Constraints for non-zero secondary loadings in confirmatory factor analysis

TL;DR

This paper proposes a new constraint-based approach for confirmatory factor analysis that balances positive and negative loadings to achieve a more parsimonious and less restrictive model, using buffered scales as optimal indicators.

Contribution

It introduces a novel method to specify buffered simple structure constraints in confirmatory factor analysis, improving model flexibility and interpretability.

Findings

Buffered simple structure constraints effectively balance loadings.

Simulation study demonstrates improved model fit.

Empirical example confirms practical applicability.

Abstract

In the context of confirmatory factor analysis, the independent clusters model has been found to be overly restrictive in several research contexts. Therefore, a less restrictive criterion for parsimony of non-salient loadings in confirmatory factor analysis was proposed. The criterion is based on 'buffered scales', which have been introduced by Cattell and Tsujioka (1964) as optimal indicators of corresponding factors. Variables with positive and negative loadings on an unwanted factor are balanced out in a buffered scale, so that the variance of the unwanted factor is at minimum. It is proposed here to specify a balance of positive and negative secondary loadings by means of model constraints in order to achieve parsimony of loading patterns. The specification of buffered simple structure by means of model constraints was illustrated by means of a simulation study and an empirical example.