Peter H. Schönemann
Professor Emeritus • Department of Psychological Sciences • Purdue University


Peter H. Schonemann and James H. SteigerOn the validity of indeterminate factor scoresBulletin of the Psychonomic Society, 1978, 12, 287-290


A partition of the vectorspace of all deviation score vectors for fixed sample size N is used to show that the (indeterminate) factors of the factor model can always be constructed so as to predict any criterion perfectly, including all those that are entirely uncorrelated with the observed variables.



Prepublication History

We submitted the paper on April 7, 1976, to the British Journal of Mathematical and Statistical Psychology which had previously  published our Regression Component Analysis paper without  any problems.

On October 5, 1976, the editor

"had one favorable report ... Perhaps you will be sufficiently encouraged to leave the paper with me for another, say four weeks?"

Of course we were. After 5 more months I inquired about the state of affairs. The editor sent us 2 reviews, both negative. One reviewer wrote:

"... I have not read the paper, as clearly as my opinion is negative".

However, the editorial communication still did not contain any decision. On June 16, 1977, more than one year after submission, there were definite signs of trouble:

"Frankly, I have only recently become aware of the high emotion which the issue of indeterminacy has raised in various quarters in re cent years. ... I then received a reply to your published paper in journal [X ] from [Y], which caused me to think. My impression is that all the algebra in the world will not resolve the issue between you, and that there is a simple conceptual problem."

There still was no decision. Finally, on March 1, 1978, more than 22 months afer submission, the editor finally made up his mind:

"I note ... with some considerable anguish, the marked delay in responding properly to your long and helpful letter of nearly a year ago ... Unfortunately ... I allowed my attention to the matter to lapse. True, I was awakened by the arrival of the paper from [Y] to which you also referred in your recent letter, but that too, complicated our problems and diverted our attention from the still unanswered letter.

... So, if you must have a decision, it must be negative, and I should not hold out any hope that I can gain wholly new views from anyone."

Such delaying tactics can easily ruin the career prospects of aspiring junior faculty, should their findings displease their elders. Luckily, I was already Full Professor at the time.


The results of this paper, together with various  illustrative data sets, formed the basis of Schonemann (1981), Schonemann (1987), and Schonemann and Haagen (1987).