Modeling Differential Item Functioning Using a Generalization of the Multiple-Group Bifactor Model

The authors present a generalization of the multiple-group bifactor model that extends the classical bifactor model for categorical outcomes by relaxing the typical assumption of independence of the specific dimensions. In addition to the means and variances of all dimensions, the correlations among the specific dimensions are allowed to differ between groups. By including group-specific difficulty parameters, the model can be used to assess differential item functioning (DIF) for testlet-based tests. The model encompasses various item response models for polytomous data by allowing for different link functions, and it includes testlet and second-order models as special cases. Importantly, by assuming that the testlet dimensions are conditionally independent given the general dimension, the authors show, using a graphical model framework, that the integration over all latent variables can be carried out through a sequence of computations in two-dimensional subspaces, making full-information maximum likelihood estimation feasible for high-dimensional problems and large datasets. The importance of relaxing the orthogonality assumption and allowing for a different covariance structure of the dimensions for each group is demonstrated in the context of the assessment of DIF. Through a simulation study, it is shown that ignoring between-group differences in the structure of the multivariate latent space can result in substantially biased estimates of DIF.