A "mixed model" is proposed in which the problem of the appropriate assumptions to make about the joint distribution of the random main effects and interactions is solved by letting this joint distribution follow from more basic and "natural" assumptions about the cell means. The expectations of the mean squares ordinarily calculated turn out, with suitable definition of the variance components, to have the same values as those usually found in more restrictive models, and some of the customary tests and confidence intervals are justified, but some aspects appear to be novel. For example, the over-all test found for the fixed main effects and the associated multiple-comparison method require Hotelling's $T$.
Henry Scheffe. "A "Mixed Model" for the Analysis of Variance." Ann. Math. Statist. 27 (1) 23 - 36, March, 1956. https://doi.org/10.1214/aoms/1177728348