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 desktop programs for becoming such versions is probably going to extend their attractiveness. This publication makes an attempt to introduce such versions to utilized statisticians and examine staff 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 functional software of the systems instead of on distinctive dialogue in their mathe­ matical and statistical homes. it's assumed that the reader understands the main conventional statistical suggestions and strategies, fairly 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 worthy reviews at the e-book, to Mrs Bertha Lakey for her cautious typing of a tough manuscript and to Peter Cuttance for counsel with the LlSREL package deal. additionally the textual content essentially 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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Here we shall consider only data from 1967 and 1971. Indicators of the latent variable, alienation, were considered to be the anomia scale and the powerlessness scale. Indications of the respondents socioeconomic status were respondents education (years of schooling completed) and Duncan's socioeconomic index. The model considered for the data is illustrated in Fig. 3. The latent variable socioeconomic status affects alienation at both time points, and alienation in 1967 affects alienation in 1971.

The primary aim of this method is to rotate the factors in such a way that the new loadings tend to be either relatively large or relatively small in absolute magnitude compared with the originals. 7 ROTATION OF FACTORS 2S squared loadings for each variable. Details are given in Lawley and Maxwell (1971), Chapter 6. Varimax rotation leads to orthogonal factors, but methods which allow correlated factors are also available. For example, the oblimin criterion (Harman, 1976) produces a rotation that maximizes, averaging over all pairs of axes, a weighted average of the covariance and raw cross product moment of the squared loadings.

When dealing with a two-factor model this graphical method of rotation is generally sufficient to find a new position for the axes which eases interpretation. However, with more than two factors the problem becomes more difficult. It may be possible to consider each pair of factors in turn and arrive at a suitable position for the axes using the simple graphical approach. ) In many cases, however, such an approach would be unsatisfactory and so other methods have been devised. Perhaps the most well known of these is the varimax method suggested by Kaiser (1958) and discussed by Horst (1965, Chapter 18).

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