In this digital ITEMS module, we introduce the framework of nonparametric item response theory (IRT), in particular Mokken scaling, which can be used to evaluate fundamental measurement properties with less strict assumptions than parametric IRT models. We walk through the key distinction between parametric and nonparametric models, introduce the…

Some IRT models can be equivalently modeled in alternative frameworks such as logistic regression. Logistic regression can also model time-to-event data, which concerns the probability of an event occurring over time. Using the relation between time-to-event models and logistic regression and the relation between logistic regression and IRT, this…

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 (MSA) is a probabilistic-nonparametric approach to item response theory (IRT) that can be used to evaluate fundamental measurement properties with less strict assumptions than parametric IRT models. This instructional module provides an introduction to MSA as a probabilistic-nonparametric framework in which to explore…

Item response theory (IRT) has so many advantages than its precedent Classical Test Theory (CTT) such as non-changing item parameters, ability parameter estimations free from the items. However, in order to get these advantages, some assumptions should be met and they are; unidimensionality, normality and local independence. However, it is not…

Unmotivated test takers using rapid guessing in item responses can affect validity studies and teacher and institution performance evaluation negatively, making it critical to identify these test takers. The authors propose a new nonparametric method for finding response-time thresholds for flagging item responses that result from rapid-guessing…

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…

A framework is introduced for considering dimensionality assessment procedures for multidimensional item response models. The framework characterizes procedures in terms of their confirmatory or exploratory approach, parametric or nonparametric assumptions, and applicability to dichotomous, polytomous, and missing data. Popular and emerging…

Item response models typically assume that the item characteristic (step) curves follow a logistic or normal cumulative distribution function, which are strictly monotone functions of person test ability. Such assumptions can be overly-restrictive for real item response data. We propose a simple and more flexible Bayesian nonparametric IRT model…

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…

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…

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 contrast to dichotomous item response theory (IRT) models, most well-known polytomous IRT models do not imply stochastic ordering of the latent trait by the total test score (SOL). This has been thought to make the ordering of respondents on the latent trait using the total test score questionable and throws doubt on the justifiability of using…

In Ramsay curve item response theory (RC-IRT, Woods & Thissen, 2006) modeling, the shape of the latent trait distribution is estimated simultaneously with the item parameters. In its original implementation, RC-IRT is estimated via Bock and Aitkin's (1981) EM algorithm, which yields maximum marginal likelihood estimates. This method, however,…

A Bayesian nonparametric model is introduced for score equating. It is applicable to all major equating designs, and has advantages over previous equating models. Unlike the previous models, the Bayesian model accounts for positive dependence between distributions of scores from two tests. The Bayesian model and the previous equating models are…