By David Bartholomew, Martin Knott, Irini Moustaki(auth.), Walter A. Shewhart, Samuel S. Wilks(eds.)
Chapter 1 uncomplicated rules and Examples (pages 1–18):
Chapter 2 the overall Linear Latent Variable version (pages 19–46):
Chapter three the conventional Linear issue version (pages 47–81):
Chapter four Binary info: Latent Trait types (pages 83–117):
Chapter five Polytomous facts: Latent Trait types (pages 119–156):
Chapter 6 Latent classification versions (pages 157–189):
Chapter 7 types and techniques for appear Variables of combined variety (pages 191–211):
Chapter eight Relationships among Latent Variables (pages 213–228):
Chapter nine comparable recommendations for Investigating Dependency (pages 229–245):
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Extra info for Latent Variable Models and Factor Analysis: A Unified Approach, 3rd Edition
In essence we ask what it is that these variables have in common. It often happens that the dominant latent variable has a large influence on all manifest variables, in which case it is sometimes called a general factor. In tests of ability, for example, general ability is indicated by a tendency to score similarly on all items. The idea of ‘looking for what is common’ to a set of manifest variables is central to interpretation. We begin with defining the notion of simple structure for a loading matrix because this is particularly easy to interpret.
Alternatives include numerical evaluation, analytic approximations and Monte Carlo integration. Markov chain Monte Carlo To avoid the integration required in the posterior expectation, Monte Carlo integration is used to approximate that integral by a sample average of quantities calculated by the method. R samples are drawn from the posterior distribution of all the unknown P1: TIX/XYZ JWST070-02 P2: ABC JWST070-Bartholomew May 9, 2011 22:18 Printer Name: Yet to Come THE GENERAL LINEAR LATENT VARIABLE MODEL 33 parameters, h(v | x).
Lee and Song (2003), Lee (2007) and Palomo et al. (2007) have also proposed Bayesian estimation methods for structural equation models for continuous and categorical responses. Lopez and West (2004) also looked at the problem of estimating the number of factors in the classical factor analysis model using reversible jump MCMC algorithms. Earlier, researchers such as Birnbaum (1969) and Owen (1975) proposed Bayes estimates of ability parameters in an item response model under the assumptions that the item parameters are known.