New PDF release: An Introduction to Latent Variable Models

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 desktop applications for becoming such versions is probably going to extend their attractiveness. This e-book makes an attempt to introduce such versions to utilized statisticians and examine employees attracted 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 techniques instead of on distinctive dialogue in their mathe­ matical and statistical homes. it's assumed that the reader understands the main usual statistical options and techniques, fairly regression, and in addition 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 valuable reviews at the ebook, 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 sincerely 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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The two factors are fairly simple to interpret, the first being a 'non-violent' and the second a 'violent' crime dimension. 6. This arises from a study of the selection of airmen reported by Fleishman and Hempel (1954), in which 18 tests were given to a sample of 197 individuals. The tests were concerned with mechanical aptitude, rate of movement, the comprehension of spatial relations and similar problems of a technical nature. Maximum likelihood factor analysis was applied to the correlation matrix and the parameters for a three-factor solution estimated.

Having found A'I' in this way the minimization of f is accomplished by using a method due to Fletcher and Powell (1963). Details are given in Appendix A, but the essence ofthe method is that in each iteration a second-degree approximation to the function f is used to estimate the minimum point. This results in a sequence of matrices '1'(1), '1'(2), ... 30) The sequence converges rapidly to a final matrix of estimates. With each new 'I'(h) there is an associated new A(h). Thus, there is also a sequence of A matrices which converge to a final matrix of estimates of factor loadings.

Unfortunately, no general and practically useful, necessary and sufficient conditions for identification are available for the general LISREL model. However, indications of whether a model is identified or not can be obtained by checking whether the matrix of second-order derivatives of the fitting function used to estimate the model is positive definite or not. If a model is identified the matrix will be positive definite. If the matrix is singular the model is not identified and the rank of the matrix indicates which parameters are not identified.

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


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