Title: Congruence-Based Factor Matching for Exploratory Factor Analysis

Authors: Aniko Lovik, Vahid Nassiria, Geert Verbeke, Geert Molenberghs

Affiliation: KU Leuven - University of Leuven, I-BioStat, Leuven, Belgium;
Hasselt University, I-BioStat, Diepenbeek, Belgium

Abstract:
Exploratory factor analysis and principal component analysis assume
independent observations and, in case of missing data, by default a complete
case analysis is performed. Ignoring clustering and/or missing data may result
in bias. Previously we proposed a method combining multiple imputation (to
deal with incompleteness) and multiple out-putation (to account for
clustering) with EFA/PCA that solved both issues in a fast and flexible way at
the cost of dealing with the analysis of multiple datasets where the order of
the obtained factors/principal components varied and the number of factors had
to be fixed before matching (Lovik et al., 2018). Our method, based on the
maximisation of modified congruence coefficients to match the different
datasets/analyses, also required the analyses to be rotated before matching
for optimal results. In this study we extend this method to unknown number of
factors at the start of the analysis only assuming a simple factor structure
in the Thurstonian sense.

References:
Lovik A., Nassiri V., Verbeke G., & Molenberghs G. (2018). Combining Factors
from Different Factor Analyses Based on Factor Congruence. In: Wiberg M.,
Culpepper S., Janssen R., Gonzalez J., Molenaar D. (eds) Quantitative
Psychology. IMPS 2017. Springer Proceedings in Mathematics & Statistics, vol
233. Springer, Cham.