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 ebook makes an attempt to introduce such types to utilized statisticians and study 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 functional software of the approaches instead of on specified dialogue in their mathe matical and statistical homes. it's assumed that the reader understands the main conventional statistical options and strategies, 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 invaluable reviews at the publication, to Mrs Bertha Lakey for her cautious typing of a tough manuscript and to Peter Cuttance for counsel with the LlSREL package deal. moreover the textual content in actual fact 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
The procedure continues with k increasing by 1 at each step, until Hk is accepted for some value of k or until v :=;; 0 in which case there is no non-trivial factor model which fits the data. This procedure is open to criticism because the critical values of the test criterion have not been adjusted to allow for the fact that a set of hypotheses is being tested in sequence, with each one dependent on the rejection of all predecessors. Lawley and Maxwell (1971) suggest that this problem is unlikely to cause serious error in practice.
However, such a procedure has little to recommend it since the results are, in general, very difficult to interpret. A detailed comparison of rotation methods can be found in Gorsuch (1974), including some comments on their stability under repeated sampling. Rotation methods have acquired a certain notoriety primarily because the choice of rotation technique can often affect the final interpretation of the analysis. Many statisticians have complained that investigators can choose to rotate factors in such a way as to get the answer they are looking for, and Blackith and Reyment (1971) go so far as to suggest that the method has persisted precisely because it allows experimenters to impose their preconceived ideas on the raw data.
Details of the technique are given in Mardia et al. (1979), but its essential points may be illustrated by means of a small example. Let us suppose that we are interested in obtaining estimates of the loadings in a factor model with six observed and two latent variables. The scales of the two latent variables are fixed to be the same as the first two observed variables by placing unities appropriately in Ax, so the form of the model is 1 0 0 1 X= A,31 A, 32 A,41 A,42 A,Sl A,S2 A,61 A,62 where x is a vector of observed variables, variables and 8 a vector of residuals.
An Introduction to Latent Variable Models by B. S. Everitt (auth.)