Modified Bayesian Information Criterion for Item Response Models in Planned Missingness Test Designs

The Bayesian information criterion (BIC) is a widely used statistical tool originally derived for fully observed data. The BIC formula includes the sample size and the number of estimated parameters in the penalty term. However, not all variables are available for every subject in planned missingness designs. This article demonstrates that a modified BIC, tailored for planned missingness designs, outperforms the original BIC. The modification adjusts the penalty term by using the average number of estimable parameters per subject rather than the total number of model parameters. This new criterion was successfully applied to item response theory models in two simulation studies. We recommend that future studies utilizing planned missingness designs adopt the modified BIC formula proposed here.