Combining Factors from Different Factor Analyses Based on Factor Congruence

Abstract

While factor analysis is one of the most often used techniques in psychometrics, comparing or combining solutions from different factor analyses can be cumbersome even though it is necessary in several situations. For example, when applying multiple imputation (to account for incompleteness) or multiple outputation (which can be used to deal with clustering in multilevel data) often tens or hundreds of results have to be combined into one final solution. While different solutions have been in use, we propose a simple and easy to implement solution to match factors from different analyses based on factor congruence. To demonstrate this method, the Big Five Inventory data collected under the auspices of the Divorce in Flanders study was analysed combining multiple outputation and factor analysis. This multilevel sample consists of 7533 individuals coming from 4460 families with about 10% of missing values.