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An Alternative Matrix Transformation To The F Test Statistic For Clustered Data

Author

Listed:
  • Intarapak Sukanya

    (Department of Mathematics, Faculty of Science, Srinakharinwirot University, Bangkok, Thailand .)

  • Supapakorn Thidaporn

    (Department of Statistics, Faculty of Science, Kasetsart University, Bangkok, Thailand .)

Abstract

For the regression analysis of clustered data, the error of cluster data violates the independence assumption. Consequently, the test statistic based on the ordinary least square method leads to incorrect inferences. To overcome this issue, the transformation is required to apply to the observations. In this paper we propose an alternative matrix transformation that adjusts the intra-cluster correlation with Householder matrix and apply it to the F test statistic based on generalized least squares procedures for the regression coefficients hypothesis. By Monte Carlo simulations of the balanced and unbalanced data, it is found that the F test statistic based on generalized least squares procedures with Adjusted Householder transformation performs well in terms of the type I error rate and power of the test.

Suggested Citation

  • Intarapak Sukanya & Supapakorn Thidaporn, 2019. "An Alternative Matrix Transformation To The F Test Statistic For Clustered Data," Statistics in Transition New Series, Polish Statistical Association, vol. 20(1), pages 153-169, March.
    • Handle: RePEc:vrs:stintr:v:20:y:2019:i:1:p:153-169:n:6
    DOI: 10.21307/stattrans-2019-009
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    References listed on IDEAS

    as
    1. Rao, J. N. K. & Wang, S. G., 1995. "The Power of F Tests Under Regression Models with Nested Error Structure," Journal of Multivariate Analysis, Elsevier, vol. 53(2), pages 237-246, May.
    2. Sandra M. Eldridge & Obioha C. Ukoumunne & John B. Carlin, 2009. "The Intra‐Cluster Correlation Coefficient in Cluster Randomized Trials: A Review of Definitions," International Statistical Review, International Statistical Institute, vol. 77(3), pages 378-394, December.
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