Pitfalls in Factor Analytic Techniques

To the Editor: We read with great interest the article by John P. Alsobrook II, Ph.D., and David L. Pauls, Ph.D. (1), in which they used factor analytic techniques to reveal underlying structures in Gilles de la Tourette’s syndrome. The main applications of factor analytic techniques are to reduce the number of variables and to detect structure in the relationship among variables. We want to point out some pitfalls that go along with the use of factor analysis in general and the application of Drs. Alsobrook and Pauls in particular.

A preliminary step in factor analysis is the determination of the number of factors one wishes to retain. Drs. Alsobrook and Pauls applied the widely used Kaiser rule (eigenvalues >1). Zwick and Velicer (2) compared five different methods for the determination of the number of factors and demonstrated that use of this rule consistently leads to an overestimation of the number of factors. An alternative method of determining the number of factors may be combination of the Kaiser rule with inspection of the scree plot.

After factor analysis, rotational strategies (e.g., varimax) can be used to obtain a clear pattern of loadings. An orthogonal method of rotation, such as the varimax rotation used by Drs. Alsobrook and Pauls, requires that the resulting factors do not correlate. The appropriateness of this method is questionable since symptoms in psychiatric syndromes may inherently show a certain degree of correlation. Oblique rotation (in which factors are allowed to correlate) should be considered since oblique rotation methods produce orthogonal solutions, if appropriate (3).

Loadings are simply correlations between an item and a factor; therefore, they need to be statistically significant, and consequently, group size should be taken into account. Drs. Alsobrook and Pauls used an absolute value of 0.200 as a threshold for the interpretation of factor loadings. According to Stevens (4), a group size of 670 patients would be required for such a threshold. Drs. Alsobrook and Pauls included 85 patients, a group size that allows loadings of merely >0.556. Anyhow, regardless of the group size, loadings with values of 0.200 explain only as little as 4% of the shared variance between an item and a factor.

Statistical software packages such as SPSS offer default options for performing factor analyses. A principal components analysis with varimax rotation based on eigenvalues >1, used by Drs. Alsobrook and Pauls, is an example of such a standardized option. Unfortunately, when followed too obediently, these options may seriously compromise research data.