The usefulness of item response theory (IRT) models depends, in large part, on the accuracy of item and person parameter estimates. For the standard 3 parameter logistic model, for example, these parameters include the item parameters of difficulty, discrimination, and pseudo-chance, as well as the person ability parameter. Several factors impact…

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…

A primary assumption underlying several of the common methods for modeling item response data is unidimensionality, that is, test items tap into only one latent trait. This assumption can be assessed several ways, using nonlinear factor analysis and DETECT, a method based on the item conditional covariances. When multidimensionality is identified,…

The accuracy of item parameter estimates in the multidimensional item response theory (MIRT) model context is one that has not been researched in great detail. This study examines the ability of two confirmatory factor analysis models specifically for dichotomous data to properly estimate item parameters using common formulae for converting factor…

This article introduces a bootstrap generalization to the Modified Parallel Analysis (MPA) method of test dimensionality assessment using factor analysis. This methodology, based on the use of Marginal Maximum Likelihood nonlinear factor analysis, provides for the calculation of a test statistic based on a parametric bootstrap using the MPA…

This Monte Carlo study compares the ability of the parametric bootstrap version of DIMTEST with three goodness-of-fit tests calculated from a fitted NOHARM model to detect violations of the assumption of unidimensionality in testing data. The effectiveness of the procedures was evaluated for different numbers of items, numbers of examinees,…

DETECT is a nonparametric "full" dimensionality assessment procedure that clusters dichotomously scored items into dimensions and provides a DETECT index of magnitude of multidimensionality. Four factors (test length, sample size, item response theory [IRT] model, and DETECT index) were manipulated in a Monte Carlo study of bias, standard error,…

One set of approaches to the problem of clustering with dichotomous data in cluster analysis (CA) was studied. The techniques developed for clustering with binary data involve calculating distances between observations based on the variables and then applying one of the standard CA algorithms to these distances. One of the groups of distances that…

This study examines the performance of a new method for assessing and characterizing dimensionality in test data using the NOHARM model, and comparing it with DETECT. Dimensionality assessment is carried out using two goodness-of-fit statistics that are compared to reference X[2] distributions. A Monte Carlo study is used with item parameters…

This study compares the ability of the multiple indicators, multiple causes (MIMIC) confirmatory factor analysis model to correctly identify cases of differential item functioning (DIF) with more established methods. Although the MIMIC model might have application in identifying DIF for multiple grouping variables, there has been little…