A computationally efficient method for obtaining standard error estimates for the promax and related solutions

Area of Science:

• Psychometrics
• Statistical Computing
• Factor Analysis

Background:

• Accurate estimation of asymptotic standard errors is crucial for interpreting factor analysis solutions.
• Existing methods for calculating standard errors in promax rotation can be computationally intensive.
• The promax rotation is a widely used method for oblique factor rotation.

Purpose of the Study:

• To propose a computationally efficient algorithm for calculating asymptotic standard errors for the promax factor solution.
• To extend the algorithm's applicability to various promax rotation scenarios and Procrustean rotations.
• To evaluate the algorithm's performance through simulations and a real data example.

Main Methods:

• Development of a novel, computationally efficient algorithm for asymptotic standard error computation.
• The algorithm accommodates promax rotation with or without row normalization and different promax targets.
• Adaptation of the algorithm for Procrustean rotations with fixed or random independent targets.

Main Results:

• Simulation results indicate that the proposed algorithm provides reasonable approximate standard errors for the promax solution.
• The algorithm demonstrates efficiency compared to the augmented information approach.
• Numerical results from a real data example align with an existing augmented information-based method.

Conclusions:

• The proposed algorithm offers an efficient and accurate method for computing asymptotic standard errors in promax factor analysis.
• The algorithm's flexibility extends its utility to related rotation techniques.
• This advancement can improve the speed and reliability of factor analysis interpretations.