IDENTIFICATION OF CONFIRMATORY FACTOR-ANALYSIS MODELS OF ARBITRARY COMPLEXITY - THE SIDE-BY-SIDE RULE

All statistical models must be identified if the estimates are to be m eaningful. Determining the identification status of the measurement po rtion of a structural equation model can be difficult because the resu lting system of covariance equations is nonlinear. The recent literatu re on identification rules for the measurement portion of a structural equation model has concentrated on models of factor complexity 1, tha t is, models in which each observed variable loads on one and only one factor. Building on the existing literature, the authors consider mod els of arbitrary complexity. A method is presented, called model decom position, 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 identif ication status of almost all models of higher complexity that appear i n the literature (an exception being the multitrait-multimethod model) . Examples from the literature are given.