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…

A distinction is made between statistics based on scientific theory and theory-free statistics. This distinction is discussed in the contexts of hypothesis testing, Bayesian inference, a priori planned contrasts, a new simple computational method, and alternative data interpretations. (TJH)