The Effects of Overextraction on Factor and Component Analysis

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 =...

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Bibliographic Details
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
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Summary: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.
ISSN:0027-3171
1532-7906
DOI:10.1207/s15327906mbr2703_5