Sample size and subject to item ratio in principal components analysis

Abstract

Statisticians have wrestled with the question of sample size in exploratory factor analysis and principal component analysis for decades, some looking at total N, some at the ratio of subjects to items. Although many articles attempt to examine this issue, few examine both possibilities comprehensively enough to be definitive. This study examines a previously published data set to examine whether N or subject to item ratio is more important in predicting important outcomes in PCA. The results indicate an interaction between the two, where the best outcomes occur in analyses where large Ns and high ratios are present.