By B. S. Everitt (auth.)
Latent variable versions are utilized in many parts of the social and behavioural sciences, and the expanding availability of machine applications for becoming such types is probably going to extend their acceptance. This e-book makes an attempt to introduce such versions to utilized statisticians and examine employees attracted to exploring the constitution of covari ance and correlation matrices when it comes to a small variety of unob servable constructs. The emphasis is at the sensible software of the strategies instead of on certain dialogue in their mathe matical and statistical houses. it truly is assumed that the reader understands the main usual statistical suggestions and techniques, really regression, and in addition has a good wisdom of matrix algebra. My thank you are because of my colleagues Dr David Hand and Dr Graham Dunn for valuable reviews at the ebook, to Mrs Bertha Lakey for her cautious typing of a tough manuscript and to Peter Cuttance for counsel with the LlSREL package deal. furthermore the textual content basically owes very much to the paintings on structural equation versions released by means of Karl Joreskog, Dag Sorbom, Peter Bentler, Michael Browne and others.
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Extra resources for An Introduction to Latent Variable Models
For example, this. method of positioning the axes often tends to produce a 'general factor', that is, an axis on which most variables load rather highly, with subsequent axes differentiating to a limited extent between small groups of variables. It is almost always the case that a clearer picture may be obtained by rotating the axes to some other position. 1 shows the correlation coefficients between six school subjects for a sample of 220 boys. 2. These loadings may be represented visually by a plot in which orthogonal axes are taken to represent the factors and points plotted using the loadings as coordinates.
If a model is identified the matrix will be positive definite. If the matrix is singular the model is not identified and the rank of the matrix indicates which parameters are not identified. However, Bentler (1980) suggests that this approach, although practically useful, is theoretically unsound. He argues that identification is a problem of population, independent of sampling considerations, so that data-based evaluation of identifiability may be inappropriate. e. 8)). There are (p+q)(p+q+ 1)/2 equations (this is the number of different elements of ~x, ~y and ~Xy), in t unknown parameters, t representing the total number of parameters in the model.
By specifying particular forms for the matrices Fj and P, this formulation allows a large number of models to be specified comparatively simply, and a computer program, COSAN (Covariance Structure Analysis), is available which allows estimation of the parameters using any of the three discrepancy functions described in Chapter 1. Details of this program are given in AppendixB. The final approach to a general, but practically useful, formulation oflatent variable models that we shall consider and concentrate on in this chapter, is a model developed independently by a number of workers including Joreskog (1973), Keesling (1972) and Wiley (1973), which has now become generally known as the LISREL model, the mnemonic standing for linear structural relationships.
An Introduction to Latent Variable Models by B. S. Everitt (auth.)