By B. S. Everitt (auth.)

ISBN-10: 9400955642

ISBN-13: 9789400955646

ISBN-10: 940108954X

ISBN-13: 9789401089548

Latent variable types are utilized in many parts of the social and behavioural sciences, and the expanding availability of machine programs for becoming such versions is probably going to extend their attractiveness. This ebook makes an attempt to introduce such types to utilized statisticians and examine 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 strategies instead of on distinct dialogue in their mathe matical and statistical homes. it's assumed that the reader understands the main universal statistical ideas 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 precious reviews at the publication, to Mrs Bertha Lakey for her cautious typing of a tricky manuscript and to Peter Cuttance for advice with the LlSREL package deal. additionally the textual content sincerely owes greatly to the paintings on structural equation types released through Karl Joreskog, Dag Sorbom, Peter Bentler, Michael Browne and others.

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**Extra info for An Introduction to Latent Variable Models**

**Example text**

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'.

33) by n-1-(2p+5)j6-2kj3. 35) When using factor analysis in its exploratory mode the number of factors, k, is initially unknown, and so a sequential procedure for determining k is used. 33). If this is not significant at some chosen significance level we accept H k with k = k1 • If, however, the test criterion is significant we repeat the fitting procedure with k = kl + 1. 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.

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. 20) is an example of a linear regression model in which both dependent and explanatory variables are measured with error; consequently, the usual least squares regression of X3 on X2 and Xl cannot be used to provide estimates of A31 and A32.

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

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