TITLE:
Dealing with Multicollinearity in Factor Analysis: The Problem, Detections, and Solutions
AUTHORS:
Theodoros Kyriazos, Mary Poga
KEYWORDS:
Multicollinearity, Factor Analysis, Biased Factor Loadings, Unreliable Factor Structure, Reduced Stability, Variance Inflation Factor
JOURNAL NAME:
Open Journal of Statistics,
Vol.13 No.3,
June
28,
2023
ABSTRACT: Multicollinearity
in factor analysis has negative effects, including unreliable factor structure,
inconsistent loadings, inflated standard errors, reduced discriminant validity,
and difficulties in interpreting factors. It also leads to reduced stability,
hindered factor replication, misinterpretation of factor importance, increased
parameter estimation instability, reduced power to detect the true factor
structure, compromised model fit indices, and biased factor loadings.
Multicollinearity introduces uncertainty, complexity, and limited
generalizability, hampering factor analysis. To
address multicollinearity, researchers can examine the correlation matrix to
identify variables with high correlation coefficients. The Variance Inflation
Factor (VIF) measures the inflation of regression coefficients due to
multicollinearity. Tolerance, the reciprocal of VIF, indicates the proportion
of variance in a predictor variable not shared
with others. Eigenvalues help assess multicollinearity, with values greater than 1 suggesting the retention of factors. Principal Component Analysis (PCA)
reduces dimensionality and identifies highly correlated variables. Other diagnostic measures include the condition
number and Cook’s distance. Researchers can center or standardize data,
perform variable filtering, use PCA instead of factor analysis, employ factor
scores, merge correlated variables, or apply clustering techniques for the
solution of the multicollinearity problem. Further
research is needed to explore different types of multicollinearity, assess
method effectiveness, and investigate the relationship with other factor
analysis issues.