Stan is a new Bayesian statistical software program that implements the powerful and efficient Hamiltonian Monte Carlo (HMC) algorithm. To date there is not a source that systematically provides Stan code for various item response theory (IRT) models. This article provides Stan code for three representative IRT models, including the…

General diagnostic models (GDMs) and Bayesian networks are mathematical frameworks that cover a wide variety of psychometric models. Both extend latent class models, and while GDMs also extend item response theory (IRT) models, Bayesian networks can be parameterized using discretized IRT. The purpose of this study is to examine similarities and…

A common theme of models of conceptual growth is to establish the hierarchical structures of abilities that can be interpreted along developmental lines. Integrating the literature on the development of mathematical concepts and skills in children, a comprehensive 6 level model for describing, explaining and predicting the development of key…

The ultimate goal of physics education research (PER) is to develop a theoretical framework to understand and improve the learning process. In this journey of discovery, assessment serves as our headlamp and alpenstock. It sometimes detects signals in student mental structures, and sometimes presents the difference between expert understanding and…

Test data generated according to two different multidimensional item response theory (IRT) models were compared at both the item response level and the test score level to determine whether measurable differences between the models could be detected when the data sets were constrained to be equivalent in terms of item "p"-values. The…

The main purposes of this study were to investigate, by means of simulation: (1) whether the difference likelihood ratio chi-square statistic (G2-dif) for comparing item response theory (IRT) models is asymptotically distributed as a chi-square distribution; and (2) the accuracy rate of applying G2-dif in selection of nested IRT models. Two…

Relations between latent trait and latent class models for item response data are examined. Conditions are given for two-latent class and two-parameter normal ogive models to agree, and relations between their item parameters are presented. Results are illustrated with data from the Law School Admission Test. (SLD)

This paper considers the following questions: (1) what is the relationship between the method of paired comparisons and Rasch measurement theory? (2) what is the relationship between the method of paired comparisons and graph theory? and (3) what can graph theory contribute to the understanding of Rasch measurement theory? It is specifically shown…

At the Educational Testing Service, the Mantel-Haenszel procedure is used for differential item functioning (DIF) detection, and the standardization procedure is used to describe DIF. This report describes these procedures. First, an important distinction is made between DIF and impact, pointing to the need to compare the comparable. Then, these…

Multidimensional scaling (MDS) and exploratory and confirmatory factor analyses were compared in the assessment of the dimensionality of data sets, using sets generated to be one-dimensional or two-dimensional and differing in degree of interdimensional correlation and number of items defining a dimension. (SLD)

This National Council on Measurement in Education (NCME) instructional module compares classical test theory and item response theory and describes their applications in test development. Related concepts, models, and methods are explored; and advantages and disadvantages of each framework are reviewed. (SLD)

Compared the fit of several Item Response Theory (IRT) models to two personality assessment instruments using data from 13,059 individuals responding to one instrument and 1,770 individuals responding to the other. Two- and three-parameter logistic models fit some scales reasonably well, but not others, and the graded response model generally did…

In a simulation study, factor analysis and multidimensional item response theory (IRT) models are compared with respect to estimates of item parameters. For multidimensional data, a common factor analysis on the matrix of tetrachoric correlations performs at least as well as the multidimensional IRT model. (SLD)

Studied the extent to which three appropriateness indexes, Z(sub 3), ECIZ4, and W, are well standardized in a Monte Carlo study. The ECIZ4 most closely approximated a normal distribution, and its skewness and kurtosis were more stable and less affected by test length and item response theory model than the others. (SLD)

Accuracy of three exact person tests for assessing model-data fit in the Rasch model was investigated in a simulation study. Empirical Type I error rates and statistical power of the person tests were computed. The exact person test conditioned on total score is a promising tool for assessing consistency of response patterns with the Rasch model.…