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Permuting longitudinal data in spite of the dependencies

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  • Friedrich, Sarah
  • Brunner, Edgar
  • Pauly, Markus

Abstract

For general repeated measures designs the Wald-type statistic (WTS) is an asymptotically valid procedure allowing for unequal covariance matrices and possibly non-normal multivariate observations. The drawback of this procedure is its poor performance for small to moderate samples, i.e., decisions based on the WTS may become quite liberal. It is the aim of the present paper to improve the small-sample behavior of the WTS by means of a novel permutation procedure. In particular, it is shown that a permutation version of the WTS inherits its good large-sample properties while yielding a very accurate finite-sample control of the type-I error as shown in extensive simulations. Moreover, the new permutation method is motivated by a practical data set of a split plot design with a factorial structure on the repeated measures.

Suggested Citation

  • Friedrich, Sarah & Brunner, Edgar & Pauly, Markus, 2017. "Permuting longitudinal data in spite of the dependencies," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 255-265.
    • Handle: RePEc:eee:jmvana:v:153:y:2017:i:c:p:255-265
    DOI: 10.1016/j.jmva.2016.10.004
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    References listed on IDEAS

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    1. Rauf Ahmad, M. & Werner, C. & Brunner, E., 2008. "Analysis of high-dimensional repeated measures designs: The one sample case," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 416-427, December.
    2. Kenward, Michael G. & Roger, James H., 2009. "An improved approximation to the precision of fixed effects from restricted maximum likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2583-2595, May.
    3. Markus Pauly & Edgar Brunner & Frank Konietschke, 2015. "Asymptotic permutation tests in general factorial designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 461-473, March.
    4. Bruno Lecoutre, 1991. "A Correction for the ε̃ Approximate Test in Repeated Measures Designs With Two or More Independent Groups," Journal of Educational and Behavioral Statistics, , vol. 16(4), pages 371-372, December.
    5. Samuel Greenhouse & Seymour Geisser, 1959. "On methods in the analysis of profile data," Psychometrika, Springer;The Psychometric Society, vol. 24(2), pages 95-112, June.
    6. Fortunato Pesarin & Luigi Salmaso, 2010. "Finite-sample consistency of combination-based permutation tests with application to repeated measures designs," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(5), pages 669-684.
    7. Arnold Janssen, 2005. "Resampling student'st-type statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(3), pages 507-529, September.
    8. Konietschke, Frank & Bathke, Arne C. & Harrar, Solomon W. & Pauly, Markus, 2015. "Parametric and nonparametric bootstrap methods for general MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 291-301.
    9. Janssen, Arnold, 1997. "Studentized permutation tests for non-i.i.d. hypotheses and the generalized Behrens-Fisher problem," Statistics & Probability Letters, Elsevier, vol. 36(1), pages 9-21, November.
    10. Huynh Huynh & Leonard S. Feldt, 1976. "Estimation of the Box Correction for Degrees of Freedom from Sample Data in Randomized Block and Split-Plot Designs," Journal of Educational and Behavioral Statistics, , vol. 1(1), pages 69-82, March.
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    Cited by:

    1. Friedrich, Sarah & Pauly, Markus, 2018. "MATS: Inference for potentially singular and heteroscedastic MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 166-179.
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    4. Dennis Dobler & Markus Pauly, 2018. "Bootstrap- and permutation-based inference for the Mann–Whitney effect for right-censored and tied data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 639-658, September.
    5. Zimmermann, Georg & Pauly, Markus & Bathke, Arne C., 2020. "Multivariate analysis of covariance with potentially singular covariance matrices and non-normal responses," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    6. Umlauft, Maria & Placzek, Marius & Konietschke, Frank & Pauly, Markus, 2019. "Wild bootstrapping rank-based procedures: Multiple testing in nonparametric factorial repeated measures designs," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 176-192.
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    8. Amitava Mukherjee & Marco Marozzi, 2019. "A class of percentile modified Lepage-type tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(6), pages 657-689, August.
    9. Pini, Alessia & Sørensen, Helle & Tolver, Anders & Vantini, Simone, 2023. "Local inference for functional linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).

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