Structural Equation Models

Heywood cases represent the most common form of a series of related problems in confirmatory factor analysis and structural equation modeling. Other problems include factor loadings and factor correlations outside the usual range, large variances of parameter estimates, and high correlations between parameter estimates. The concept of empirical underidentification is used here to show how these problems can arise, and under what conditions they can be controlled. The discussion is centered around examples showing how small factor loadings, factor correlations near zero, and factor correlations near one can lead to empirical underidentification.