Estimation in SEM: A Concrete Example

Abstract

A concrete example is used to illustrate maximum likelihood estimation of a structural equation model with two unknown parameters. The fitting function is found for the example, as are the vector of first-order partial derivatives, the matrix of second-order partial derivatives, and the estimates obtained from each iteration of the Newton-Raphson algorithm. The goal is to provide a concrete illustration to help those learning structural equation modeling bridge the gap between the verbal descriptions of estimation procedures and the mathematical definition of these procedures provided in the technical literature.