SIMPLE STRUCTURE AND THE NUMBER OF FACTORS PROBLEM

Area of Science:

• Psychometrics
• Multivariate Statistics
• Data Analysis

Background:

• Determining the number of common factors is crucial in factor analysis.
• Existing methods for factor matrix rank determination often lack clarity.
• Principal axes and varimax rotation are common techniques.

Purpose of the Study:

• To propose and evaluate a novel method for determining the number of common factors.
• To assess the clarity of latent structure using varimax criterion values.
• To compare this procedure with existing rules of thumb.

Main Methods:

• Calculating varimax criterion values for successive principal axes rotations.
• Analyzing the unimodality of the distribution of these values.
• Identifying the peak value to indicate the number of common factors.
• Applying the procedure to nine published example problems.

Main Results:

• The unimodality of varimax criterion values reflects the clarity of the latent structure.
• The peak value of the varimax criterion distribution reliably indicates the number of common factors.
• The proposed method provides a clear criterion for factor matrix rank determination.

Conclusions:

• The varimax criterion provides a robust and interpretable method for determining the number of common factors.
• This approach enhances the clarity and reliability of factor analysis.
• The findings offer a valuable tool for researchers in various fields utilizing factor analysis.