Permutation Tests for Random Effects in Linear Mixed Models

Biometrics

Volumn 68, Issue 2, 2012, Pages 486-493

  Lee, Oliver E ^a   Braun, Thomas M ^a  

^a UNIVERSITY OF MICHIGAN SCHOOL OF PUBLIC HEALTH   (United States)

Author keywords

Hypothesis testing; Longitudinal data; Variance components

Indexed keywords

RANDOM PROCESSES;

ASYMPTOTICS; HYPOTHESIS TESTING; LIKELIHOOD RATIO TESTS; LINEAR MIXED MODELS; LONGITUDINAL DATA; NULL HYPOTHESIS; PARAMETER SPACES; PERMUTATION TESTS; RANDOM EFFECTS; VARIANCE COMPONENTS;

STATISTICAL TESTS;

CANCER; COMPUTER SIMULATION; DATA SET; LINEARITY; NUMERICAL MODEL; STATISTICAL ANALYSIS;

EID: 84862880796     PISSN: 0006341X     EISSN: 15410420     Source Type: Journal    
DOI: 10.1111/j.1541-0420.2011.01675.x     Document Type: Article

References (25)

1. Bates, D., Maechler, M., and Bolker, B. (2011). lme4: Linear Mixed-Effects Models using S4 Classes. R package version 0.999375-39. Vienna, Austria: CRAN.
2. Breslow, N. E. and Clayton, D. G. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 88, 9-25.
3. Commenges, D. (2003). Transformations which preserve exchangeability and application to permutation tests. Journal of Nonparametric Statistics 15, 171-185.
4. Crainiceanu, C. M. and Ruppert, D. (2004). Likelihood ratio tests in linear mixed models with one variance component. Journal of the Royal Statistical Society, Series B 66, 165-185.
5. Dwass, M. (1957). Modified randomization tests for nonparametric hypotheses. Annals of Mathematical Statistics 28, 181-187.
6. Fitzmaurice, G. M. and Ibrahim, J. G. (2007). A note on permutation tests for variance components in multilevel generalized linear mixed models. Biometrics 63, 942-946.
7. Good, P. I. (2005). Permutation, Parametric, and Bootstrap Tests of Hypotheses, 3rd edition. New York: Springer-Verlag Inc.
8. Greven, S., Crainiceanu, C. M., Küchenhoff, H., and Peters, A. (2008). Restricted likelihood ratio testing for zero variance components in linear mixed models. Journal of Computational and Graphical Statistics 17, 870-891.
9. Henderson, C. R. (1950). Estimation of genetic parameters. Annals of Mathematical Statistics 21, 309-310.
10. Hoeffding, W. (1952). The large-sample power of tests based on permutation of observations. Annals of Mathematical Statistics 23, 169-192.
11. Kinney, S. K. and Dunson, D. B. (2008). Fixed and random effects selection in linear and logistic models. Biometrics 63, 690-698.
12. Klein, J. P., Klotz, J. H., and Grever, M. R. (1984). A biological marker model for predicting disease transitions. Biometrics 40, 927-936.
13. Laird, N. M. and Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics 38, 963-974.
14. Molenberghs, G. and Verbeke, G. (2007). Likelihood ratio, score, and Wald tests in a constrained parameter space. The American Statistician 61, 22-27.
15. Morrell, C. H. (1998). Likelihood ratio testing of variance components in the linear mixed-effects model using restricted maximum likelihood. Biometrics 54, 1560-1568.
16. Öfversten, J. (1993). Exact tests for variance components in unbalanced mixed linear models. Biometrics 49, 45-57.
17. Robinson, G. K. (1991). That BLUP is a good thing: The estimation of random effects. Statistical Science 6, 15-51.
18. Ruppert, D., Wand, M. P., and Carroll, R. J. (2003). Semiparametric Regression. Cambridge; New York: Cambridge University Press.
19. Saville, B. R. and Herring, A. H. (2009). Testing random effects in the linear mixed model using approximate Bayes factors. Biometrics 65, 369-376.
20. Schmoyer, R. L. (1994). Permutation tests for correlation in regression errors. Journal of the American Statistical Association 89, 1507-1516.
21. Self, S. G. and Liang, K. Y. (1987). Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. Journal of the American Statistical Association 82, 605-610.
22. Silvapulle, M. J. (1992). Robust Wald-type tests of one-sided hypotheses in the linear model. Journal of the American Statistical Association 87, 156-161.
23. Silvapulle, M. J. and Silvapulle, P. (1995). A score test against one-sided alternatives. Journal of the American Statistical Association 90, 342-349.
24. Stram, D. O. and Lee, J. W. (1994). Variance components testing in the longitudinal mixed effects model. Biometrics 50, 1171-1177.
25. Verbeke, G. and Molenberghs, G. (2003). The use of score tests for inference on variance components. Biometrics 59, 254-262.