Schonemann P. H. and Haagen K
On the use of factor scores for prediction
Biometrical Journal, 1987, 29, 835-847
There are two types of indeterminacy problems in factor analysis: the indeterminacy of the parameters, which is also known as the problem of identification, and the indeterminacy of factor scores. The second problem, which will be treated here, is of great importance to the social sciences, given that the factor model was historically developed with the theory of measuring intelligence, where the main interest was to determine one person's intelligence numerically.
As a consequence of the indeterminacy of factor scores we will show, by means of a numerical example, that any criterion, including the dates of easter sunday, can be perfectly predicted by the intelligence factors.
The original working title of this manuscript was "On the use of factor scores for the prediction of easter sunday". This formulation was deemed too provocative by some people, so we toned it down. This paper is essentially an illustrative follow-up to the more technical treatment in Schonemann and Steiger (1978). See also Schonemann (1981) for a relatively non-technical treatment of this topic in the broader context of a comprehensive critique of the classical factor model by Spearman and Thurstone.