Identification of Confirmatory Factor Analysis Models of Arbitrary Complexity

Abstract

All statistical models must be identified if the estimates are to be meaningful. Determining the identification status of the measurement portion of a structural equation model can be difficult because the resulting system of covariance equations is nonlinear. The recent literature on identification rules for the measurement portion of a structural equation model has concentrated on models of factor complexity 1, that is, models in which each observed variable loads on one and only one factor. Building on the existing literature, the authors consider models of arbitrary complexity. A method is presented, called model decomposition, which permits factor complexity 1 identification rules to be applied to models of arbitrary factor complexity. In addition, a rule is presented, called the side-by-side rule, which determines the identification status of almost all models of higher complexity that appear in the literature (an exception being the multitrait-multimethod model). Examples from the literature are given.