Journal ArticleDOI
Posterior analysis of the factor model
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TLDR
It is argued here that, if all variables in the model are random, then Bayes' theorem provides the logical link between the data and the unobserved latent variables.Abstract:
The term posterior analysis is used in this paper to refer to methods of drawing inferences about the latent variables in factor analysis after the model has been fitted. In particular with the problem of locating each individual in the latent space on the basis of the values of the observed variables. This problem has been traditionally treated by determining factor scores. It is argued here that, if all variables in the model are random, then Bayes' theorem provides the logical link between the data and the unobserved latent variables. Viewed in this perspective the indeterminacy of factor scores is simply an expression of the fact that the latent variables are still random variables after the manifest variables have been observed. The name, factor scores, can then reasonably be given to the location parameters of the posterior distributions. The paper is primarily expository and it contains no new mathematics. Its concern is with the logical framework within which the analysis should be carried out and interpreted.read more
Citations
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Factor Analysis and AIC
TL;DR: The information criterion AIC was introduced to extend the method of maximum likelihood to the multimodel situation by relating the successful experience of the order determination of an autoregressive model to the determination of the number of factors in the maximum likelihood factor analysis as discussed by the authors.
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Generalized latent trait models
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TL;DR: A unified maximum likelihood method for estimating the parameters of the generalized latent trait model will be presented and in addition the scoring of individuals on the latent dimensions is discussed.