Mixture Rasch (MixRasch) models conventionally assume normal distributions for latent ability. Previous research has shown that the assumption of normality is often unmet in educational and psychological measurement. When normality is assumed, asymmetry in the actual latent ability distribution has been shown to result in extraction of spurious…

Current methods for detecting growth of students' problem-solving skills in math focus mainly on analyzing changes in test scores. Score-level analysis, however, may fail to reflect subtle changes that might be evident at the item level. This article demonstrates a method for studying item-level changes using data from a multiwave experiment with…

The ability estimates of Gibbs sampling and the magnitudes of the posterior standard deviations were investigated. Item parameters of the Q-E intelligence test (J. Fraenkel and N. Wallen, 2000) for 44 examinees were obtained using Gibbs sampling, marginal Bayesian estimation, and BILOG. Two normal priors were used in item parameter estimation.…

Continuation ratio logits are used to model the possibilities of obtaining ordered categories in a polytomously scored item. This model is an alternative to other models for ordered category items such as the graded response model and the generalized partial credit model. The discussion includes a theoretical development of the model, a…

Investigated Type I error rates of the likelihood-ratio test for the detection of differential item functioning (DIF) using Monte Carlo simulations under the graded-response model. Type I error rates were within theoretically expected values for all six combinations of sample sizes and ability-matching conditions at each of the nominal alpha…

Examined the accuracy of the Gibbs sampling Markov chain Monte Carlo procedure for estimating item and person (theta) parameters in the one-parameter logistic model. Analyzed four empirical datasets using the Gibbs sampling, conditional maximum likelihood, marginal maximum likelihood, and joint maximum likelihood methods. Discusses the conditions…

Hierarchical Bayes procedures for the two-parameter logistic item response model were compared for estimating item and ability parameters through two joint and two marginal Bayesian procedures. Marginal procedures yielded smaller root mean square differences for item and ability, but results for larger sample size and test length were similar.…

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,…

Type I error rates of the likelihood ratio test for the detection of differential item functioning (DIF) were investigated using Monte Carlo simulations. The graded response model with five ordered categories was used to generate data sets of a 30-item test for samples of 300 and 1,000 simulated examinees. All DIF comparisons were simulated by…

Hierarchical Bayes procedures were compared for estimating item and ability parameters in item response theory. Simulated data sets from the two-parameter logistic model were analyzed using three different hierarchical Bayes procedures: (1) the joint Bayesian with known hyperparameters (JB1); (2) the joint Bayesian with information hyperpriors…