Title: Computation of Model Scores for Multidimensional Item Response Theory
Models Fitted with the WLS Estimator

Authors: Franz Classe, Christoph Kern, Rudolf Debelak 

Abstract:
In this paper, we present the R package estfun.WLS designed for computing
model scores for multidimensional item response theory (MIRT) models,
particularly multidimensional Graded Response Models, estimated with the
Weighted Least Squares (WLS) estimator. The WLS estimator allows fast
estimation of intricate MIRT model parameters through the limited information
approach. The new R package makes it possible to compute model scores, i.e.,
the first-order derivatives of the objective function, for models fitted with
the WLS estimator. This way, the package facilitates rapid execution of
numerous parameter instability tests for MIRT models. The efficient
computation of parameter instability tests is crucial for various
applications, such as model-based recursive partitioning algorithms. Such
algorithms may be used to detect groups of subjects exhibiting Differential
Item Functioning (DIF) which are not pre-specified but result from
combinations of covariates. We performed a comparative analysis of the
performance of parameter stability tests for models fitted with a limited
information approach (here: the WLS estimator) using the lavaan package vs.
those fitted with a full information approach using the mirt package. The new
approach has a good Type I error rate, high power, and is computationally
faster than analysis via mirt.

Keywords: MIRT, parameter instability, DIF, latent variable scores