Combined R- and Q-factors resulting biased loadings in R-factor analysis

The effect of combined, generating R- and Q-factors of measured variables on the loadings resulting from R-factor analysis was investigated. It was found algebraically that R-factor analysis of measured variables generated by a combination of R- and Q-factors results in biased population R-factor loadings. In this context, the loadings of the generating R-factors cannot be perfectly estimated by means of R-factor analysis. This effect was also shown in a simulation study at the population level. Moreover, the simulation study based on the samples drawn from the populations revealed that the R-factor loadings averaged across samples were substantially larger than the population loadings of the generating R-factors. This effect was due to between sample variability of measured variables resulting from generating Q-factors at the population level which does not occur when a single sample is investigated. These results indicate that -in data that are generated by a combination of R- and Q-factors- the effect of the Q-factors may lead to substantial over-estimation of the R-factor loadings in sample-based R-factor analysis.