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Methods for estimating variance components from unbalanced data are given, in Henderson 1953 for both the random model and the mixed model. The calculations involved in the latter case are somewhat tedious and usually not computationally feasible for data having many classes. This paper outlines the analysis for unbalanced data from a two-way classification with one classification considered fixed. Simplified computing procedures are presented suitable for a large number of levels in the random classification and a reasonable number of levels of the fixed classification.
Searle et al. (1961) studied this question.