Item response theory models (IRT) are increasingly becoming established in social science research, particularly in the analysis of performance or attitudinal data in psychology, education, medicine, marketing and other fields where testing is relevant. We propose the R package eRm (extended Rasch modeling) for computing Rasch models and several extensions. A main characteristic of some IRT models, the Rasch model being the most prominent, concerns the separation of two kinds of parameters, one that describes qualities of the subject under investigation, and the other relates to qualities of the situation under which the response of a subject is observed. Using conditional maximum likelihood (CML) estimation both types of parameters may be estimated independently from each other. IRT models are well suited to cope with dichotomous and polytomous responses, where the response categories may be unordered as well as ordered. The incorporation of linear structures allows for modeling the effects of covariates and enables the analysis of repeated categorical measurements. The eRm package fits the following models: the Rasch model, the rating scale model (RSM), and the partial credit model (PCM) as well as linear reparameterizations through covariate structures like the linear logistic test model (LLTM), the linear rating scale model (LRSM), and the linear partial credit model (LPCM). We use an unitary, efficient CML approach to estimate the item parameters and their standard errors. Graphical and numeric tools for assessing goodness-of-fit are provided. (authors' abstract)

Item response theory models (IRT) are increasingly becoming established in social science research, particularly in the analysis of performance or attitudinal data in psychology, education, medicine, marketing and other fields where testing is relevant. We propose the R package eRm (extended Rasch modeling) for computing Rasch models and several extensions. A main characteristic of some IRT models, the Rasch model being the most prominent, concerns the separation of two kinds of parameters, one that describes qualities of the subject under investigation, and the other relates to qualities of the situation under which the response of a subject is observed. Using conditional maximum likelihood (CML) estimation both types of parameters may be estimated independently from each other. IRT models are well suited to cope with dichotomous and polytomous responses, where the response categories may be unordered as well as ordered. The incorporation of linear structures allows for modeling the effects of covariates and enables the analysis of repeated categorical measurements. The eRm package fits the following models: the Rasch model, the rating scale model (RSM), and the partial credit model (PCM) as well as linear reparameterizations through covariate structures like the linear logistic test model (LLTM), the linear rating scale model (LRSM), and the linear partial credit model (LPCM). We use an unitary, efficient CML approach to estimate the item parameters and their standard errors. Graphical and numeric tools for assessing goodness-of-fit are provided. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

Ziel der Arbeit ist die Entwicklung von Modellen zur Entdeckung von Fehlspezifikation im Linear Logistic Test Model ( = LLTM) und verwandten Modellen der Verände\-rungs\-mes\-sung. Fehlspezifikation bedeutet hierbei, dass dem Modell ein unzutreffendes Muster latenter Traits zugrundegelegt wurde. Dies kann, vgl. z.B. [Baker,1993], zu bedeutenden Schätzfehlern führen. Die hier vorgestellten Methoden ermöglichen es unter leicht zu erfüllenden Annahmen, Aussagen über das Ausmaß der Unkorrektheit der verwendeten Modellspezifikation zu machen, ohne die in der Modellschätzung bestimmten Parameterwerte verwenden zu müssen. Zunächst wird eine auf dem Mantel-Haenszel-Test beruhende Methodik vorgestellt, die bei Tests bezüglich der Veränderungsparameter eines LLTMs als direkte Konkurrenz zu den bekannten Likelihood-Ratio-Tests für das LLTM anzusehen ist, wie sie z.B. bei [Fischer,1995a] vorgestellt werden. Weiterhin werden für das LLTM optimierte Personenfittests und daraus abgeleitete Effektgrößen vorgestellt. Diese ermöglichen das Auffinden von Subpopulationen, bei denen eine Abweichung zum angenommenen Modell aufgetreten ist. Es werden die statistischen Eigenschaften dieser Tests resp. Effektgrößen mittels Simulation und Teststärkeberechnung untersucht und Anwendungsbeispiele für diese Methoden vorgestellt. / In this thesis, new methods are developed for the detection of misspecification within Linear Logistic Test Models (=LLTM) and similar model classes for the measurement of change. The phrase "misspecification" will be used if a wrong selection of latent traits is chosen for the estimation of the LLTM. Misspecification can lead to erronious estimation [Baker,1993]). Using the newly developed methods, it is possible to measure the extent of deviations between the proposed model and the data. This can be done without using estimated parameter values. First a method is introduced which is based on the well-known Mantel-Haenszel-test. For some hypotheses, this method can be used instead of a Likelihood Ratio Test (e.g. [Fischer,1995a]). The Main topic of this thesis are uniformly most powerful tests for the measurement of person fit and related effect measures. These effect measures can be used for the identification of subpopulations where the proposed model does not hold. Statistical properties of these tests resp. effect measures are examined by simulations and power calculations using the SAS software. Furthermore, examples of the application of these methods are given.

