Variance-component estimation from human sibship data.

The large-sample relative efficiencies of the analysis-of-variance (ANOVA) estimators of variance components and the intraclass correlation coefficient rho are investigated for the unbalanced single classification in the context of family studies. The efficiency of an analysis based on the method of unweighted group means is also investigated. From a Monte Carlo study which generates the group sizes from typical family-size distributions it is found that the relative efficiency of the ANOVA estimators of the between-group variance component exceeds 95% for values of .2 less than or equal to rho less than or equal to .4, but can fall below 60% for values of rho that are very close to zero. For the estimation of the between-group variance component the method of unweighted means tends to be preferable to the ANOVA method only if rho greater than .5.

[1]  S. R. Searle,et al.  A Comparison of Variance Component Estimators , 1976 .

[2]  G. Koch.  A general approach to estimation of variance components , 1967 .

[3]  A Donner,et al.  The estimation of intraclass correlation in the analysis of family data. , 1980, Biometrics.

[4]  C. A. Smith,et al.  ON THE ESTIMATION OF INTRACLASS CORRELATION , 1957 .

[5]  A. Donner,et al.  The large sample variance of an intraclass correlation , 1980 .

[6]  Alan Robertson,et al.  180. Note: Weighting in the Estimation of Variance Components in the Unbalanced Single Classification , 1962 .

[7]  L. Lamotte.  Invariant Quadratic Estimators in the Random, One-Way ANOVA Model , 1976 .

[8]  D. Harville.  Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems , 1977 .

[9]  Gary G. Koch,et al.  Some Further Remarks Concerning "A General Approach to the Estimation of Variance Components" , 1968 .

[10]  L. Herbach.  Properties of Model II--Type Analysis of Variance Tests, A: Optimum Nature of the $F$-Test for Model II in the Balanced Case , 1959 .

[11]  S. R. Searle.  A Biometrics Invited Paper. Topics in Variance Component Estimation , 1971 .

[12]  S. R. Searle,et al.  Restricted Maximum Likelihood (REML) Estimation of Variance Components in the Mixed Model , 1976 .

[13]  Crump Sl,et al.  The present status of variance component analysis. , 1951 .

[14]  H. D. Patterson,et al.  Recovery of inter-block information when block sizes are unequal , 1971 .

[15]  R. Anderson,et al.  Comparisons of Designs and Estimation Procedures for Estimating Parameters in a Two-Stage Nested Process , 1967 .