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New progress in enumeration of mixed models. (English) Zbl 1060.62074

From the paper: The number of non-isomorphic fixed effects ANOVA models is know for \(n\leq 16\), since there is a one-to-one correspondence with posets. A. Hess and H. Iyer [Enumeration of mixed linear models and SAS macro for computation of confidence intervals for variance components. Conf. Appl. Stat. Agriculture; Kansas State Univ. (2001)] have worked on the problem of enumerating non-isomorphic mixed models (with or without constraints). A mixed model is said to be constrained if no fixed factor is nested with a random factor. They obtained results for mixed models of size at most 5, proving there are 576 mixed models with constraints. In this article, using previous results about posets, we present a new algorithm, and obtain results for mixed models of size at most 10.

MSC:

62J10 Analysis of variance and covariance (ANOVA)
62J12 Generalized linear models (logistic models)
06A07 Combinatorics of partially ordered sets

Software:

OEIS; SAS
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