Nonparametric modeling via two-way mixed effects design

Year 2021, Volume: 70 Issue: 1, 194 - 204, 30.06.2021

Sevgi Demircioğlu , Bilgehan Güven

https://doi.org/10.31801/cfsuasmas.726132

Abstract

The classical F-test for testing the hypothesis of no fixed main effects in a mixed effects design is valid under the assumption of normality, symmetry and variance homogeneity of the error terms assumption. We consider the two-way mixed effects design which does not require these three assumptions. A test procedure for the hypothesis of no main fixed effects is developed under this flexible model. The asymptotic distribution of the test statistic is studied for a large number of levels of the random effects.

Keywords

Two-way Mixed Effects Design, Symmetry Assumption, Hypothesis Testing, Asymptotic Normality

References

• Anderson, T. W., An Introduction to Multivariate Statistical Analysis (2d ed.), Wiley, New York, 1984.
• Gaugler, T., Akritas, M. G., Testing for interaction in two-way random and mixed effects models: the fully nonparametric approach, Biometrics, 67 (4) (2011), 1314-1320.
• Gaugler, T., Akritas, M. G., Mixed effects design: the symmetry assumption and missing data, Journal of the American Statistical Association, 107 (499) (2012), 1230-1238.
• Gaugler, T., Akritas, M. G., Testing for main random effects in two-way random and mixed models: modifying the F statistic, Journal of Probability and Statistics, 2013 (2013), Article ID 708540, 11 pages.
• Güven, B., A mixed model for complete three or higher way layout with two random effects factors, Journal of Multivariate Analysis, 139 (2015), 45-55.
• Imhof, J. P., A mixed model for complete three or higher way layout with two random effects factors, Annals of Mathematical Statistics, 31 (4) (1960), 906-928.
• Khattree, R., Rao, C. R., Handbook of Statistics 22, North-Holland, Amsterdam, 2003.
• Khuri, A. I., Sinha, B. K., Statistical Test for Mixed Linear Models, Wiley, New York, 1998.
• Scheffé, H., The Analysis of Variance, Wiley, New York, 1959.
• Serfling, R. J., Approximation Theorems of Mathematical Statistics, Wiley, New York, 2002.