The aim of the monograph is to contribute towards bridging the gap between methodological developments that have evolved in the social sciences, in particular in psychometric research, and methods of statistical modelling in a more general framework. The first part surveys certain special psychometric models (often referred to as Rasch family of models) that share common properties: separation of parameters describing qualities of the subject under investigation and parameters related to properties of the situation under which the response of a subject is observed. Using conditional maximum likelihood estimation, both types of parameters may be estimated independently from each other. In particular, the Rasch model, the rating scale model, the partial credit model, hybrid types, and linear extensions thereof are treated. The second part reviews basic ideas of generalized linear models (GLMs) as an an excellent framework for unifying different approaches and providing a natural, technical background for model formulation, estimation and testing. This is followed by a short introduction to the software package GLIM chosen to illustrate the formulation of psychometric models in the GLM framework. The third part is the main part of this monograph and shows the application of generalized linear models to psychometric approaches. It gives a unified treatment of Rasch family models in the context of log-linear models and contains some new material on log-linear longitudinal modelling. The last part of the monograph is devoted to show the usefulness of the latent variable approach in a variety of applications, such as panel, cross-over, and therapy evaluation studies, where standard statistical analysis does not necessarily lead to satisfactory results. (author´s abstract) / Series: Research Report Series / Department of Statistics and Mathematics

Wie die meisten westlichen Streitkräfte, bewegt sich die Bundeswehr im Spannungsfeld zwischen hohem Personalbedarf und Fachkräftemangel. Durch ein Onlineassessment kann der Bewerbungsprozess dahingehend optimiert werden, dass fähiges Personal schneller gebunden wird. Onlineassessment hat diverse Vorteile, gleichzeitig sind damit jedoch Herausforderungen verbunden. Die wahrscheinlich größte ist es, Betrug zu minimieren, da Onlineassessment in einer weitestgehend unkontrollierten Umgebung stattfindet. Zur Entgegnung dieser Problematik dienen verschiedene Ansätze, wie beispielsweise große Itempools, wodurch einer Verbreitung der Lösung im Internet entgegengewirkt werden kann. Dieser Ansatz ist jedoch mit hohen Kosten verbunden. Automatische Itemgenerierung hingegen ermöglicht es, kostengünstig und zeiteffizient psychometrisch hochwertige Items zu erstellen. Aus diesem Grund wurden in der vorliegenden Arbeit zwei Arbeitsgedächtnistests mit automatischer Itemgenerierung für das Onlineassessment der Bundeswehr entwickelt und evaluiert, mit dem Ziel einer hohen prädiktiven Validität auf die Diagnostik vor Ort. In der ersten Studie (N = 330) wurde gezeigt, dass automatische Itemgenerierung für die entwickelten Arbeitsgedächtnistests eingesetzt werden kann. Hierbei wurden zudem zwei verschiedene zeitliche Varianten untersucht, wobei sich diejenige mit der längeren Stimulusrepräsentationszeit als vorteilhafter erwies. In der zweiten Studie (N = 621) wurden Nachweise für Reliabilität und Validität erbracht. Die Tests zeigten eine gute konvergente und diskriminante Validität. Zudem konnte einer der beiden Tests eine sehr gute prädiktive Validität aufweisen. Unter Gesamtberücksichtigung der Testgütekriterien wurde dieser Test schließlich für das Onlineassessment der Bundeswehr vorgeschlagen. Somit steht der Bundeswehr nun ein wissenschaftlich fundierter Arbeitsgedächtnistest für das Onlineassessment zur Verfügung. / Like most Western armed forces, the Bundeswehr faces both high personnel requirements and a shortage of skilled personnel. Online assessment can optimize the application process to ensure that capable personnel are retained more quickly. Online assessment has various advantages, but also challenges associated with it. Probably the biggest of these challenges is minimizing cheating, as online assessment takes place in a largely unsupervised environment. Various approaches are used to counter this problem, such as large item pools, which can be used to counter the dissemination of solutions on the Internet. However, this approach is associated with high costs. Automatic item generation, on the other hand, makes it possible to create psychometrically high-quality items in a cost-effective and time-efficient manner. For this reason, two working memory tests with automatic item generation for the German Armed Forces’ online assessment were developed and evaluated in the present study, with the aim of matching the high predictive validity of on-site diagnostics. The first study (N = 330) demonstrated that automatic item generation can be used for the developed working memory tests. Two different temporal variants were also investigated, with the longer stimulus presentation time proving to be more beneficial. The second study (N = 621) provided reliability and validity evidence. The tests showed good convergent and discriminant validity. In addition, one of the two tests demonstrated very good predictive validity. Taking into account the overall test quality criteria, this test was ultimately proposed for use in the German Armed Forces’ online assessment. Thus, the Bundeswehr now has a scientifically-grounded working memory test available for its online assessment.