The Impact of Various Class-Distinction Features on Model Selection in the Mixture Rasch Model

ABSTRACT

The purpose of the current study is to examine the performance of four information criteria (Akaike's information criterion [AIC], corrected AIC [AICC] Bayesian information criterion [BIC], sample-size adjusted BIC [SABIC]) for detecting the correct number of latent classes in the mixture Rasch model through simulations. The simulation study manipulated various class-distinction features (percentages of class-variant items, magnitudes, and patterns of item difficulty differences) and mixing proportions, assuming that a mixture Rasch model with two latent classes was the true model. Unlike previous studies that showed BIC's superiority to other indices, our findings from this study suggested that the four information criteria had differential performance depending on the percentage of class-variant items and the magnitude and pattern of item difficulty differences under a two-class structure. Furthermore, the present study revealed that AICC and SABIC generally performed as good as or better than their counterparts, AIC and BIC, respectively, for the class-class structure with a sample of 3,000.

KEYWORDS:

• Item response theory
• mixture item response models
• latent class analysis
• information criteria
• model selection