An estimate of the covariance between variables which are not jointly observed |
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Authors: | Robert Cudeck |
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Institution: | (1) Department of Psychology, University of Minnesota, 75 East River Road, 55455 Minneapolis, MN |
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Abstract: | Situations sometimes arise in which variables collected in a study are not jointly observed. This typically occurs because
of study design. An example is an equating study where distinct groups of subjects are administered different sections of
a test. In the normal maximum likelihood function to estimate the covariance matrix among all variables, elements corresponding
to those that are not jointly observed are unidentified. If a factor analysis model holds for the variables, however, then
all sections of the matrix can be accurately estimated, using the fact that the covariances are a function of the factor loadings.
Standard errors of the estimated covariances can be obtained by the delta method. In addition to estimating the covariance
matrix in this design, the method can be applied to other problems such as regression factor analysis. Two examples are presented
to illustrate the method.
This research was partially supported by NIMH grant MH5-4576 |
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Keywords: | missing data covariance matrix estimation factor analysis |
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