Are the Signs of Factor Loadings Arbitrary in Confirmatory Factor Analysis? Problems and Solutions

TL;DR

This paper investigates the problem of accurately estimating the signs of factor loadings in confirmatory factor analysis, revealing current methods' shortcomings and proposing effective solutions to improve reliability.

Contribution

It identifies a neglected issue in CFA—incorrect loading signs—and introduces three effective solutions to address this problem, enhancing analysis validity.

Findings

Current methods often misestimate loading signs

Proposed solutions effectively correct sign estimation issues

Improved reliability in CFA results with new methods

Abstract

The replication crisis in social and behavioral sciences has raised concerns about the reliability and validity of empirical studies. While research in the literature has explored contributing factors to this crisis, the issues related to analytical tools have received less attention. This study focuses on a widely used analytical tool - confirmatory factor analysis (CFA) - and investigates one issue that is typically overlooked in practice: accurately estimating factor-loading signs. Incorrect loading signs can distort the relationship between observed variables and latent factors, leading to unreliable or invalid results in subsequent analyses. Our study aims to investigate and address the estimation problem of factor-loading signs in CFA models. Based on an empirical demonstration and Monte Carlo simulation studies, we found current methods have drawbacks in estimating loading signs. To address this problem, three solutions are proposed and proven to work effectively. The applications of these solutions are discussed and elaborated.