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A Method for Comparing Profiles of Repeated Measurements

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  • Michael G. Kenward

Abstract

A method for the comparison of profiles of repeated measurements is described which is based on Gabriel's ante‐dependence covariance structure. The method is intended for experiments in which no specific features of the profiles are known to be of interest a priori. The establishment of the appropriate order of ante‐dependence structure is discussed and a test statistic for the overall comparison of profiles under the structure is defined. It is shown how this statistic can be decomposed into statistically independent components which can be used to investigate the form of the differences among profiles. In particular the use of these components is proposed as an improvement over the practice of calculating a separate t‐test for each time of measurement. All the statistics described can be constructed from standard analysis of covariance sums of squares.

Suggested Citation

  • Michael G. Kenward, 1987. "A Method for Comparing Profiles of Repeated Measurements," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 296-308, November.
    • Handle: RePEc:bla:jorssc:v:36:y:1987:i:3:p:296-308
    DOI: 10.2307/2347788
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    Cited by:

    1. Karim, Md Aktar Ul & Bhagat, Supriya Ramdas & Bhowmick, Amiya Ranjan, 2022. "Empirical detection of parameter variation in growth curve models using interval specific estimators," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. Daniels, M.J. & Pourahmadi, M., 2009. "Modeling covariance matrices via partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2352-2363, November.
    3. 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.
    4. W. J. Krzanowski, 1999. "Antedependence models in the analysis of multi-group high-dimensional data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(1), pages 59-67.
    5. Mohsen Pourahmadi, 2002. "Graphical Diagnostics for Modeling Unstructured Covariance Matrices," International Statistical Review, International Statistical Institute, vol. 70(3), pages 395-417, December.
    6. 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.
    7. Arūnas P. Verbyla & Joanne Faveri & John D. Wilkie & Tom Lewis, 2018. "Tensor Cubic Smoothing Splines in Designed Experiments Requiring Residual Modelling," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(4), pages 478-508, December.
    8. Paul Zhang, 2005. "Multiple imputation of missing data with ante-dependence covariance structure," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(2), pages 141-155.
    9. Luo, Renwen & Pan, Jianxin, 2022. "Conditional generalized estimating equations of mean-variance-correlation for clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    10. Lin, Lijing & Higham, Nicholas J. & Pan, Jianxin, 2014. "Covariance structure regularization via entropy loss function," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 315-327.
    11. Vicente Núñez-Antón & Dale L. Zimmerman, 2000. "Modeling Nonstationary Longitudinal Data," Biometrics, The International Biometric Society, vol. 56(3), pages 699-705, September.
    12. Krishna Saha & B. Sutradhar, 1999. "On the Distribution of the Extremes of Unequally Correlated Normal Variables with Applications to Antedependent Cluster Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(2), pages 301-322, June.
    13. R. W. Payne, 2003. "DAVIES, C. S. Statistical Methods for the Analysis of Repeated Measurements. Springer, New York, 2002. xxiv + 415 pp. $79.95/£56.00. ISBN 0-387-95370-1," Biometrics, The International Biometric Society, vol. 59(1), pages 205-206, March.
    14. Dengke Xu & Zhongzhan Zhang & Liucang Wu, 2014. "Bayesian analysis of joint mean and covariance models for longitudinal data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(11), pages 2504-2514, November.
    15. Carter, Christopher K. & Wong, Frederick & Kohn, Robert, 2011. "Constructing priors based on model size for nondecomposable Gaussian graphical models: A simulation based approach," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 871-883, May.
    16. Huang, Chao & Farewell, Daniel & Pan, Jianxin, 2017. "A calibration method for non-positive definite covariance matrix in multivariate data analysis," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 45-52.
    17. Li, Erning & Pourahmadi, Mohsen, 2013. "An alternative REML estimation of covariance matrices in linear mixed models," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1071-1077.

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