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The Intraclass Covariance Matrix

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Introduced by C.R. Rao in 1945, the intraclass covariance matrix has seen little use in behavioral genetic research, despite the fact that it was developed to deal with family data. Here, I reintroduce this matrix, and outline its estimation and basic properties for data sets on pairs of relatives. The intraclass covariance matrix is appropriate whenever the research design or mathematical model treats the ordering of the members of a pair as random. Because the matrix has only one estimate of a population variance and covariance, both the observed matrix and the residual matrix from a fitted model are easy to inspect visually; there is no need to mentally average homologous statistics. Fitting a model to the intraclass matrix also gives the same log likelihood, likelihood-ratio (LR) χ2, and parameter estimates as fitting that model to the raw data. A major advantage of the intraclass matrix is that only two factors influence the LR χ2—the sampling error in estimating population parameters and the discrepancy between the model and the observed statistics. The more frequently used interclass covariance matrix adds a third factor to the χ2—sampling error of homologous statistics. Because of this, the degrees of freedom for fitting models to an intraclass matrix differ from fitting that model to an interclass matrix. Future research is needed to establish differences in power—if any—between the interclass and the intraclass matrix.

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References

  • S. Konishi C. G. Khatri C. R. Rao (1991) ArticleTitleInferences on multivariate measures on interclass and intraclass correlations in familial data J. Roy. Stat. Soc B. (Met) 53 649–659

    Google Scholar 

  • S. A. Mulaik (1972) The Foundations of Factor Analysis McGraw Hill New York

    Google Scholar 

  • M. C. Neale S. M. Boker G. Xie H. Maes (2002) Mx: Statistical Modeling EditionNumber6 Virginia Institute for Psychiatric and Behavioral Genetics Virginia Commonwealth University Richmond VA

    Google Scholar 

  • C. R. Rao (1945) ArticleTitleFamilial correlations or the multivariate generalizations of the intraclass correlation Curr. Sci. 14 66–67

    Google Scholar 

  • M. S. Srivastava K. J. Keen R. S. Katapa (1988) ArticleTitleEstimation of interclass and intraclass correlations in multivariate family data Biometrics 44 141–150

    Google Scholar 

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Correspondence to Gregory Carey.

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Carey, G. The Intraclass Covariance Matrix. Behav Genet 35, 667–670 (2005). https://doi.org/10.1007/s10519-005-5877-1

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  • DOI: https://doi.org/10.1007/s10519-005-5877-1

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