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…

Stochastic ordering properties are investigated for a broad class of item response theory (IRT) models for which the monotone likelihood ratio does not hold. A taxonomy is given for nonparametric and parametric models for polytomous models based on the hierarchical relationship between the models. (SLD)

The absence of the invariant item ordering (IIO) property in two nonparametric polytomous item response theory (IRT) models is discussed, and two nonparametric models are discussed that imply an IIO. Only two parametric polytomous IRT models are found to imply an IIO. A method is proposed to investigate whether an IIO is implied with empirical…

Studied the use of the person response function (PRF) for identifying nonfitting item score patterns. Proposed a person-fit method reformulated in a nonparametric item response theory (IRT) context. Conducted a simulation study to compare the use of the PRF with a person-fit statistic, resulting in the conclusion that the PRF can be used as a…

Introduces this special issue on nonparametric item response theory and discusses its use in psychological and sociological research. Outlines each of the eight articles in the issue. (SLD)

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…

Methods for detecting item score patterns that are unlikely (aberrant) given that a parametric item response theory (IRT) model gives an adequate description of the data or given the responses of the other persons in the group are discussed. The emphasis here is on the latter group of statistics. These statistics can be applied when a…

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…

Methods for detecting item score patterns that are unlikely, given that a parametric item response theory model gives an adequate description of the data or given the responses of other persons in the group, are discussed. The use of person-fit statistics in empirical data analysis is briefly discussed. (SLD)

Reviews developments in nonparametric item-response theory (NIRT), from its historic origins in item-response theory (IRT) and scale analysis to new theoretical results for practical test construction. Discusses theoretical results from NIRT often relevant to IRT. Contains 134 references. (SLD)

A method is proposed for investigating the intersection of item response functions in the nonparametric item-response-theory model of R. J. Mokken (1971). Results from a Monte Carlo study support the proposed use of the transposed data matrix H(sup T) as an extension to Mokken's approach. (SLD)

Person-fit statistics test whether the likelihood of a respondent's complete vector of item scores on a test is low given the hypothesized item response theory model. This binary information may be insufficient for diagnosing the cause of a misfitting item-score vector. The authors propose a comprehensive methodology for person-fit analysis in the…

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…