Em testes nos quais uma quantidade considerável de indivíduos não dispõe de tempo suciente para responder todos os itens temos o que é chamado de efeito de Speededness. O uso do modelo unidimensional da Teoria da Resposta ao Item (TRI) em testes com speededness pode nos levar a uma série de interpretações errôneas uma vez que nesse modelo é suposto que os respondentes possuem tempo suciente para responder todos os itens. Nesse trabalho, desenvolvemos uma análise Bayesiana do modelo tri-dimensional da TRI proposto por Wollack e Cohen (2005) considerando uma estrutura de dependência entre as distribuições a priori dos traços latentes a qual modelamos com o uso de cópulas. Apresentamos um processo de estimação para o modelo proposto e fazemos um estudo de simulação comparativo com a análise realizada por Bazan et al. (2010) na qual foi utilizada distribuições a priori independentes para os traços latentes. Finalmente, fazemos uma análise de sensibilidade do modelo em estudo e apresentamos uma aplicação levando em conta um conjunto de dados reais proveniente de um subteste do EGRA, chamado de Nonsense Words, realizado no Peru em 2007. Nesse subteste os alunos são avaliados por via oral efetuando a leitura, sequencialmente, de 50 palavras sem sentidos em 60 segundos o que caracteriza a presença do efeito speededness. / In tests where a reasonable amount of individuals does not have enough time to answer all items we observe what is called eect of Speededness. The use of a unidimensional model from Item Response Theory (IRT) in tests with speededness can lead us to erroneous interpretations, since this model assumes that the respondents have enough time to answer all items. In this work, we propose a Bayesian analysis of the three-dimensional item response models (IRT) proposed by Wollack and Cohen et al (2005) considering a dependency structure between the prior distributions of the latent traits which is modeled using Copulas. We propose and develop a MCMC algorithm for the estimation of the model. A simulation study comparing with the analysis in Bazan et al (2010), wherein an independent prior distribution assumption was presented. Finally, we apply our model in a set of real data from EGRA, called Nonsense Words, held in Peru in 2007, where students are evaluated for their performance in reading.

Em testes nos quais uma quantidade considerável de indivíduos não dispõe de tempo suciente para responder todos os itens temos o que é chamado de efeito de Speededness. O uso do modelo unidimensional da Teoria da Resposta ao Item (TRI) em testes com speededness pode nos levar a uma série de interpretações errôneas uma vez que nesse modelo é suposto que os respondentes possuem tempo suciente para responder todos os itens. Nesse trabalho, desenvolvemos uma análise Bayesiana do modelo tri-dimensional da TRI proposto por Wollack e Cohen (2005) considerando uma estrutura de dependência entre as distribuições a priori dos traços latentes a qual modelamos com o uso de cópulas. Apresentamos um processo de estimação para o modelo proposto e fazemos um estudo de simulação comparativo com a análise realizada por Bazan et al. (2010) na qual foi utilizada distribuições a priori independentes para os traços latentes. Finalmente, fazemos uma análise de sensibilidade do modelo em estudo e apresentamos uma aplicação levando em conta um conjunto de dados reais proveniente de um subteste do EGRA, chamado de Nonsense Words, realizado no Peru em 2007. Nesse subteste os alunos são avaliados por via oral efetuando a leitura, sequencialmente, de 50 palavras sem sentidos em 60 segundos o que caracteriza a presença do efeito speededness. / In tests where a reasonable amount of individuals does not have enough time to answer all items we observe what is called eect of Speededness. The use of a unidimensional model from Item Response Theory (IRT) in tests with speededness can lead us to erroneous interpretations, since this model assumes that the respondents have enough time to answer all items. In this work, we propose a Bayesian analysis of the three-dimensional item response models (IRT) proposed by Wollack and Cohen et al (2005) considering a dependency structure between the prior distributions of the latent traits which is modeled using Copulas. We propose and develop a MCMC algorithm for the estimation of the model. A simulation study comparing with the analysis in Bazan et al (2010), wherein an independent prior distribution assumption was presented. Finally, we apply our model in a set of real data from EGRA, called Nonsense Words, held in Peru in 2007, where students are evaluated for their performance in reading.

