Noniterative estimation and the choice of the number of factors in exploratory factor analysis

Based on the usual factor analysis model, this paper investigates the relationship between improper solutions and the number of factors, and discusses the properties of the noniterative estimation method of Ihara and Kano in exploratory factor analysis. The consistency of the Ihara and Kano estimator is shown to hold even for an overestimated number of factors, which provides a theoretical basis for the rare occurrence of improper solutions and for a new method of choosing the number of factors. The comparative study of their estimator and that based on maximum likelihood is carried out by a Monte Carlo experiment.The author would like to express his thanks to Masashi Okamoto and Masamori Ihara for helpful comments and to the editor and referees for critically reading the earlier versions and making many valuable suggestions. He also thanks Shigeo Aki for his comments on physical random numbers.