Type of Document Dissertation Author Binici, Salih Author's Email Address firstname.lastname@example.org URN etd-05082007-190825 Title Random-Effect Differential Item Functioning via Hierarchical Generalized Linear Model and Generalized Linear Latent Mixed Model: A Comparison of Estimation Methods Degree Doctor of Philosophy Department Educational Psychology and Learning Systems, Department of Advisory Committee
Advisor Name Title Akihito Kamata Committee Chair Albert C. Oosterhof Committee Member Florentina Bunea Committee Member Richard L. Tate Committee Member Keywords
- Multilevel Models
- Differential Item Functioning
- Generalized Linear Latent Mixed Model
- Hierarchical Generalized Linear Model
- Estimation Methods
Date of Defense 2007-01-30 Availability unrestricted AbstractThis study treated DIF as a random parameter varying over group units and formulated it following the Generalized Linear Latent and Mixed Model (GLLAMM) and Hierarchical Liner Model (HLM) frameworks. Such an alternative formulation was used to compare the HLM and GLLAMM estimates across several simulation conditions, since HLM and GLLAMM utilize different estimation methods to approximate the marginal maximum likelihood. HLM employs Penalized Quasi Maximum Likelihood (PQL) and Laplace approximations, while GLLAMM uses the Adaptive Gaussian Quadrature (AGQ) method.
In general, the Laplace and AGQ methods provided more stable random parameter estimates (the variation of abilities at student and school levels, as well as the variation of DIF across group units) than the PQL method. However, the PQL performed better for the fixed parameters (item difficulty and ability difference between groups, DIF parameters), especially when there were limited observation units at level-2 and level-3. Furthermore, it was found that the performances of the Laplace and AGQ were similar across all simulation conditions, but the amount of time spent by GLLAMM during computation was considerably larger than the amount of time spent by HLM.
Accuracy of DIF detection evaluated by means of Type I error rate for Non-DIF items and by power for DIF item. In general, Type I error rates of the PQL and Laplace methods were below or at the expected nominal alpha level (0.05), but the Laplace algorithm always provided smaller Type I error rates than the PQL algorithm across all conditions. The power of the PQL and Laplace methods in detecting DIF was inadequate (below 0.80) in many simulation conditions except the larger cluster size and the number of clusters, and when the magnitude of DIF was small. The PQL method in detecting DIF was more powerful than the Laplace method. On the other hand, power improved very quickly for both estimation methods depending on the increase in the number of units at student and school levels, suggesting that the larger cluster size and number of clusters would provide the required accuracy.
In this study, the ratio of a variance estimate to its standard error was referred to as hit rate and this ratio was used in order to evaluate the point estimates of the random parameter estimates. Hit rates for the variance of student and school abilities level were always satisfactory (over 0.80) in all conditions. However, hit rates for the variance of DIF across school units were different depending on the magnitude of DIF variance. Once the magnitude of DIF variance was small, hit rates were always inadequate across all conditions. Once the magnitude of DIF variance was large, hit rates were satisfactory only in a few simulation conditions, but hit rates increased as the number of units at student and school levels increased. This suggests that larger number of units at level-2 and level-3 would provide satisfactory hit rates or the more stable estimates of the random DIF over group units.
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