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Testing of multivariate repeated measures data with block exchangeable covariance structure

Author

Listed:
  • Ivan Žežula

    (P. J. Šafárik University)

  • Daniel Klein

    (P. J. Šafárik University)

  • Anuradha Roy

    (The University of Texas at San Antonio)

Abstract

A new hypothesis testing of equality of mean vectors in two populations using $$D^2$$ D 2 statistic for multivariate repeated measures data on q response variables at p sites or time points in a block exchangeable covariance matrix setting is proposed. The minimum sample size needed for our new test is only $$q +1$$ q + 1 , unlike $$pq +1$$ p q + 1 in Hotelling’s $$T^2$$ T 2 test. The new test is very efficient in small sample scenario, when the number of observations is not adequate to estimate the $$pq \times pq$$ p q × p q dimensional unknown unstructured variance–covariance matrix. Some simulation studies are performed to compare the power of the new $$D^2$$ D 2 test and the existing $$BT^2$$ B T 2 test. The performance of the proposed $$D^2$$ D 2 test is demonstrated with the two medical data sets.

Suggested Citation

  • Ivan Žežula & Daniel Klein & Anuradha Roy, 2018. "Testing of multivariate repeated measures data with block exchangeable covariance structure," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 360-378, June.
    • Handle: RePEc:spr:testjl:v:27:y:2018:i:2:d:10.1007_s11749-017-0549-z
    DOI: 10.1007/s11749-017-0549-z
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    References listed on IDEAS

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    1. Roy, Anuradha & Leiva, Ricardo & Žežula, Ivan & Klein, Daniel, 2015. "Testing the equality of mean vectors for paired doubly multivariate observations in blocked compound symmetric covariance matrix setup," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 50-60.
    2. Viroli, Cinzia, 2012. "On matrix-variate regression analysis," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 296-309.
    3. Lin, Tsung I. & Ho, Hsiu J. & Chen, Chiang L., 2009. "Analysis of multivariate skew normal models with incomplete data," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2337-2351, November.
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