Estimation of two-parameter multilevel item response models with predictor variables: simulation and substantiation for an urban school district
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The most recent development in the field of Item Response Theory (IRT) has been the evaluation of IRT models as multilevel models, known as Multilevel IRT models (MLIRT). These models offer several statistical and practical advantages over ordinary IRT models. However, models such as 2-PL MLIRT models have not been studied yet. This dissertation consists of two studies, a simulation and a substantiation for an urban school district dataset. The simulation study tested the performance of twoparameter (2-PL) MLIRT models with predictor variables under various conditions that included 3 test lengths (15, 30, and 60 items), 4 sample sizes (200, 500, 1000, and 2000), 2 correlation conditions between the predictor variable and the ability (or attitude) parameter (rpb=.35 and .8), and 4 binomial distributions of the predictor variable (p=0.1, 0.25, 0.4, and 0.5). The bias and Root Mean Square Deviation (RMSD) values of the item parameters indicated that the distribution of the predictor variable and the correlation between the predictor and the ability (or attitude) parameter did not affect the estimates of 2-PL MLIRT models. These models performed well for sample sizes as low as 500 and test lengths as low as 15 which is lower than the required sample size for ordinary IRT models. Even for a sample size of 200, sufficiently accurate estimates were obtained with more than 300 iterations. The second study investigated the characteristics of the items that measured urban teachers’ perceptions of cultural awareness and beliefs about teaching African American children and tested whether these perceptions were influenced by the teachers’ gender, ethnicity, or teaching experience. Teacher beliefs about teaching African American students, culturally responsive management, and cultural awareness factors were influenced by the ethnicity of the teachers. Culturally responsive management, home and community support, and curriculum and instructional strategies factors were influenced by the teaching experience of the teachers. Items that were biased based on ethnicity or teaching experience were identified. None of the items exhibited gender bias. The study identified items that could be used over other items when the need for a shorter instrument or more informative categories arises.
Natesan, Prathiba (2007). Estimation of two-parameter multilevel item response models with predictor variables: simulation and substantiation for an urban school district. Doctoral dissertation, Texas A&M University. Available electronically from