A simple Gauss-Newton procedure for covariance structure analysis with high-level computer languages

An implementation of the Gauss-Newton algorithm for the analysis of covariance structures that is specifically adapted for high-level computer languages is reviewed. With this procedure one need only describe the structural form of the population covariance matrix, and provide a sample covariance matrix and initial values for the parameters. The gradient and approximate Hessian, which vary from model to model, are computed numerically. Using this approach, the entire method can be operationalized in a comparatively small program. A large class of models can be estimated, including many that utilize functional relationships among the parameters that are not possible in most available computer programs. Some examples are provided to illustrate how the algorithm can be used.We are grateful to M. W. Browne and S. H. C. du Toit for many invaluable discussions about these computing ideas. Thanks also to Scott Chaiken for providing the data in the first example. They were collected as part of the U.S. Air Force's Learning Ability Measurement Project (LAMP), sponsored by the Air Force Office of Scientific Research (AFOSR) and the Human Resource Directorate of the Armstrong Laboratory (AL/HRM).