Confirmatory factor analysis: a preface to LISREL by J. (John) Scott Long

By J. (John) Scott Long

A statistical process that may attract teams particularly - people who find themselves at present utilizing the extra conventional means of exploratory issue research and those that have an interest within the research of covariance constructions, generally known as the LISREL version. the 1st crew will locate that this method might be extra acceptable to the research in their learn difficulties whereas the second one workforce will locate that confirmatory issue research is an invaluable first step to realizing the LISREL version. This ebook, and its better half quantity, Covariance constitution versions, are designed to be learn consecutively. The proofs provided are easy, however the reader needs to suppose pleased with matrix algebra which will comprehend the version.

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Second, those who are interested in the analysis of covariance structures, more commonly known as the LISREL model, will find study of the confirmatory factor model to be a useful first step in understanding the more complex LISREL model. It is for this reason that the monograph has been subtitled A Preface to LISREL. Members of the first group are likely to find themselves evolving into members of the second group, since the advantages of the confirmatory factor model over the exploratory factor model are more than equaled by the advantages of the covariance structure model over the confirmatory factor model.

If each of the common factors was standardized with a unit variance, F would be a correlation matrix with ones on the diagonal and correlations between common factors on the off-diagonals. The covariances among the residual factors are contained in the population matrix Q, a (q × q) symmetric matrix. The (i,j)th element of Q, qij, is the covariance between unique factors di and dj. The unique factors are assumed to have means of zero, in the same way that the errors in equations in regression analysis are assumed to have means of zero.

These new parameter matrices have the same dimensions as the first set of matrices, which satisfies the first requirement. Substituting the "(2)" parameters into the covariance equation reproduces the population covariance matrix S. That is, S = L(2)F(2)L(2)´ + Q(1). Hence, the second requirement is satisfied. ) Since both sets of parameter matrices reproduce S, they can both be thought of as solutions to the covariance equation. While both solutions are acceptable in terms of reproducing the covariance matrix, each suggests a different structure.

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