Models for Hierarchical-Structured Item Response Data and a Longitudinal Multilevel Logistic Regression Model on DIF Analyses
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The presented journal article formatted dissertation investigated the performance of two models for hierarchical-structured item response data (i.e., Kamata’s MLIRT model, and Multiple Regression IRT model) and discussed an application of the multilevel IRT modeling, i.e., a longitudinal multilevel logistic regression model for DIF analyses. Study I compared the estimates of abilities and IRT difficulty parameters of the two models for multilevel-structured IRT data. Bias and RMSE were compared under 8 conditions (2 test lengths, 4 intraclass correlation coefficients, i.e., ICC). Study II sought to learn the causes of DIF, specifically investigating if DIF arises through higher-level clusters, such as different schools, and longitudinal sources, such as multiple time points of test (e.g., beginning v.s. end of year). The accuracies of DIF detection at each level were evaluated under 48 conditions (2 test lengths, 2 percentages of DIF items at school-level, 2 percentages of DIF items of time-level, 3 sample sizes, 2 magnitude of DIF) by power and Type I error rate. Findings of Study I provided guidelines for model selection between MLIRT and MR-IRT model. Results indicated more accurate estimates of school abilities but less accurate estimates of student abilities with MLIRT model. MR-IRT was found more appropriate to use when sample size was small. For both the MLIRT and MR-IRT models, the longer test length resulted in more accurate estimates. ICC played an important role in estimating the school variances of abilities. Study II examined the power and Type I error of DIF detection with the proposed model. Results showed an overall powerful DIF detection. Type I error rates at each level roughly fell into the liberal range of Bradley (1978), 0.025 to 0.075. Consistent with previous study, the magnitude of DIF at each level and the sample was found to be the most important factors for a powerful DIF detection. In general, the time-level detection had higher power than the school-level.
Francis, Xueying Hu (2015). Models for Hierarchical-Structured Item Response Data and a Longitudinal Multilevel Logistic Regression Model on DIF Analyses. Doctoral dissertation, Texas A & M University. Available electronically from