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Related Experiment Video

Updated: Mar 26, 2026

Whole-cell Super-Resolution Imaging via DNA-PAINT on a Spinning Disk Confocal with Optical Photon Reassignment
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Convergence Properties of Certain Minres Algorithms.

J M Ten Berge, F E Zegers

    Multivariate Behavioral Research
    |January 29, 2016
    PubMed
    Summary
    This summary is machine-generated.

    The Harman and Jones Minres factor analysis method is guaranteed to converge monotonically. Levin

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    Area of Science:

    • Multivariate statistics
    • Psychometrics
    • Factor analysis

    Background:

    • The Harman and Jones (1966) method for Minres factor analysis has been a subject of debate regarding its convergence properties.
    • Levin (1988) questioned the guaranteed convergence of this method and proposed an alternative with a modified algorithm.

    Purpose of the Study:

    • To rigorously evaluate the convergence claims made by Levin (1988) concerning the Harman and Jones (1966) Minres factor analysis method.
    • To assess the validity of Levin's proposed modifications and alternative methods for factor analysis.

    Main Methods:

    • Theoretical analysis of iterative algorithms in factor analysis.
    • Mathematical proofs of convergence properties for the Harman and Jones method.
    • Comparison of the Harman and Jones method with Levin's proposed modifications and the Comrey and Ahumada method.

    Main Results:

    • The Harman and Jones (1966) method demonstrates guaranteed monotone convergence.
    • Levin's (1988) claims regarding the lack of guaranteed convergence for the Harman and Jones method are invalidated.
    • Levin's proposed modified method may converge to an incorrect solution.
    • The rank-one version of the Harman and Jones method, as implemented by Zegers and ten Berge (1983), possesses a valid convergence proof, contrary to Levin's assertions.

    Conclusions:

    • The Harman and Jones (1966) Minres factor analysis method is reliable due to its guaranteed monotone convergence.
    • Levin's (1988) criticisms and proposed alternatives are shown to be unfounded, with potential drawbacks in his modified approach.