Title: Marginal Maximum Likelihood Estimation Algorithms for Uni- and
Multidimensional Count Item Response Models 

Authors: Marie Beisemann, Philipp Doebler

Abstract:
In different fields of psychology, tests and self-reports generate count data
responses, e.g., error counts in educational assessment or number of symptoms
in clinical psychology. Count Item Response Theory (CIRT) models offer a means
of analysis for such responses; most prominently the unidimensional Rasch’s
Poisson Counts Model (RPCM), the analogue to the logistic Rasch (1PL) model.
In our work, we have extended CIRT models to address restrictive assumptions,
namely equal-discriminations and equidispersion of the Poisson distribution
(conditional mean = conditional variance) and to generalize the unidimensional
to the multidimensional case. These generalizations are enabled by replacing
the Poisson with the Conway-Maxwell-Poisson (CMP) distribution, which can
handle over- (conditional mean < conditional variance) and underdispersion
(conditional mean > conditional variance) by generalizing the former.
Throughout different projects, we conceived Expectation-Maximization (EM)
algorithms for unidimensional (explanatory) CIRT models as well as for
(exploratory) multidimensional CIRT models including variants which
incorporate lasso penalization to obtain a simply structured discrimination
matrix. Computationally, the CMP distribution poses challenges as multiple
infinite series must be approximated numerically and efficiency in terms of
computation time is not trivially achieved. In this presentation, we aim to
give an overview of the developed models and algorithms as well as their
implementation in the R package countirt.