| In computer-administered tests, response times can be recorded conjointly with the corresponding responses. This broadens the scope of potential modeling approaches because response times can be analyzed in addition to analyzing the responses themselves. Current models for response times, however, mainly focus on parametric models that have the advantage of conciseness, but may suffer from a reduced flexibility to fit real data. This thesis presents two types of semi-parametric models that combine the flexibility of nonparametric modeling and the brevity as well as interpretability of the parametric modeling. They are.;1. Hierarchical proportional hazard model: This model adopts the hierarchical structure suggested by van der Linden (2007) with the well-known Cox proportional hazard (PH) model in survival analysis. The PH model is comprised of two parts: the non-parametric baseline hazard and the parametric form of the examinee's latent speed. This model acts on the hazard rate, the instantaneous rate at which the event occurs conditioning on the fact that the event has not occurred so far, and it assumes that a unit increase in a latent speed is multiplicative with respect to the hazard rate. The model includes the exponential regression model, Weibull regression model, and many other parametric models as special cases.;2. Hierarchical linear transformation model: This model is a further extension of the Cox PH model. In this model, the response times, after some non-parametric monotone transformation, become a linear model with latent speed as a covariate plus an error term. The distribution of the error term implicitly defines the relationship between the RT and examinees' latent speeds; whereas the non-parametric transformation is able to describe various shapes of RT distributions. The linear transformation model represents a rich family of models that includes the Cox proportional hazard model, the Box-Cox normal model, and many other models as special cases. The linear transformation model is again embedded in a hierarchical framework so that both RTs and responses are modeled simultaneously.;For both new models, we propose two-stage estimation methods. The model checking techniques for both models are provided to help practitioners decide whether the model is appropriate for a real data set. Finally, the applicability of the new models are demonstrated with simulation studies and applications to actual responses to items. |
