The parallel analysis method for determining the number of components to retain in a principal components analysis has received a recent resurgence of support and interest. However, researchers and practitioners desiring to use this criterion have been hampered by the required Monte Carlo analyses needed to develop the criteria. Two recent…

The effects of skewed theta distributions on indices of differential item functioning (DIF) were studied, comparing Mantel Haenszel (N. Mantel and W. Haenszel, 1959) and DFIT (N. S. Raju, W. J. van der Linden, and P. F. Fleer) (noncompensatory DIF). The significance of the study is that in educational and psychological data, the distributions one…

Computerized adaptive tests (CATs) are efficient because of their optimal item selection procedures that target maximally informative items at each estimated ability level. However, operational administration of these optimal CATs results in a relatively small subset of items given to examinees too often, while another portion of the item pool is…

The accuracy of the Markov chain Monte Carlo procedure, Gibbs sampling, was considered for estimation of item and ability parameters of the one-parameter logistic model. Four data sets were analyzed to evaluate the Gibbs sampling procedure. Data sets were also analyzed using methods of conditional maximum likelihood, marginal maximum likelihood,…

This paper seeks to extend the application of Markov chain Monte Carlo (MCMC) methods in item response theory (IRT) to include the estimation of equating relationships along with the estimation of test item parameters. A method is proposed that incorporates estimation of the equating relationship in the item calibration phase. Item parameters from…