New roles for public health in cancer screening

Abstract

The statistical models used in structural equation modeling are described. The estimation theory for these models is reviewed for the case when all variables are continuous. Estimation theory for the case when all observed variables are ordinal is developed. This involves fitting the structural equation model to a matrix of polychoric correlations by weighted least squares. The weight matrix is a consistent estimate of the inverse of the asymptotic covariance matrix of the polychoric correlations. The asymptotic covariance matrix of the estimated polychoric correlations is derived for the case when the thresholds are estimated from the univariate marginals and the polychoric correlations are estimated from the bivariate marginals for given thresholds. Computational aspects are also discussed. Lincolnwood, IL: Scientific Software International