Estimation and Hypothesis Testing in Linear Models Containing Measurement Error

Abstract

This paper reviews Joreskog's model for the analysis of covariance structures by first introducing the simpler case of confirmatory factor analysis. The mathematical results necessary for estimation and hypothesis testing are presented in a way which should be more accessible to sociologists than the original sources. The usefulness of Joreskog's techniques is indicated by reformulating a series of models which have been estimated by sociologists using techniques without statistical justification in the format of covariance structures. Identification is considered in this context. The argument is made that these methods can greatly extend our ability to construct structural equation models containing measurement error.