Assessing Sampling Variation Relative to Number-of-Factors Criteria

Abstract

Employment of the bootstrap method to approximate the sampling variation of eigenvalues is explicated, and its usefulness is amplified by an illustration in conjunction with two commonly used number-of-factors criteria: eigenvalues larger than one and the scree test. Confidence intervals for eigenvalues are approximated for sample correlation matrices that have ones and squared multiple correlation coefficients on the diagonals. The results demonstrate the usefulness of the bootstrap method in providing information about the sampling variability of eigenvalues-knowledge that affords a basis for more informed decisions regarding the number of factors when employing common criteria. Further, this information can be obtained with little difficulty, and the approach avoids tenuous assumptions of symmetric confidence intervals.