Researchers frequently use Mokken scale analysis (MSA), which is a nonparametric approach to item response theory, when they have relatively small samples of examinees. Researchers have provided some guidance regarding the minimum sample size for applications of MSA under various conditions. However, these studies have not focused on item-level…

Large-scale assessments often use a computer adaptive test (CAT) for selection of items and for scoring respondents. Such tests often assume a parametric form for the relationship between item responses and the underlying construct. Although semi- and nonparametric response functions could be used, there is scant research on their performance in a…

The questionnaire method has always been an important research method in psychology. The increasing prevalence of multidimensional trait measures in psychological research has led researchers to use longer questionnaires. However, questionnaires that are too long will inevitably reduce the quality of the completed questionnaires and the efficiency…

This study aimed to assess the accuracy of the empirical item characteristic curve (EICC) preequating method given the presence of test speededness. The simulation design of this study considered the proportion of speededness, speededness point, speededness rate, proportion of missing on speeded items, sample size, and test length. After crossing…

Molenaar extended Mokken's original probabilistic-nonparametric scaling models for use with polytomous data. These polytomous extensions of Mokken's original scaling procedure have facilitated the use of Mokken scale analysis as an approach to exploring fundamental measurement properties across a variety of domains in which polytomous ratings are…

Mokken scale analysis is a probabilistic nonparametric approach that offers statistical and graphical tools for evaluating the quality of social science measurement without placing potentially inappropriate restrictions on the structure of a data set. In particular, Mokken scaling provides a useful method for evaluating important measurement…

The multilevel latent class model (MLCM) is a multilevel extension of a latent class model (LCM) that is used to analyze nested structure data structure. The nonparametric version of an MLCM assumes a discrete latent variable at a higher-level nesting structure to account for the dependency among observations nested within a higher-level unit. In…

Standard approaches for estimating item response theory (IRT) model parameters generally work under the assumption that the latent trait being measured by a set of items follows the normal distribution. Estimation of IRT parameters in the presence of nonnormal latent traits has been shown to generate biased person and item parameter estimates. A…

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…

In recent studies, different methods were proposed to investigate invariant item ordering (IIO), but practical IIO research is an unexploited field in questionnaire construction and evaluation. In the present study, the authors explored the usefulness of different IIO methods to analyze personality scales and clinical scales. From the authors'…

This study combined the kernel smoothing procedure and a nonparametric differential item functioning statistic--Cochran's Z--to statistically test the difference between the kernel-smoothed item response functions for reference and focal groups. Simulation studies were conducted to investigate the Type I error and power of the proposed…

The distance between nonparametric and parametric item characteristic curves has been proposed as an index of goodness of fit in item response theory in the form of a root integrated squared error index. This article proposes to use the posterior distribution of the latent trait as the nonparametric model and compares the performance of an index…

A nonparametric tree classification procedure is used to detect differential item functioning for items that are dichotomously scored. Classification trees are shown to be an alternative procedure to detect differential item functioning other than the use of traditional Mantel-Haenszel and logistic regression analysis. A nonparametric…

The purpose of this study was to assess the model fit of a 2PL through comparison with the nonparametric item characteristic curve (ICC) estimation procedures. Results indicate that three nonparametric procedures implemented produced ICCs that are similar to that of the 2PL for items simulated to fit the 2PL. However for misfitting items,…

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…