Rotational Uniqueness Conditions Under Oblique Factor Correlation Metric

TL;DR

This paper examines the conditions for rotational uniqueness in oblique factor analysis, revealing that previous assumptions about their equivalence are incorrect and proposing necessary amendments for global rotational uniqueness.

Contribution

It clarifies and corrects the conditions for global rotational uniqueness in oblique factor solutions under different metrics, challenging prior claims of their equivalence.

Findings

Conditions for oblique factor correlation structure need amendment

Previous condition sets are not equivalent for global uniqueness

Provides revised criteria for rotational identification

Abstract

In an addendum to his seminal 1969 article J\"{o}reskog stated two sets of conditions for rotational identification of the oblique factor solution under utilization of fixed zero elements in the factor loadings matrix. These condition sets, formulated under factor correlation and factor covariance metrics, respectively, were claimed to be equivalent and to lead to global rotational uniqueness of the factor solution. It is shown here that the conditions for the oblique factor correlation structure need to be amended for global rotational uniqueness, and hence, that the condition sets are not equivalent in terms of unicity of the solution.