Contributions to the joint modeling of responses and response times

In this dissertation, response time modeling, in the context of computerized based testing, has been discussed. Response times reveal information about the working speed of test takers. Taking response times and responses into account results in more information that can be used to improve insights in test taker’s behavior during the test. Therefore, several chapters in this dissertation have been dedicated to response times as well as responses. In Chapter 2, three person-fit statistics referred to as the , , and are discussed. These test statistics have approximately normal sampling distributions and an exact chi-squared distribution, respectively. Through simulation studies, the performance of the person-fit statistics for RT patterns was evaluated. Different types of aberrant response behavior were considered and the best results were obtained for random response behavior using or with a detection rate close to one under different conditions. In Chapter 3, a dynamic factor model for modeling working speed is presented, which describe the transition of changes in working speed over blocks of items. Test takers who work under a stationary or a nonstationary process can be identified by a mixture modeling approach. Results of the simulation study showed that in order to obtain accurate parameter estimates of the dynamic speed model, around 10 blocks of items, each containing at least two items were required. In Chapter 4, a latent growth modeling approach for working speed is presented, which can be used to measure variable working speed according to a time scale defined by the order in which the items were solved. According to the simulation study, satisfied estimation results were obtained using MCMC. A random slope and a random quadratic speed component were added to model deviations from a constant speed trajectory. More higher-order terms can be included to describe more flexible latent trajectories of speed. The fit of the distribution of the response time residuals was evaluated using a Kolmogorov-Smirnov test (KS test). Person-fit statistics were proposed to detect aberrant patterns of responses and/or response times. In Chapter 5, these methods have been illustrated for both simulated and real data. Based on a simulation study, it was shown that the performance of the person-fit statistics worked well in identifying aberrant patterns. The model evaluation tools can be used for a joint model, which also can include a component for guessing behavior and a component for variable working speed behavior. The log-normal and IRT models in this dissertation have been applied to real data. The MCMC methods for estimating the model parameters were implemented in R and are referred to as: Log-Normal Response Times (LNRT), Log-Normal Response Times Moving Average (LNRTMA), and Log Normal Item Response Theory (LNIRT). The programs are discussed in appendix (G, H).