By B. S. Everitt (auth.)

ISBN-10: 9400955642

ISBN-13: 9789400955646

ISBN-10: 940108954X

ISBN-13: 9789401089548

Latent variable versions are utilized in many components 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 booklet makes an attempt to introduce such types to utilized statisticians and learn 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 program of the approaches instead of on special dialogue in their mathe­ matical and statistical houses. it truly is assumed that the reader understands the main usual statistical suggestions and strategies, really regression, and likewise has a good wisdom of matrix algebra. My thank you are as a result of my colleagues Dr David Hand and Dr Graham Dunn for priceless reviews at the publication, to Mrs Bertha Lakey for her cautious typing of a tough manuscript and to Peter Cuttance for tips with the LlSREL package deal. moreover the textual content essentially owes very much to the paintings on structural equation versions released by way of Karl Joreskog, Dag Sorbom, Peter Bentler, Michael Browne and others.

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Extra info for An Introduction to Latent Variable Models

Example text

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. 10) t ~ (p+q)(p+q+ 1)/2. Unfortunately, the equations are usually complex and non-linear and explicit solutions for all the parameters seldom exist; however, it is not necessary to actually solve them in considering the identification problem, only to try to assess which of the parameters have unique solutions and which do not.

In practice this is often not the most useful choice and can complicate the problem of interpretation. 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.

The most general approach would be to work directly with a formulation which said that the latent variable model of interest implied that the covariance matrix of the manifest variables has the form (Jjk = Jjk(fJ), j = 1, ... •. 0t] contains the parameters of the model and Jjk(8) is some particular function of the parameter values. 1). The user must supply subroutines evaluating the covariance matrix as a function of 8 and the first derivatives of the likelihood function with respect to O. However, this completely general approach is unlikely to be particularly helpful in encouraging the routine application of these techniques and, consequently, a number of less general, but practically more useful, approaches have been described.

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An Introduction to Latent Variable Models by B. S. Everitt (auth.)


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