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…

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.…

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…