×

Interaction testing: residuals-based permutations and parametric bootstrap in continuous, count, and binary data. (English) Zbl 1416.92153

Summary: To obtain statistical inference about interaction hypotheses without making strong distributional assumptions, permutation tests based on permuting the outcomes are often being used. It was shown that in continuous and binary data these tests might not be even approximately valid and parametric bootstrap was suggested as a viable alternative, outperforming such permutation tests. We describe an alternative permutation test, permuting the null hypothesis residuals rather than the outcome. Using simulations, we compare accuracy across the permutation tests and parametric bootstrap, studying continuous, binary, and additionally count data. Finally, we address power.

MSC:

92D30 Epidemiology
62P10 Applications of statistics to biology and medical sciences; meta analysis

Software:

R; bootlib
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Anderson, M. J. (2001). Permutation tests for univariate and multivariate analysis of variance and regression. Canadian Journal of Fisheries and Aquatic Sciences, 58:626-639.; Anderson, M. J., Permutation tests for univariate and multivariate analysis of variance and regression, Canadian Journal of Fisheries and Aquatic Sciences, 58, 626-639 (2001)
[2] Anderson, M. J., and Robinson, J. (2001). Permutation tests for linear models. Australina & New Zealand Journal of Statistics, 43:75-88.; Anderson, M. J.,; Robinson, J., Permutation tests for linear models, Australina & New Zealand Journal of Statistics, 43, 75-88 (2001) · Zbl 0992.62043
[3] Bůžková, P., Lumley, T., and Rice, K. (2011). Permutation and parametric bootstrap tests for gene-gene and gene-environment interactions. Annals of Human Genetics, 75:36-45.; Bůžková, P.; Lumley, T.,; Rice, K., Permutation and parametric bootstrap tests for gene-gene and gene-environment interactions, Annals of Human Genetics, 75, 36-45 (2011)
[4] Brown, B. M., and Maritz, J. S. (1982). Distribution-free methods in regression. Australian Journal of Statistic, 24:318-331.; Brown, B. M.,; Maritz, J. S., Distribution-free methods in regression, Australian Journal of Statistic, 24, 318-331 (1982) · Zbl 0507.62038
[5] Cox, D. R. (1984). Interaction (with discussion. International Statistical Review, 52:1-31.; Cox, D. R., Interaction (with discussion, International Statistical Review, 52, 1-31 (1984) · Zbl 0562.62061
[6] Cox, D. R., and Hinkley, D. V. (1979). Theoretical Statistics. Boca Raton, FL, USA: CRC Press.; Cox, D. R.; Hinkley, D. V., Theoretical Statistics (1979) · Zbl 0334.62003
[7] Davison, A. C., and Hinkley, D. V. (1997). Bootstrap Methods and Their Applications. New York, NY, USA: Cambridge University Press.; Davison, A. C.; Hinkley, D. V., Bootstrap Methods and Their Applications (1997) · Zbl 0886.62001
[8] Ernst, M. D. (2004). Permutation methods: A basis for exact inference. Statistical Science, 19:676-685.; Ernst, M. D., Permutation methods: A basis for exact inference, Statistical Science, 19, 676-685 (2004) · Zbl 1100.62563
[9] Fisher, R. A. (1935). The Design of Experiments. Edinburgh: Oliver and Boyd.; Fisher, R. A., The Design of Experiments (1935)
[10] Freedman, D., and Lane, D. (1983). A nonstochastic interpretation of reported significance levels. Journal of Business and Economic Statistics, 1:292-298.; Freedman, D.,; Lane, D., A nonstochastic interpretation of reported significance levels, Journal of Business and Economic Statistics, 1, 292-298 (1983) · Zbl 0523.62041
[11] Higgins, J. J. (2004). An Introduction to Modern Nonparametric Statistics. Pacific Grove, CA: Thomson, Brooks/Cole.; Higgins, J. J., An Introduction to Modern Nonparametric Statistics (2004)
[12] Manly, B. F. J. (1997). Randopmization, Bootstrap and Monte Carlo Methods in Biology. 2nd Edition. London: Chapman & Hall/CRC.; Manly, B. F. J., Randopmization, Bootstrap and Monte Carlo Methods in Biology (1997) · Zbl 0918.62081
[13] O’Gorman, T. W. (2012). Adaptive Tests of Significance Using Permutations of Residuals with R and SAS. Hoboken, NJ, USA: John Wiley & Sons.; O’Gorman, T. W., Adaptive Tests of Significance Using Permutations of Residuals with R and SAS (2012) · Zbl 1281.62010
[14] R Core Team (2014). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, http://www.R-project.org/.; (2014)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.