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Latent variable models and factor analysis. 3rd edition. By David J. Bartholomew & Martin Knott. Kendall's Library of Statistics 7. London: Arnold. 1999. Cased, L35. ISBN 0-340-6943-X.
Latent variable models come in many shapes and sizes: factor analysis (for metrical latent and metrical manifest variables), latent profile analysis (for categorical latent and metrical manifest variables), latent trait analysis (for metrical latent and categorical manifest variables), latent class analysis (for categorical latent and categorical manifest variables) and mixed-type manifest variable modelling. These techniques were developed for different situations and in different disciplines, and therefore have advanced relatively independently. Bartholomew and Knott, in a complete reworking of Bartholomew's 1987 book, unify these approaches as special cases of the general linear latent variable model (GLLVM). The main purpose of the modelling is to find the distribution of the latent variables conditional on the manifest variables. The book goes through all five of the techniques above, using the single framework of GLLVM, and stressing the commonalities.
For each technique the authors show the statistical derivations and give several examples. Further, the authors direct readers to a web page of programs that they and their colleagues have written for some of these...