Title: Examining Exams with the psycho* Family of R Packages

Author: Achim Zeileis

Affiliation: Universitaet Innsbruck

Abstract: The psycho* family of R packages (psychotools, psychotree,
psychomix) started out as a set of functions for assessing certain
psychometric models - mostly from item response theory (IRT) - for
measurement invariance and differential item functioning (DIF).  By now it
has grown in a rather mature set of packages and here we give a tour of its
functionality by examining the result of large-scale exams in the
"Mathematics 101" course for business and economics students at
Universitaet Innsbruck.

To give an overview, the psychotools package (Zeileis, Strobl, Wickelmaier,
Abou El-Komboz, Kopf 2014) contains basic infrastructure for representing
paired comparison and item response data, provides lean and fast
implementations of many standard models, and comes with several empirical
data sets.  Based on psychotools and the flexmix package(Gruen & Leisch
2008), the psychomix package (Frick, Strobl, Leisch, Zeileis 2012) assess
invariance by using finite mixture models (with or without further
concomitant variables).  In contrast, the psychotree package (Strobl,
Wickelmaier, Zeileis 2011; Strobl, Kopf, Zeileis 2015; Abou El-Komboz,
Zeileis, Strobl 2014) assesses invariance along further covariates by
recursive partitioning.  It is also based on psychotools but also uses
recent additions to the parameter instability tests in the strucchange
package (Wang, Merkle, Zeileis 2014) and the infrastructure provided by the
partykit package (Hothorn & Zeileis 2014).  In summary this yields a
unified approach to estimating, visualizing, testing, mixing, and
partitioning a range of models: Bradley-Terry (btmodel, btmix, bttree),
Rasch (raschmodel, raschmix, raschtree), partial credit (pcmodel, pctree),
rating scale (rsmodel, rstree), and multinomial processing tree (mptmodel,
mpttree).

For illustrating the IRT methods, especially the Rasch model, for assessing
DIF, empirical data from large-scale exams at the Universitaet Innsbruck
are analyzed.  The data comes from written single-choice exams of the
first-year "Mathematics 101" course for business and economics students.
The exams have been generated and evaluated using the exams package (Grün &
Zeileis 2009; Zeileis, Umlauf, Leisch 2014) and here the items and answer
patters of the exam are examined.