To reduce the chance of Heywood cases or nonconvergence in estimating the 2PL or the 3PL model in the marginal maximum likelihood with the expectation-maximization (MML-EM) estimation method, priors for the item slope parameter in the 2PL model or for the pseudo-guessing parameter in the 3PL model can be used and the marginal maximum a posteriori…

The aim of this study was to examine the precision of item parameter estimation in different sample sizes and test lengths under three parameter logistic model (3PL) item response theory (IRT) model, where the trait measured by a test was not normally distributed or had a skewed distribution. In the study, number of categories (1-0), and item…

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…

Student misconceptions have been studied for decades from a curricular/instructional perspective and from the assessment/test level perspective. Numerous misconception assessment tools have been developed in order to measure students' misconceptions relative to the correct content. Often, these tools are used to make a variety of educational…

This study analysed polytomous items' psychometric properties according to nonparametric item response theory (NIRT) models. Thus, simulated datasets--three different test lengths (10, 20 and 30 items), three sample distributions (normal, right and left skewed) and three samples sizes (100, 250 and 500)--were generated by conducting 20…

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)

A simple scheme is proposed for smoothly approximating the ability distribution for relatively long tests, assuming that the item characteristic curves (ICCs) are known or well estimated. The scheme works for a general class of ICCs and is guaranteed to completely recover the theta distribution as the test length increases. The proposed method of…

The feasibility of quick norms derived by the procedure described by B. D. Wright and M. H. Stone (1979) was investigated. Norming differences between traditionally calculated means and Rasch "quick" means were examined for simulated data sets of varying sample size, test length, and type of distribution. A 5 by 5 by 2 design with a…

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…