Selecting the Number of Factors in Exploratory Factor Analysis via Locally Conic Parameterization

• Activity Number: 431
• Type: Topic Contributed
• Date/Time: Wednesday, August 5, 2009 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Yoshiyuki Ninomiya*+ and Hirokazu Yanagihara and Ke-Hai Yuan
• Companies: Kyushu University and Hiroshima University and University of Notre Dame
• Keywords: asymptotic distribution ; information criterion ; likelihood ratio test ; locally conic parameterization ; model selection ; non-identifiability

Abstract

When selecting the number of factors in exploratory factor analysis (EFA), a well-known procedure is to compare m-factor models with (m+1)-factor models using the likelihood ratio test (LRT). Less well-known is that such a procedure encounters the difficulty of the so-called non-identifiability. Then the LRT statistic does not converge to the nominal chi-square distribution. Other criterion such as AIC also performs poorly in such a case. In this presentation, a new formulation of the EFA model is proposed by using the so-called locally conic parameterization and the LRT statistic is shown to converge to a simple form. The commonly used formula of AIC is reevaluated and a new AIC based on the reevaluation is proposed. Empirical results indicate that the new AIC provides much more reasonable model selection than the existing AIC for the EFA model, which often selects too many factors.