Several statistical procedures have been suggested for detecting
differential item functioning (DIF) and differential step
functioning (DSF) in polytomous items. However, standard
procedures are designed for the comparison of pre-specified
reference and focal groups, such as males and females.
Here, we propose a framework for the detection of DIF and DSF in
polytomous items under the rating scale and partial credit model,
that employs a model-based recursive partitioning algorithm. In contrast to existing
procedures, with this approach no pre-specification of reference
and focal groups is necessary, because they are detected in a
data-driven way. The resulting groups are characterized by
(combinations of) covariates and thus directly interpretable.
The statistical background and construction of the new procedures
are introduced along with an instructive example. Four simulation
studies illustrate and compare their statistical properties to
the well-established likelihood ratio test (LRT). While both the
LRT and the new procedures respect a given significance level,
the new procedures are in most cases equally (simple DIF groups)
or more powerful (complex DIF groups) and can also detect
DSF. The sensitivity to model misspecification is
investigated. An application example with empirical data
illustrates the practical use.
A software implementation of the new procedures is freely
available in the R system for statistical computing
