Estimation of Mixture Rasch Models from Skewed Latent Ability Distributions

ABSTRACT

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 latent classes in MixRasch models. In this study, the assumption of a skew-t distribution for the latent ability was examined for its effect on reducing extraction of spurious latent classes. A simulation study was conducted with eight different latent ability distributions with varying levels of skewness and kurtosis, two sample sizes (600 and 2,000), and two test lengths (10-item and 30-item). Results showed that the 30-item test but not the 10-item test were robust to extraction of spurious latent classes independent of the sample size or the shape of the ability distribution. Use of a skew-t prior, on the other hand, reduced spurious latent class extraction for the 10-item test, particularly for the sample size of 2,000 for high levels of skewness compared to use of a normal prior. Thus, a skew-t prior was useful for reducing spurious latent class extraction for short tests, although it did not improve item parameter estimation compared to a normal prior.

KEYWORDS:

• Mixture Rasch model
• skew-t distribution
• extraction of latent classes
• item parameter recovery
• spurious latent classes