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    This study introduces an iterative algorithm for finding orthogonal simple structure solutions. The method is proven to converge and successfully solves complex problems like Thurstone's 26-variable box problem.

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    Area of Science:

    • Psychometrics
    • Mathematical Psychology
    • Data Analysis

    Background:

    • Orthogonal simple structure is a key concept in factor analysis.
    • Existing methods may face challenges in achieving robust solutions.

    Purpose of the Study:

    • To propose a novel iterative process for obtaining orthogonal simple structure solutions.
    • To demonstrate the convergence and applicability of the proposed algorithm.

    Main Methods:

    • An iterative algorithm is developed.
    • A target matrix is constructed at each step, majorizing original contributions.
    • Convergence of the iterative procedure is mathematically proven.

    Main Results:

    • The proposed iterative process reliably yields orthogonal simple structure solutions.
    • The algorithm demonstrates convergence.
    • Successful application to Thurstone's 26-variable box problem is shown.

    Conclusions:

    • The developed iterative algorithm provides an effective method for achieving orthogonal simple structure.
    • This approach offers a robust solution for complex factor analysis problems.