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    Factor transformation methods were compared for their ability to accurately recover population factor structures from data samples. The study evaluated methods based on their approximation accuracy and sampling stability for both simple and complex data structures.

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    Area of Science:

    • Psychometrics
    • Statistical Modeling
    • Data Analysis

    Background:

    • Factor transformation methods are crucial for interpreting complex datasets.
    • Evaluating these methods requires understanding their performance with varying data structures.
    • Orthogonal and oblique factor models provide foundational frameworks for data analysis.

    Purpose of the Study:

    • To compare the efficacy of various factor transformation methods.
    • To assess the ability of these methods to approximate population parameter patterns.
    • To evaluate the sampling variability associated with different transformation techniques.

    Main Methods:

    • Generated populations with factorially simple and complex data structures.
    • Utilized both oblique and orthogonal factor models for data generation.
    • Compared solutions derived from special cases of the general orthomax criterion.

    Main Results:

    • Identified factor transformation methods that closely approximate parameter patterns.
    • Quantified the sampling variability for each evaluated method.
    • Demonstrated performance differences across simple and complex data structures.

    Conclusions:

    • Certain factor transformation methods exhibit superior performance in recovering factor structures.
    • Practical implications for selecting appropriate methods in data analysis are discussed.
    • The choice of method impacts the accuracy and stability of factor analysis results.