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…

The impact of outliers on Cronbach's coefficient [alpha] has not been documented in the psychometric or statistical literature. This is an important gap because coefficient [alpha] is the most widely used measurement statistic in all of the social, educational, and health sciences. The impact of outliers on coefficient [alpha] is investigated for…

Proposes a modified version of commonly employed item response models in a fully Bayesian framework and obtains inferences under the model using Markov chain Monte Carlo techniques. Demonstrates use of the model in a series of simulations and with operational data from the North Carolina Test of Computer Skills and the Test of Spoken English…

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)

The Dutch Identity is presented as a useful tool for expressing the basic equations of item response models that relate the manifest probabilities to the item response functions and the latent trait distribution. Ways in which the identity may be exploited are suggested and illustrated. (SLD)

Statistical properties of person fit indices are reviewed as indicators of the extent to which a person's score pattern is in agreement with a measurement model. Distribution of a fit index and ability-free fit evaluation are discussed. The null distribution was simulated for a test of 20 items. (SLD)

Describes a goodness-of-fit statistic that considers the imprecision with which ability is estimated and involves constructing item fit tables based on each examinee's posterior distribution of ability, given the likelihood of the response pattern and an assumed marginal ability distribution. Also describes a Monte Carlo resampling procedure to…

A statistical method, W. F. Stout's statistical test of essential unidimensionality (1990), for exploring the lack of unidimensionality in test data was studied using Monte Carlo simulations. The statistical procedure is a hypothesis test of whether the essential dimensionality is one or exceeds one, regardless of the traditional dimensionality.…

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)

The effectiveness of two iterative methods of item response theory (IRT) item bias detection was examined in a simulation study. A modified form of the iterative item parameter linking method of F. Drasgow and an adaptation of the test purification procedure of F. M. Lord were compared. (SLD)

Previous person-fit research is extended through explication of an unexplored model for generating aberrant response patterns. The proposed model is then implemented to investigate the influence of test properties on the aberrancy detection power of a person-fit statistic. Difficulties of aberrancy detection are discussed. (SLD)

Multi-indicator growth models were formulated as special three-level hierarchical generalized linear models to analyze growth of a trait latent variable measured by ordinal items. Items are nested within a time-point, and time-points are nested within subject. These models are special because they include factor analytic structure. This model can…

To demonstrate that some methods used to assess item fit can be applied to assess person fit and vice versa, performance of a chi-squared item-fit statistic was compared with that of a likelihood-based person-fit statistic for examinees and items under Monte Carlo conditions. (SLD)

This article proposes an item response theory (IRT) approach to constructing and scoring multidimensional pairwise preference items. Individual statements are administered and calibrated using a unidimensional single-stimulus model. Tests are created by combining multidimensional items with a small number of unidimensional pairings needed to…

This Monte Carlo study examined strategies for forming the matching variable for the Mantel-Haenszel (MH) differential item functioning (DIF) procedure. Data were generated using a three-parameter logistic item response theory model, with common guessing parameters. The number of subjects and test length were manipulated, as were the difficulty,…