Balancing simple models and complex reality

Abstract

The first part of the dissertation dealt with conditional independence and conditional dependence between response time and accuracy. Conditional independence - as formulated by most joint models for response times and accuracy applied in the context of educational measurement - means that given the latent variables of speed and ability the response accuracy and the response time of the same item are independent. Conditional dependence, on the other hand, means that the relationship between the response time and accuracy cannot be fully explained by the higher-level relationship between the persons’ latent variables, or between the item characteristics related to time and accuracy. The first two chapters of Part I developed tools that help to answer the question of whether relatively simple response time and accuracy models assuming conditional independence adequately represent the complex relationships between time and accuracy in the data. The last chapter of Part I proposed to give up some of the model simplicity in order to explain the complex structure in the data and gain more insight into the substantively interesting response processes. The second part of the dissertation dealt with three different research questions, all answered using a Bayesian approach. In Chapter 5 the multi-scale Rasch model consisting of Rasch homogenous scales was proposed and a tool for unmixing Rasch scales was provided. The choice of the model was directly motivated by the idea of optimally balancing the simplicity of the model with the complexity of the data: It keeps an important measurement property of the simple Rasch model - sufficiency of the sumscore within each scale for the corresponding person parameter - but relaxes other assumptions of the Rasch model (equality of discriminations of all items in the test and unidimensionality) which often do not match the complexity of the educational data.