Thesis (Ph.D.)--University of Delaware, 2006. / Principal faculty advisor: Ratna Nandakumar, School of Education. Includes bibliographical references.

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.

Computerized adaptive testing attempts to provide the most suitable question for an examinee depending on the examinee¡¦s ability to achieve the best result. Although Maximum Likelihood Estimation (MLE) and Bayesian Likelihood Estimation (BLE) have been provided to solve ability estimation and have good results in the literature, little attention has been paid to the situation when the answer of an item does not conform with the examinee¡¦s ability as expected nor standard derivation changes of the ability estimation. We hypothesized that the Adaptive-Network-Based Fuzzy Inference System (ANFIS) can be used to infer flexible examinee¡¦s ability estimation automically by analyzing the relevant data of the examinee in a test. Consequently, the study presents a novel learning ability model based on ANFIS, which can adaptively choose questions by Item Response Theory. Taking the item discrimination, difficulty, guessing, and the examinee¡¦s ability before he/she answers a question as parameters, the proposed method can infer the adjustment of the examinee¡¦s ability to update its value after he/she answers the question. The ANFIS model of the experiments were developed using MATLAB. The examinees were simulated and the training data were collected under three different situations. Through different combination of ANFIS fuzzy rules, the adjustment of ability is inferred to improve the accuracy of the estimated ability. The error between the true ability and the estimated ability obtained by the proposed model is compared with MLE and BLE. The simulation results show that the estimated ability error of ANFIS is smaller than MLE and BLE when the value of the test information is larger. The proposed method could provide better accuracy of the examinee¡¦s ability and offer more appropriate questions for examinees. Keywords: ANFIS, Item Response Theory, Computerized Adaptive Testing

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Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1991. / Vita. Abstract. Includes bibliographical references (leaves 79-83). Also available via the Internet.

Thesis (Ph. D.)--University of North Texas, Aug., 2009. / Title from title page display. Includes bibliographical references.

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