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    Area of Science:

    • Psychometrics
    • Statistical Modeling

    Background:

    • Determining the optimal number of factors in factor analysis is crucial for accurate interpretation.
    • Existing decision rules, including Kaiser-Guttman, scree, and likelihood ratio tests, have varying degrees of effectiveness.

    Purpose of the Study:

    • To empirically evaluate the performance of the Kaiser-Guttman, scree, and likelihood ratio tests in factor retention.
    • To investigate how factors such as the number of variables, factor-to-variable ratio, communality, and factorial complexity influence rule accuracy.

    Main Methods:

    • Simulation study involving 144 population and 288 sample data sets with known factor structures.
    • Application of Kaiser-Guttman and scree rules to population data (Part I).
    • Application of Kaiser-Guttman, scree, and likelihood ratio tests to sample data (Part II).

    Main Results:

    • Performance of the Kaiser-Guttman and scree rules varied significantly across different data conditions.
    • All three rules showed differential accuracy when applied to sample data, influenced by examined variables.
    • Detailed analysis of trends and interactions between data characteristics and rule performance.

    Conclusions:

    • No single decision rule consistently outperforms others across all scenarios in factor analysis.
    • Methods for assessing the quality of factor retention indicated by specific rules are presented.
    • Understanding the impact of data characteristics is vital for selecting appropriate factor analysis decision rules.