Costner [3], Blalock [1], and Heise [6] have demonstrated the application of path analysis to problems involving multiple indicators of underlying constructs. In this type of problem, the researcher is frequently called on to deal with overidentified systems; for example, Costner has demonstrated the use of the “consistency criterion” (Spearman tetrad difference) as a test of the fit of the data to the hypothetical model in simple two construct systems with two independent measures of each construct. The purpose of this note is to discuss the use of a general method for factor analysis (Jöreskog [8]) to obtain a single “best fit” estimate of each parameter and an overall goodness of fit test for the consistency of the data with the model. Factor analysis is a special case of Jöreskog's [10] general method for the analysis of covariance structures that could be used instead of the confirmatory factor analysis procedure discussed in this chapter.