Zur Interpretation von Hauptkomponenten und Faktoren: eine Wiederaufnahme der kritischen Diskussion faktorenanalytischer Verfahren - Bathelt, Harald; Erb, Wolf-Dieter (ERDKUNDE, 1991)
The article stresses problems associated with real world applications and interpretations of factor analysis. Although focussed on a spatial context, the results and implications are not only limited to geographical fields. Originally it was aimed to make use of factor analysis to analyse the economic structure of the administrative districts of Hesse. Rotated factor solutions were obtained through the varimax method and factor scores computed accordingly. Surprisingly, many of the rotated factor scores were not consistent with the original variable scores. For instance, the economic performance of Giessen county was considerably underestimated as compared to 11 other counties if factor scores of the corresponding factor were used instead of variable scores of the high-Ioading variables. Similar problems were identified for each factor in various solutions. If regional policy in Hesse had to be based on the results of the factor analysis presented, wrong conclusions could be drawn from the factor score distributions. Although the problems identified seem quite confusing, an explanation can be more easily given than might be expected. Inconsistent factor score distributions are directly related to the procedure of orthogonal rotation which results in compensation effects between variables. If variables originally correlating are associated with different factors, a compensation effect will have to take place between the corresponding variables in order to assure orthogonality of the factors extracted. From these characteristics, several implications can be derived. First, factor analysis should not be used without sufficient mathematical background. Secondly, in the case of rotated factor solutions, the interpretation of the factors cannot be solely. based on factor loadings as gene rally recommended. In addition, factor score coefficients have to be used for interpretation purposes to understand the compensation effects between variables. Thirdly, subsequent analysis should be based on surrogate variable scores instead of factor scores in order to assure political applicability of results. Alternatively, oblique rotation procedures might be implemented, as opposed to the orthogonal case.