Recommended Readings

See the following texts for more information on variance components analysis (for complete bibliographic information, click on the reference) :

A discussion of choosing the appropriate type of sum of squares for the ANOVA method can be found in 1.

For a summary of the MINQUE method, see 2. For an in-depth discussion of the method, see 3. Further details of the MINQUE estimation procedure can be found in 4.

For technical details of computing the maximum likelihood estimates, see 5, 6, and 7.

For details about the restricted maximum likelihood estimates, see 8, 9, and 10.

1 Speed, F. M. 1979. Choice of sums of squares for estimation of components of variance. In: Proceedings of the Statistical Computing Section, . , eds. Alexandria, Va.: American Statistical Association.
2 Rao, C. R. 1973. Linear statistical inference and its applications, 2nd ed. New York: John Wiley and Sons.
3 Rao, C. R., and J. Kleffe. 1988. Estimation of variance components and applications. Amsterdam: North-Holland.
4 Giesbrecht, F. G. 1983. An efficient procedure for computing MINQUE of variance components and generalized least squares estimates of fixed effects. Communications in Statistics, Part A - Theory and Methods, 12:, 2169-2177.
5 Hemmerle, W. J., and H. O. Harley. 1973. Computing maximum likelihood estimates for the mixed A.O.V. model using the W transformation. Technometrics, 15:, 819-831.
6 Jennrich, R. I., and P. F. Sampson. 1976. Newton-Raphson and related algorithms for maximum likelihood variance component estimation. Technometrics, 18:, 11-17.
7 Searle, S. R., G. Casella, and C. E. McCulloch. 1992. Variance Components. New York: John Wiley and Sons.
8 Patterson, H. D., and R. Thompson. 1971. Recovery of inter-block information when block sizes are unequal. Biometrika, 58:, 545-554.
9 Corbeil, R. R., and S. R. Searle. 1976. Restricted maximum likelihood (REML) estimation of variance components in the mixed model. Technometrics, 18:, 31-38.
10 Searle, S. R., G. Casella, and C. E. McCulloch. 1992. Variance Components. New York: John Wiley and Sons.