MODEL PERSAMAAN STRUKTURAL DENGAN MATRIKS KOVARIANS YANG HAMPIR SINGULAR - , DIAN AGUSTINA ([Yogyakarta] : Universitas Gadjah Mada, 2013)
A structural equation modeling involves structural model fitting in the covariance matrix. One of the assumptions for covariance matrix to be an input matrix is that it has to be non singular. If the input matrix is near singular, a problem of being not convergent will occur in the estimation process, so that a goodness of model or parameter estimation cannot be evaluated. To solve it, a structural model with a small constant a is fitted using a covariance matrix Sa ï½ S ï« aI . In this study, a S is used as a covariance matrix sample in maximum likelihood procedure. The implication of a S modeling can be seen in the data of near singular covariance matrix of 9 variables studied by Holzinger and Swineford in their psychological research in 1939. A consistent parameter estimation can be obtained here. An asymptotic distribution and the parameter estimation is studied and compared with the ones obtained in conventional maximum likelihood procedure. An empirical result shows that estimation of a S modeling is more efficient than structural model fitting using S. This application example also shows that a S modeling allows us to evaluate the overall structural model.