Extensions and Applications of Multilevel and Multidimensional Item Response Models
Multilevel and multidimensional item response models are two commonly used examples as extensions of the conventional item response models. In this dissertation, I investigate extensions and applications of multilevel and multidimensional item response models, with a primary focus on longitudinal item response data that include students' school switching, classification of examinees into latent classes based on multidimensional aspects, and measurement models for complicated learning progressions. In the first paper, multilevel item response models for longitudinal data are extended to the crossed-classified models (Rasbash & Goldstein, 1994; Raudenbush, 1993) and multiple membership models (Hill & Goldstein, 1998; Rasbash & Browne, 2001) to incorporate students' school mobility. If students switch school over time in longitudinal studies, the data structure is not strictly hierarchical; therefore, conventional multilevel models are not applicable. In this study, two types of school mobility and corresponding models are specified. Furthermore, this study investigates the impacts of misspecification of school membership in the analysis of longitudinal data. In the second and third paper, mixture models and measurement models based on multidimensional item response models are presented respectively. The second paper investigates possible usefulness of the mixture random weights linear logistic test model (MixRWLLTM) as a means to identify subgroups of examinees as well as to improve interpretations of differences between latent classes. In the proposed MixRWLLTM, examinees are classified with respect to their multidimensional aspects, a general propensity (intercept) and random coefficients of the item properties. In the third paper, a structured constructs model (SCM) for the continuous latent trait is developed to deal with complicated learning progressions, in which relations between levels across multiple constructs are assumed in advance. Based on the multidimensional Rasch model, discontinuity parameters are incorporated to model the hypothesized relations as the advantage or disadvantage for respondents belonging into a certain level in one construct to reach a level in another construct.