Explanatory Item Response Modeling of Structurally Involved Educational Data. With Applications to Electronic Learning Environments

Statistical modeling of e-learning data, however, can be challenging due to common problems likemissing item responses, in addition to complicating data patterns like multilevel structures, growth trends and manifest and latent groups of subjects with distinctive features. In this thesis, we adapt and extend the IRT modeling framework for multilevel educational data sets, mainly from e-learning environments, addressing three specific challenges: missing data, modeling of persons growth or change in ability over time, and modeling latent person groups. In Chapter 2, we show and explain why some common missing-data methods like simple forms of imputation are inappropriate for the considered multilevel data sets. On the contrary, a direct likelihood analysis approach is shown to give unbiased estimates under certain flexible conditions. In Chapter 3, we propose an imputation model to effectively impute missing item scores in multilevel item response data, and the results are compared to those obtained under the direct likelihood analysis approach. This model is shown to perform as good as the direct likelihood approach, but has some extra advantages. In Chapters 4 and 5, we describe methods that can be used to model growth or changes in persons ability over time for the considered e-learning item response data. Two empirical examples are used to illustrate and compare the presented models. Results show that by incorporating time spent within and between study sessions into an IRT model, one is able to model changes in persons ability or for groups of persons at any time of the e-learning process. In Chapter 6, we present a longitudinal mixture IRT model that allows for the possibility of detecting latent person groups with similar response (growth) behaviors for item response learning data.