台大心理系

Parallel analysis proposed by Horn (1965) is one of the highly recommended methods for deciding number of factors in factor analysis. Horn suggested comparing the eigenvalues of the data correlation matrix to the mean random eigenvalues to mimic the effect of sampling error. The mean random eigenvalues refer to the average eigenvalues from several random correlation matrices with uncorrelated variables. Horn enthusiastically expected the theoretical distribution of the random eigenvalues to be derived in the future. The asymptotic distribution of random eigenvalues has just been derived in recent years under the assumption of large sample sizes and large numbers of variables (Bao et al., 2012; Jiang, 2004; Pillai & Yin, 2012). Nonetheless, the numbers of observations and variables commonly encountered in factor analysis are oftentimes limited. Under such circumstances, most of the data subject to factor analysis would fail to meet the asymptotic assumption required for the theoretical distributions to hold. The present study therefore aims to evaluate the degree of deviation of Horn’s empirical approximation to the theoretical sampling distribution of random eigenvalues under finite numbers of variables and sample sizes.