Adjustment for density maximization estimator for structural equation models

We propose a new method of estimation parameters &thetas; for Structural Equation Models (SEM): the Adjustment for Density Maximization (ADM) method. The most widely used Maximum Likelihood Estimator (MLE) for SEMs minimizes the distance between the sample covariance S and the population covariance Σ = MTM′ + D matrices of the data. Very often the mode of the likelihood Ł(Σ(&thetas;)|S) lies at a boundary point of the parameter space (i.e. |D| = 0 and/or | T| = 0). The ADM method accounts for the fact that the fitted covariance matrix of SEM is a sum of two positive definite matrices and maximized adjusted likelihood $y$(&thetas;)Ł(Σ|S). The adjustment forces the estimates of &thetas; to be in the interior of the parameters space. The ADM estimator provides better estimates than MLE especially in small samples.; The ADM method was implemented via specially designed new software. The advantages of this programs apply especially to small samples. We use a modification of Fisher's scoring algorithm to locate the mode of the adjusted likelihood function. On each step expected information is calculated analytically avoiding second derivatives. This algorithm is fast, mathematically simple, and always converges. The advantages of the new software are demonstrated over the two most popular SEM packages, LISREL and AMOS, which use MLE default method of estimation. If the mode of the likelihood Ł(&thetas;) lies at a boundary point, LISREL and AMOS give invalid estimates (i.e. variances <0) or fail to converge.; The data analysis described in the thesis involves psychosocial development and functioning longitudinal measurements from Across Generation Project (AGP) of Harvard Medical School. We demonstrate the ADM method and the new program on the AGP data, where LISREL and AMOS gave no solution.