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

TL;DR

This paper investigates how R-factor analysis on data from models with R- and Q-factors can lead to biased loadings, especially with high Q-factor variance, and proposes kurtosis tests as a diagnostic tool.

Contribution

It reveals the bias introduced in R-factor loadings due to Q-factor variance and suggests kurtosis testing to detect this issue before analysis.

Findings

Large Q-factor variance increases loading estimation variability.

R-factor analysis can produce biased loadings in mixed models.

Kurtosis tests can serve as indicators for Q-factor presence.

Abstract

Effects of performing R-factor analysis of observed variables based on population models comprising R- and Q-factors were investigated. It was noted that estimating a model comprising R- and Q-factors has to face loading indeterminacy beyond rotational indeterminacy. Although R-factor analysis of data based on a population model comprising 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 population R-factor loadings. It was shown in a simulation study that large Q-factor variance induces an increase of the variation of R-factor loading estimates beyond chance level. The results indicate that performing R-factor analysis with data based on a population model comprising R- and Q-factors may result in substantial loading bias. Tests of the multivariate kurtosis of observed variables are proposed as an indicator of possible Q-factor variance in observed variables as a prerequisite for R-factor analysis.