The Effects of Underextraction in Factor and Component Analyses

Abstract

The consequences of underextracting factors and components within and between the methods of maximum likelihood factor analysis (MLFA) and principal components analysis (PCA) were examined. Computer-simulated data sets represented a range of pattern structures. Manipulated conditions included component (factor) structure coefficients (a_ij = .8, .6, and .4), sample size (N = 75, 150, 225, and 450), and variable-to-component (factor) ratio (p:m = 6:1 and 4:1). The principal components score and the Anderson and Rubin factor score estimate were calculated for both the correct patterns and the incorrect (underextracted) patterns. In Study 1, underextraction led to substantial degradation of scores within both methods, but the component score degraded less rapidly. Score degradation was related to the number of original components (factors). In Study 2, between-method comparisons indicated very high similarity for baseline score patterns, but dissimilarity occurred with underextraction.