No. 1078

Title:

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

Author(s):

Ninomiya, Yoshiyuki (Kyushu University);
Yanagihara, Hirokazu (Hiroshima University);
Yuan, Ke-Hai (University of Notre Dame)

Key words:

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) statistically, a well-known procedure is to compare the model with $m$-factor against the model with $(m+1)$-factor using the likelihood ratio test (LRT). Less well-known is that such a procedure encounters the difficulty of the so-called non-identifiability when $m$-factor represents the null hypothesis and $(m+1)$-factor represents the alternative hypothesis. Then the LRT does not converge to the nominal chi-square distribution. Other criterion such as AIC or BIC also performs poorly in such a case. This paper proposes a new formulation of the EFA model and gives a correct asymptotic characterization of the LRT. The new formulation uses the so-called locally conic parameterization, which has been used to solve non-identifiability problems in several other difficult situations. Under this parameterization, the LRT statistic for the EFA model converges to a simpler form than for the other general models with non-identifiability. The commonly used formula of AIC is reevaluated under the non-identifiability condition and a new AIC based on the reevaluation is proposed for selecting the number of factors in EFA. 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.