Testing for interaction in two-way random and mixed effects models: The fully nonparametric approach

Biometrics

Volumn 67, Issue 4, 2011, Pages 1314-1320

  Gaugler, Trent ^a   Akritas, Michael G ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Hypothesis testing; Large number of factor levels; Model building; Symmetry assumption

Indexed keywords

ERROR ANALYSIS; RANDOM PROCESSES;

HYPOTHESIS TESTING; INTERACTION TERM; LARGE NUMBER OF FACTOR LEVEL; NUMBER OF FACTORS; RANDOM EFFECTS; RANDOM EFFECTS MODEL; RANDOM FACTORS; SYMMETRY ASSUMPTION; TEST PROCEDURES; TWO WAYS;

STATISTICAL TESTS;

DATA SET; DESIGN; ERROR ANALYSIS; HYPOTHESIS TESTING; LINEARITY; NUMERICAL MODEL; PARAMETERIZATION;

EID: 83655190516     PISSN: 0006341X     EISSN: 15410420     Source Type: Journal    
DOI: 10.1111/j.1541-0420.2011.01579.x     Document Type: Article

References (17)

1. Aitchison, J. (1986). The Statistical Analysis of Compositional Data. London: Chapman and Hall.
2. Akritas, M. G. and Arnold, S. F. (2000). Asymptotics for analysis of variance when the number of levels is large. Journal of the American Statistical Association 95, 212-226.
3. Akritas, M. G. and Papadatos, N. (2004). Heteroscedastic one-way ANOVA and lack-of-fit tests. Journal of the American Statistical Association 99, 368-382.
4. Arnold, S. F. (1981). The Theory of Linear Models and Multivariate Analysis. New York: John Wiley and Sons.
5. Arnold, S. F. (1984). The asymptotic validity of invariant procedures for the repeated measures model and multivariate linear model. Journal of Multivariate Analysis 15, 325-335.
6. Bathke, A. (2002). ANOVA for a large number of treatments. Mathematical Methods of Statistics 11, 1118-1132.
7. Boos, D. D. and Brownie, C. (1994). Type I error robustness of ANOVA and ANOVA on ranks when the number of treatments is large. Biometrics 50, 542-549.
8. Cornfield, J. and Tukey, J. W. (1956). Average values of mean squares in factorials. Annals of Mathematical Statistics 27, 907-949.
9. Gupta, A. K., Harrar, S. W., and Fujikoshi, Y. (2006). Asymptotics for testing hypothesis in some multivariate variance components model under non-normality. Journal of Multivariate Analysis 97, 148-178.
10. Hocking, R. R. (1973). A discussion of the two-way mixed model. The American Statistician 27, 148-152.
11. Khuri, A. I., Mathew, T., and Sinha, B. K. (1998). Statistical Tests for Mixed Linear Models. New York: John Wiley.
12. Scheffé, H. (1959). The Analysis of Variance. New York: John Wiley.
13. Searle, S. R. (1971). Linear Models. New York: John Wiley and Sons.
14. Searle, S. R. (1987). Linear Models for Unbalanced Data. New York: John Wiley and Sons.
15. Searle, S. R., Casella, G., and McCulloch, C. E. (1992). Variance Components. New York: John Wiley and Sons.
16. Wang, L. and Akritas, M. G. (2006). Two-way heteroscedastic ANOVA when the number of levels is large. Statistica Sinica 16, 1387-1408.
17. Winer, B. (1971). Statistical Principles in Experimental Design. New York: McGraw-Hill.