A Note on N in Bayesian Information Criterion for Item Response Models

This brief report derives the N in the penalty term of the Schwarz's (1978) Bayesian information criterion (BIC) for two-parameter logistic item response models. The results in this study show that the N is the number of persons for fixed item models, whereas it is the number of observations (the Number of Persons times the Number of Items) for random item models. Given these results, the authors recommend researchers to calculate the BIC or to validate the BIC value that shows in the output of software instead of accepting the output value without a further check of implicit assumptions made for the software.