Factor Analysis: Exploratory

Mathematical Distinction Between EFA and PCA

The difference between EFA and PCA is not just one of use cases. The factor model establishes that variance be partitioned into common variance and unique variance. Common variance is all variance in each measured indicator that can be accounted for by common factors. Unique variance is all variance in each measured indicator that is unique to that indicator (i.e., not accounted for by a common factor). EFA makes this distinction, and only considers the common variance. PCA does not make this distinction and uses all variance in each indicator in the analysis. Because of this difference, under some conditions the discrepancy between the results of PCA and EFA can be large, most notably when the commonality between variables is low, or in few variable/many [factor/component] situations. In situations in which the commonality between measured variables is high, conversely (high common variance, little unique variance), the difference between EFA and PCA might be small. In addition, by grouping unique variance and common variance together, PCA assumes error-free measurement, which is highly unlikely when dealing primarily with the indirectly measured variables that are so common in communication research.

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