Noniterative Factor Analysis Estimators, With Algorithms for Subset and Instrumental Variable Selection

Noniterative estimators of the unrestricted factor analysis model have been developed by, among others, Hägglund (1982) and Ihara and Kano (1986) that are consistent and very efficient computationally. Whereas each of these methods has several desirable properties, both require a subjective decision regarding the selection of subsets of variables that are needed to compute estimates of the parameters. An algorithm called PACE, based on an application of the sweep operator, is presented that automatically selects subsets of variables used for the Ihara-Kano estimator. A second algorithm initially presented by Du Toit (1986) is also described that automatically selects reference variables used in Hägglund’s Fabin estimators. A Monte Carlo experiment is reviewed that compares the relative performance of these estimators in addition to several others. Both new methods performed well in this experiment. Their relative merits on other criteria are discussed.