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Parameter expansion for estimation of reduced rank covariance matrices (Open Access publication)
Genetics Selection Evolution volume 40, Article number: 3 (2008)
Abstract
Parameter expanded and standard expectation maximisation algorithms are described for reduced rank estimation of covariance matrices by restricted maximum likelihood, fitting the leading principal components only. Convergence behaviour of these algorithms is examined for several examples and contrasted to that of the average information algorithm, and implications for practical analyses are discussed. It is shown that expectation maximisation type algorithms are readily adapted to reduced rank estimation and converge reliably. However, as is well known for the full rank case, the convergence is linear and thus slow. Hence, these algorithms are most useful in combination with the quadratically convergent average information algorithm, in particular in the initial stages of an iterative solution scheme.
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Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Meyer, K. Parameter expansion for estimation of reduced rank covariance matrices (Open Access publication). Genet Sel Evol 40, 3 (2008). https://doi.org/10.1186/1297-9686-40-1-3
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DOI: https://doi.org/10.1186/1297-9686-40-1-3