Hazards in Factor Analysis

Principal components and other standard factor analyses can yield misleading results if an assumed subsidiary condition is untrue or if data are missing. Principal components factor analysis is tested for its reliability, using a problem with known answers. Even when test data are complete (e.g., 70 data on 7 properties, dependent on both radii and heights of 10 cylinders), such analyses followed by varimax or other standard rotations given incorrect rank orders for factors (factor scores for radius and height for each of the 10 cylinders) and sensitivities (factor loadings for each of the 7 properties). When no data are missing, a transformation incorporating valid subsidiary conditions can be used instead of such rotations to obtain correct factors and sensitivities. However, when a moderate number (e.g., 20 or 29%) of the possible data are missing (randomly deleted), factors and sensitivities can have wrong rank orders and therefore be misleading even with this transformation. When data are missing, standard factor analysis is evidently unreliable and should be replaced by another method such as the one presented herein. (Author)