R-factor analysis of data generated by a combination of R- and Q-factors leads to biased loading estimates

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 a model based on the combination of R- and Q-factors results in loading indeterminacy beyond rotational indeterminacy. Although R-factor analysis of data generated by a combination of R- and Q-factors is nevertheless possible, this may lead to model error. Accordingly, even in the population, the resulting R-factor loadings are not necessarily close estimates of the original loadings of the generating R-factors. This effect was also shown in a simulation study. Moreover, the simulation study based on samples drawn from the populations revealed that the R-factor loadings averaged across samples were larger than the population loadings of the generating R-factors. Overall, the results indicate that -- in data that are generated by a combination of R- and Q-factors -- the Q-factors may lead to substantial loading indeterminacy and loading bias in R-factor analysis. An indicator for the detection of Q-factor variance in pairs of observed variables is proposed in order to exclude respective variables from R-factor analysis.