Finding MLE of Patterned Covariance Matrices by the EM Algorithm

Author(s):

Rubin, Donald B.; Szatrowski, Ted H.

Publication Year:

1981

Report Number:

RR-81-33

Source:

ETS Research Report

Document Type:

Report

Page Count:

8

Subject/Key Words:

Analysis of Covariance, Data Analysis, Multivariate Analysis, Statistical Analysis

Abstract

It is often useful to model multivariate normal data with a priori restrictions on the covariance matrix, and in particular, to fit normal data with patterns in the covariance matrix. However, many patterned covariance matrices do not have explicit maximum likelihood estimates (MLEs). Some of these patterned covariance matrices without explicit MLEs are submatrices of larger patterned covariance matrices with explicit MLEs. In such cases, the smaller covariance matrix can be viewed as the covariance matrix for observed variables and the larger covariance matrix can be viewed as the covariance matrix for both observed and missing variables. The advantage of this perspective is that the EM algorithm can be used to calculate the desired m.l.e.'s for the original problem. Two examples are presented.

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