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SIMPLE STRUCTURE AND THE NUMBER OF FACTORS PROBLEM.

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    Examining varimax criterion values helps identify latent structure clarity and common factor numbers in data. This method aids in determining the rank of a factor matrix, improving data analysis.

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    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.