Factors Influencing Four Rules For Determining The Number Of Components To Retain

Abstract

The performance of four rules for determining the number of components to retain (Kaiser's eigenvalue greater than unity, Cattell's SCREE, Bartlett's test, and Velicer's MAP) was investigated across four systematically varied factors (sample size, number of variables, number of components, and component saturation). Ten sample correlation matrices were generated from each of 48 known population correlation matrices representing the combinations of conditions. The performance of the SCREE and MAP rules was generally the best across all situations. Bartlett's test was generally adequate except when the number of variables was close to the sample size. Kaiser's rule tended to severely overestimate the number of components.