This 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. / A Dissertation submitted to the Department of Educational Psychology and Learning Systems in partial fulfillment of the requirements for the degree of Doctor of
Philosophy. / Summer Semester, 2007. / January 30, 2007. / Multilevel Models, Differential Item Functioning, Generalized Linear Latent Mixed Model, Hierarchical Generalized Linear Model, Estimation Methods / Includes bibliographical references. / Akihito Kamata, Professor Directing Dissertation; Florentina Bunea, Outside Committee Member; Albert C. Oosterhof, Committee Member; Richard L. Tate, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_182005 |
| Contributors | Binici, Salih, 1974- (authoraut), Kamata, Akihito (professor directing dissertation), Bunea, Florentina (outside committee member), Oosterhof, Albert C. (committee member), Tate, Richard L. (committee member), Department of Educational Psychology and Learning Systems (degree granting department), Florida State University (degree granting institution) |
| Publisher | Florida State University, Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource, computer, application/pdf |
| Rights | This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them. |
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