Reliability indicates the internal consistency of a test. In educational studies, reliability is a key feature for a test. Researchers have proposed many traditional reliability estimates, such as coefficient alpha and coefficient omega. However, traditional reliability indices do not deal with the data hierarchy, even though the multilevel…

Over the past decade educational research has been stimulated by new legislation such as the No Child Left Behind Act. Increasing emphasis is being placed on accurately quantifying the success of treatment programs through student achievement scores, so precise estimation is vital for establishing the efficacy of new methodology. Ranked set…

Nonlinear multilevel latent variable modeling has been suggested as an alternative to traditional hierarchical linear modeling to more properly handle measurement error and sampling error issues in contextual effects modeling. However, a nonlinear multilevel latent variable model requires significant computational effort because the estimation…

Maximum likelihood (ML) estimation of generalized linear mixed models (GLMMs) is technically challenging because of the intractable likelihoods that involve high dimensional integrations over random effects. The problem is magnified when the random effects have a crossed design and thus the data cannot be reduced to small independent clusters. A…

This research is motivated by an analysis of reading research data. We are interested in modeling the test outcome of ability to fluently recode letters into sounds of kindergarten children aged between 5 and 7. The data showed excessive zero scores (more than 30% of children) on the test. In this dissertation, we carefully examine the models…