The Effects of Overextraction on Factor and Component Analysis

• Published in: Multivariate behavioral research 1992-07, Vol.27 (3), p.387-415
• Main Authors: Fava, Joseph L., Velicer, Wayne F.
• Format: Article
• Language: English
• Subjects: Biological and medical sciences; Computer Simulation; Correlation; Factor Analysis; Fundamental and applied biological sciences. Psychology; Mathematical Models; Maximum Likelihood Statistics; Overextraction; Principal Components Analysis; Psychology. Psychoanalysis. Psychiatry; Psychology. Psychophysiology; Psychometrics. Statistics. Methodology; Sample Size; Scores; Specification Error; Statistics. Mathematics
• ISSN: 0027-3171; 1532-7906
• DOI: 10.1207/s15327906mbr2703_5

The effects of overextracting factors and components within and between the methods of maximum likelihood factor analysis (MLFA) and principal component analysis (PCA) were examined. Computer-simulated data sets were generated to represent a range of factor and component patterns. Saturation (a ij = .8, .6 & .4), sample size (N = 75, 150,225,450), and variable-to-component (factor) ratio (p:m = 12:1,6:1, & 4:1) were conditions manipulated. In Study 1, scores based on the incorrect patterns were correlated with correct scores within each method after each overextraction. In Study 2, scores were correlated between the methods of PCAand MLFA after each overextraction. Overextraction had a negative effect, but scores based on strong component and factor patterns displayed robustness to the effects of overextraction. Low item saturation and low sample size resulted in degraded score reproduction. Degradation was strongest for patterns that combined low saturation and low sample size. Component and factor scores were highly correlated even at maximal levels of overextraction. Dissimilarity between score methods was the greatest in conditions that combined low saturation and low sample size. Some guidelines for researchers concerning the effects of overextraction are noted, as well as some cautions in the interpretation of results.