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A linear model-based test for the heterogeneity of conditional correlations

Author

Listed:
  • Gregory Wilding
  • Xueya Cai
  • Alan Hutson
  • Zhangsheng Yu

Abstract

Current methods of testing the equality of conditional correlations of bivariate data on a third variable of interest (covariate) are limited due to discretizing of the covariate when it is continuous. In this study, we propose a linear model approach for estimation and hypothesis testing of the Pearson correlation coefficient, where the correlation itself can be modeled as a function of continuous covariates. The restricted maximum likelihood method is applied for parameter estimation, and the corrected likelihood ratio test is performed for hypothesis testing. This approach allows for flexible and robust inference and prediction of the conditional correlations based on the linear model. Simulation studies show that the proposed method is statistically more powerful and more flexible in accommodating complex covariate patterns than the existing methods. In addition, we illustrate the approach by analyzing the correlation between the physical component summary and the mental component summary of the MOS SF-36 form across a fair number of covariates in the national survey data.

Suggested Citation

  • Gregory Wilding & Xueya Cai & Alan Hutson & Zhangsheng Yu, 2011. "A linear model-based test for the heterogeneity of conditional correlations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(10), pages 2355-2366.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:10:p:2355-2366
    DOI: 10.1080/02664763.2011.559201
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    Citations

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    Cited by:

    1. Padayachee Trishanta & Khamiakova Tatsiana & Shkedy Ziv & Salo Perttu & Perola Markus & Burzykowski Tomasz, 2019. "A multivariate linear model for investigating the association between gene-module co-expression and a continuous covariate," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 18(2), pages 1-13, April.
    2. Alan D. Hutson & Gregory E. Wilding & Terry L. Mashtare & Albert Vexler, 2015. "Measures of biomarker dependence using a copula-based multivariate epsilon-skew-normal family of distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(12), pages 2734-2753, December.

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