A Superior Rotational Method in Factor Analysis or Psychometricians in Government Service

Abstract

The topic that I have chosen, “A Superior Rotational Method in Factor Analysis or Psychometricians in Government Service,” may puzzle you at first. But there is an explanation. A study in progress at the University of North Carolina requires the interpretation of 16 factors obtained from a centroid analysis of 66 variables. The task that was approached with greatest apprehension was the location of a meaningful reference frame. With so many vectors protruding into a space of such a large number of dimensions, the problem appeared practically insoluble. Hence we sought a rotational method that would obviate the necessity for the numerous graphs and the matrix multiplication associated with the commonly accepted techniques.

Perhaps some of you have had the experience of solving a difficult mathematical problem in a state of sleep and later being able to transcribe the complete solution immediately. A relatively painless approach to mathematics, it is the one which enabled me to pass a course in Mathematical Probability years ago. I scarcely dared presume that I could evoke it in the present emergency. To my astonishment, however, it worked. One day the project staff had had a particularly trying session during which we tried in vain to stretch the available funds to cover the rotational work. Upon falling asleep in my office chair, I dreamed a solution so simple that an ordinary statistical clerk, upon mere inspection of the score matrix, could visualize the most interpretable reference frame in up to an infinite number of dimensions. This was beyond our most extravagant hopes, for it rendered obsolete both the correlation matrix and the centroid solution.