By B. S. Everitt (auth.)
Latent variable versions are utilized in many parts of the social and behavioural sciences, and the expanding availability of laptop 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 study employees drawn 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 useful program of the methods instead of on certain dialogue in their mathe matical and statistical homes. it truly is assumed that the reader understands the main universal statistical recommendations and techniques, fairly 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 tough manuscript and to Peter Cuttance for guidance with the LlSREL package deal. furthermore the textual content essentially 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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Extra resources for An Introduction to Latent Variable Models
Factor 1 which has high loadings on tests such as dial and table reading, speed of identification, pattern comprehension and decoding might tentatively be associated with the ability to understand spatial relations. Factor 2 appears to have no clearly obvious interpretation but factor 3, with high loadings on tests such as rotary pursuit, reaction time and rate of movement, should obviously be labelled as a 'speed' factor. 9 Confirmatory factor analysis In some situations an investigator, perhaps on the basis of previous research, may wish to postulate in advance the number offactors and also the values of certain elements of A, cJ) and, occasionally, '1'.
The model to be fitted to these data is illustrated in Fig. 2. It postulates a one-factor model for the data. , AIO 2 those for the second occasion. 10 shows the initial values supplied to the LlSREL program together with the final estimates and their standard errors. 05 with 29 degrees of freedom. Consequently, the fit of our model is not very satisfactory. An obvious possibility to improve the fit would be to allow for more than a single factor. As a further example of longitudinal factor analysis we shall consider a study by Wheaton, Muthen, Alwin and Summers (1977) concerned with the stability over time of attitudes such as alienation and the relation to background variables such as education and occupation.
Each set of parameter values lead to the same predicted covariance matrix for the observed variables. 5. This matrix, taken from Child (1970), gives the correlations between eight tests of mental ability. Tests 1 and 2 are conventional 'intelligence tests' purporting to measure conventional thinking. 00 tests oftluency (F) and originality (0) in divergent thinking. Tests 36 require verbal responses, whilst tests 7 and 8 require non-verbal responses. On the basis of psychological theory it is believed that the tests measure three relatively distinct aspects of mental behaviour: convergent thinking, verbal divergent thinking and non-verbal divergent thinking.