The Kaiser, Hunka and Bianchini Factor Similarity Coefficients: A Cautionary Note

Area of Science:

• Psychometrics
• Multivariate Statistics

Background:

• Comparing factor loading matrices is crucial for assessing structural invariance across different groups.
• The Kaiser, Hunka, and Bianchini (1971) method proposed a rotation-based approach to quantify factor similarity.

Purpose of the Study:

• To mathematically examine the optimal rotation in the Kaiser, Hunka, and Bianchini (1971) method.
• To determine the validity of the proposed factor comparison technique.

Main Methods:

• Mathematical analysis of the rotation matrix optimization.
• Evaluation of the sum of inner products criterion for factor similarity.

Main Results:

• The mathematical examination revealed fundamental issues with the optimization process.
• The method's reliance on optimizing specific inner products was found to be mathematically unsound.

Conclusions:

• The Kaiser, Hunka, and Bianchini (1971) method for comparing factor loading matrices is demonstrated to be invalid.
• The proposed approach for assessing factor similarity across different groups is unreliable due to mathematical deficiencies.