Nonparametric Models for Crossed Mixed Effects Designs
Open Access
- Author:
- Gaugler, Trent
- Graduate Program:
- Statistics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- August 14, 2008
- Committee Members:
- Michael G Akritas, Committee Chair/Co-Chair
Rana Arnold, Committee Member
Thomas P Hettmansperger, Committee Member
D Wayne Osgood, Committee Member - Keywords:
- mixed effects models
hypothesis testing
nonparametric statistics
U-statistics
Neyman-Scott asymptotics - Abstract:
- This thesis deals with finding suitable testing procedures to test for the significance of effects in unbalanced two-way crossed mixed effects ANOVA models where both the random and fixed factors have a large number of levels. The random effects and the error term are allowed to be non-normal and heteroscedastic. The first part of the thesis is dedicated to the problem of testing for significance of the fixed main effect in a two-way crossed mixed effects design. Nonparametric testing procedures are suggested, and asymptotic calculations are carried out as the number of fixed and random factor levels tend to infinity, while the cell sample sizes remain fixed. The asymptotic theory does not rely on the normality assumption and the data are allowed to be heteroscedastic among the levels of the fixed effect and, conditionally, among the levels of the random effect. Moreover, this nonparametric model allows for unbalancedness, whereas the classical model has substantial difficulty handling this issue. We show that this testing procedure is comparable to the classical model under the classical assumptions, and outperforms the classical model when those assumptions are not met. The second part of the thesis addresses the problem of testing for significance of the random main and interaction effects in a two-way crossed mixed effects design. Nonparametric testing procedures are suggested, and asymptotic calculations are carried out as the number of fixed and random factor levels tend to infinity, while the cell sample sizes remain fixed. Again, the asymptotic theory does not rely on the normality assumption and the data are allowed to be heteroscedastic among the levels of the fixed effect and, conditionally, among the levels of the random effect. We show that this testing procedure is comparable to the classical model under the classical assumptions, and outperforms the classical model when those assumptions are not met.