparametric technique to estimate the number of dimensions in a data set, estimate an effect size for multidimensionality, and identify which dimension is predominantly measured by each item. The efficacy of…