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

By B. S. Everitt (auth.)

Latent variable types are utilized in many parts of the social and behavioural sciences, and the expanding availability of laptop applications for becoming such versions is probably going to extend their reputation. This ebook makes an attempt to introduce such types to utilized statisticians and examine employees drawn to exploring the constitution of covari­ ance and correlation matrices by way of a small variety of unob­ servable constructs. The emphasis is at the sensible program of the approaches instead of on specified dialogue in their mathe­ matical and statistical houses. it truly is assumed that the reader understands the main regular statistical strategies and strategies, rather regression, and likewise has a good wisdom of matrix algebra. My thank you are because of my colleagues Dr David Hand and Dr Graham Dunn for precious reviews at the ebook, to Mrs Bertha Lakey for her cautious typing of a tricky manuscript and to Peter Cuttance for information with the LlSREL package deal. additionally the textual content sincerely owes greatly to the paintings on structural equation versions released through Karl Joreskog, Dag Sorbom, Peter Bentler, Michael Browne and others.

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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. This is shown in Fig. 1, and we can now see that the points appear to be in two groups which subtend an acute angle at the origin.

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. 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.

Such occurrences are often known as Heywood cases. To overcome this difficulty the function f is considered only in the region where each l/I ii > B for some small positive value B. More details of this problem are given in Joreskog and Lawley (1968). 32) 22 FACTOR ANALYSIS where A is a (p x k) matrix. 33) have been suggested (see Bartlett, 1954; Swain, 1975), which result in a substantial improvement of the approximation of the chi-squared distribution under hypothesis, Hk , when n is not large.

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