Da Prüfungen und Tests häufig dazu dienen, den Zugang zu Bildungsprogrammen zu steuern und die Grundlage zur Abschlussvergabe am Ende von Bildungsprogrammen bilden, ist ihre Fairness und Validität von größter Bedeutung. Ein kontrovers diskutierter Aspekt standardisierter Tests ist die Verwendung von Zeitlimits. Unabhängig davon ob eine Testadministration Zeitdruck hervorrufen soll oder nicht, sollten Testentwickler:innen in die Lage versetzt werden, den Zeitdruck einer Testadministrationen explizit gestalten zu können. Zu diesem Zweck schlägt van der Linden (2011a, 2011b) einen Ansatz zur Kontrolle des Zeitdrucks von Tests in der automatisierten Testhefterstellung (ATA) unter Verwendung von Mixed Integer Linear Programming und eines lognormalen Antwortzeitmodells vor. Dabei hat der Ansatz von van der Linden jedoch eine zentrale Limitation: Er ist auf das zwei-parametrische lognormale Antwortzeitmodell beschränkt, das gleiche Geschwindigkeits-Sensitivitäten (d.h. Faktorladungen) für alle Items annimmt. Diese Arbeit zeigt, dass ansonsten parallele Testhefte mit unterschiedlichen Geschwindigkeits-Sensitivitäten für bestimmte Testteilnehmende unfair sind. Darüber hinaus wird eine Erweiterung des van der Linden-Ansatzes vorgestellt, die unterschiedliche Geschwindigkeits-Sensitivitäten von Items in ATA berücksichtigt. Weiter wird diskutiert, wie Testhefte mit identischen, aber unterschiedlich angeordneten Items zu Fairness-Problemen aufgrund von Item-Positionseffekten führen können und wie dies verhindert werden kann. Die vorliegende Arbeit enthält zusätzlich Anleitungen zur Verwendung des R-Pakets eatATA für ATA und zur Verwendung von Stan und rstan für Bayesianische hierarchische Antwortzeitmodellierung. Abschließend werden Alternativen, praktische Implikationen und Grenzen der vorgeschlagenen Ansätze diskutiert und Vorschläge für zukünftige Forschungsthemen gemacht. / As examinations and assessments are often used to control access to educational programs and to assess successful participation in an educational program, their fairness and validity is of great importance. A controversially discussed aspect of standardized tests is setting time limits on tests and how this practice can result in test speededness. Regardless of whether a test should be speeded or not, being able to deliberately control the speededness of tests is desirable. For this purpose, van der Linden (2011a, 2011b) proposed an approach to control the speededness of tests in automated test assembly (ATA) using mixed integer linear programming and a lognormal response time model. However, the approach by van der Linden (2011a, 2011b) has an important limitation, in that it is restricted to the two-parameter lognormal response time model which assumes equal speed sensitivities (i.e., factor loadings) across items. This thesis demonstrates that otherwise parallel test forms with differential speed sensitivities are indeed unfair for specific test-takers. Furthermore, an extension of the van der Linden approach is introduced, which incorporates speed sensitivities in ATA. Additionally, test speededness can undermine the fairness of a test if identical but differently ordered test forms are used. To prevent that the score of test-takers depends on whether easy or difficult items are located at the end of a test form, it is proposed that the same, most time intensive items should be placed at the end of all test forms. The thesis also provides introductions and tutorials on using the R package eatATA for ATA and using Stan and rstan for Bayesian hierarchical response time modeling. Finally, the thesis discusses alternatives, practical implications, and limitations of the proposed approaches and provides an outlook on future related research topics.