The R-package BCMSMI is published under R Code and Packages, it supports a Bayesian covariance analysis of DIF (differential item functioning) of discrimination and difficulty, while accounting for correlation in DIF between discrimination and difficulty. The program fits the BCSM-MI model, which can be found in the publication (Fox, 2026, Psychometrika, Bayesian covariance modeling of DIF).

The Bayes factor test for DIF is defined for discriminations and difficulties, and does not require large sample sizes. When fitting the model, BF computations are included. The paper and supplement Publications Overview also addresses comparisons with regularization DIF, which has problems in controlling the Type-1 error in testing DIF.

The BCSM-MI does not require anchors, allows for an unbalanced design (variable number of clusters), but does not account for missings, incomplete response designs, and multiple layers of DIF. This will be considered in future research.