Correlations and regressions in ‘family’ data

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 assum...

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Bibliographic Details
Published in:Journal of applied probability 1982, Vol.19 (A), p.45-57
Main Author: Smith, Cedric A. B.
Format: Article
Language:English
Subjects:
Approximation
Correlations
Gaussian distributions
Genetics
Mathematical notation
Part 1 — Genetics
Random variables
Regression coefficients
Sisters
Standard error
Statistical variance
Unbiased estimators
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Summary: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.
ISSN:0021-9002
1475-6072
DOI:10.2307/3213549