© 1974 by Biometrika Trust
Exploratory latent structure analysis using both identifiable and unidentifiable models
Department of Statistics, University of Chicago
This paper considers a wide class of latent structure models. These models can serve as possible explanations of the observed relationships among a set of m manifest polytomous variables. The class of models considered here includes both models in which the parameters are identifiable and also models in which the parameters are not. For each of the models considered here, a relatively simple method is presented for calculating the maximum likelihood estimate of the frequencies in the m-way contingency table expected under the model, and for determining whether the parameters in the estimated model are identifiable. In addition, methods are presented for testing whether the model fits the observed data, and for replacing unidentifiable models that fit by identifiable models that fit. Some illustrative applications to data are also included.
Key Words: Contingency tables • Latent structure • Log linear models • Maximum likelihood estimation • Tests of fit
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|
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|
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|
|
|
|
|
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|
|
|
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|
|
|
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|
|
|
|
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|
|
|
|
|
|
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|
|
|
|
|
|
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|
|
|
|
|
|
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|
|
|
|
|
|
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|
|
|
|
|
|
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|
|
|
|
|
|
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|
|
|
|
 |
|
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|
|
|
|
|
|
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|
|
|
|
|
|
R. R. Wilcox Determining the Length of a Criterion-Referenced Test Applied Psychological Measurement, October 1, 1980; 4(4): 425 - 446. [Abstract]
|
|
|
|
|
|
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|
|
|
|
|
|
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|
|
|
|
 |
|
 J. R. Bergan, O. M. Towstopiat, and J. W. Luiten A Computer Program for Multidimensional Contingency Table Construction 1 Educational and Psychological Measurement, April 1, 1980; 40(1): 127 - 132. [Abstract]
|
|
|
|
|
|
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|
|
|
|
|
|
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|
|
|
|
|
|
G. B. Macready and C. M. Dayton A Two-Stage Conditional Estimation Procedure for Unrestricted Latent Class Models Journal of Educational and Behavioral Statistics, January 1, 1980; 5(2): 129 - 156. [Abstract] [PDF]
|
|