By B. S. Everitt (auth.)
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 e-book makes an attempt to introduce such types to utilized statisticians and study employees 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 useful program of the systems instead of on targeted dialogue in their mathe matical and statistical homes. it really is assumed that the reader understands the main everyday statistical suggestions and strategies, quite 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 beneficial reviews at the publication, to Mrs Bertha Lakey for her cautious typing of a tricky manuscript and to Peter Cuttance for information with the LlSREL package deal. additionally the textual content basically 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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Extra resources for An Introduction to Latent Variable Models
6) where (f) = E( ~ ~') and (J6 = E(66'). 8) where 'I' = E(,,') and Oe = E(88'). The elements of ~xx' ~yy and ~xy are functions of the elements of Ay, Ax, B, r, (f), '1', (Ja and (J6' In any particular application some of these elements will be fixed (usually to zero or one), some will be unknown but constrained to equal other elements and some will be unknown and unconstrained. Thus, the elements of the eight parameter matrices are of three kinds: (1) fixed parameters which have been assigned given values; (2) constrained parameters whose values are unknown but equal to one or more other parameters; (3) free parameters which are unknown and not constrained to be equal to any other parameter.
9) 2. With the simple factor analysis model it was clear that the model was not identified unless some arbitrary constraints were placed on its parameters. With the LISREL model the situation is not so straightforward; here identifiability depends on the choice of model and on the specification of fixed, constrained and free parameters. In some cases a number of the parameters in the model may be identified, and others may not. In such cases those parameters which are idel\tified will be estimated consistently by the procedure to be discussed in the next section.
0t] contains the parameters of the model and Jjk(8) is some particular function of the parameter values. 1). The user must supply subroutines evaluating the covariance matrix as a function of 8 and the first derivatives of the likelihood function with respect to O. However, this completely general approach is unlikely to be particularly helpful in encouraging the routine application of these techniques and, consequently, a number of less general, but practically more useful, approaches have been described.