Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T20:02:41.806Z Has data issue: false hasContentIssue false
  • English
  • Français

Correlations and regressions in ‘family’ data

Published online by Cambridge University Press:  14 July 2016

Cedric A. B. Smith
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the situation in which individuals occur in ‘families' or similar groups, individuals within a ‘family' being correlated with one another, as for example a biological population. In such a population, the number of individuals will usually vary from one family to another. We assume that a sample chosen from the population consists of whole families rather than unrelated individuals. A similar situation might occur in experimental design, if individuals occur in ‘blocks' (of varying sizes) within which they share a common environment. In the simplest case considered here two measurements are made on each individual, namely y, the character of interest, and x (not necessarily a random variable), some other character which is believed to influence y. We discuss how to estimate the regression of y on x, and the within and between family variance components for y (and hence the intrafamily correlation) when the effect of x is eliminated. Generalizations of this are briefly discussed.

Keywords

REGRESSIONGENETIC CORRELATIONQUANTITATIVE GENETICSUNBALANCED BLOCKSVARIANCE COMPONENTSEFFICIENT ESTIMATIONSUPPORT FUNCTION
Type
Part 1 — Genetics
Information
Journal of Applied Probability , Volume 19 , Issue A , 1982 , pp. 45 - 57
Copyright
Copyright © 1982 Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Cauchy, A. (1840) Sur les moyens d'éviter les erreurs dans les calculs numériques. C. R. Acad. Sci. Paris 11, 789–798.Google Scholar
Colson, J. (1726) Negativo-affirmative arithmetick. Phil. Trans. R. Soc. London 34, 161–174.Google Scholar
Edwards, A. W. F. (1972) Likelihood. Cambridge University Press.Google Scholar
Fieller, ?. C. and Smith, C. A. B. (1951) Note on the analysis of variance and intraclass correlation. Ann. Eugenics 16, 97–104.Google Scholar
Fisher, R. A. (1918) The correlation between relatives on the supposition of Mendelian inheritance. Trans. R. Soc. Edinburgh 52, 399–433.Google Scholar
Fisher, R. A. (1925) Statistical Methods for Research Workers. Oliver and Boyd, Edinburgh.Google Scholar
Forrest, D. W. (1974) Francis Galton: The Life and Work of a Victorian Genius. Elek, London.Google Scholar
Galton, F. (1877) Typical laws of heredity. Proc. R. Inst., London 8, 282–301.Google Scholar
Galton, F. (1885a) Presidential address. Section H, Anthropology. British Association Reports 55, 1206–1214.Google Scholar
Galton, F. (1885b) Co-relations and their measurement, chiefly from anthropometric data. Proc. R. Soc. London 45, 135–145.Google Scholar
Galton, F. (1908) Memories of my Life. Methuen, London.Google Scholar
Li, C. C. and Sacks, L. (1954) The derivation of joint distribution and correlation between relatives by the use of stochastic matrices. Biometrics 10, 347–360.Google Scholar
Menger, K. (1953) Calculus, a Modern Approach. Illinois Institute of Technology, Chicago.Google Scholar
Pearson, K. (1930) Life Letters and Labours of Francis Galton , Vol. III?. Cambridge University Press.Google Scholar
Sahai, H. (1979) A bibiliography on variance components. Internat. Statist. Rev. 43, 177–222.Google Scholar
Smith, C. A. B. (1969) Biomathematics , Vol. 2. Griffin, London.Google Scholar
Smith, C. A. B. (1974) Looking glass numbers. J. Recreational Math. 7, 299–305.Google Scholar
Smith, C. A. B. (1980a) Estimating genetic correlations. Ann. Hum. Genet. 43, 265–284.Google Scholar
Smith, C. A. B. (1980b) Further remarks on estimating genetic correlations. Ann. Hum. Genet. 44, 95–105.CrossRefGoogle ScholarPubMed
Wright, S. (1920) The relative importance of heredity and environment in determining the piebald pattern of guinea pigs. Proc. Nat. Acad. Sci. 6, 320–332.Google Scholar
Wright, S. (1923) The theory of path coefficients. Genetics 8, 239–255.Google Scholar