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Estimation of a Model with Multiple Indicators and Multiple Causes of a Single Latent Variable

Karl G. Joreskog and Arthur S. Goldberger
Journal of the American Statistical Association
Vol. 70, No. 351 (Sep., 1975), pp. 631-639
DOI: 10.2307/2285946
Stable URL: http://www.jstor.org/stable/2285946
Page Count: 9
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Estimation of a Model with Multiple Indicators and Multiple Causes of a Single Latent Variable
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Abstract

We consider a model in which one observes multiple indicators and multiple causes of a single latent variable. In terms of the multivariate regression of the indicators on the causes, the model implies restrictions of two types: (i) the regression coefficient matrix has rank one, (ii) the residual variance-covariance matrix satisfies a factor analysis model with one common factor. The first type of restriction is familiar to econometricians and the second to psychometricians. We derive the maximum-likelihood estimators and their asymptotic variance-covariance matrix. Two alternative "limited information" estimators are also considered and compared with the maximum-likelihood estimators in terms of efficiency.

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