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<p>For communality estimation in factor analysis, a method called anti-ridge (AR) regression using a negative ridge parameter is presented to improve the squared multiple correlation coefficient (SMC) for a lower bound of the communality. The optimal improved SMC called the ARSMC is obtained when the anti-ridge parameter (the absolute value of the negative ridge parameter) is the smallest uniqueness in a correlation matrix. When the one-factor model holds, a method to have the smallest uniqueness is provided, which gives the exact communalities. For the multi-factor model, a communality estimator using the Moore–Penrose generalized inverse in the ARSMC is provided.</p>

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Anti-ridge regression for communality estimation in factor analysis

  • 期刊论文

  • 发表日期：

    2025年7月5日

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  • Haruhiko Ogasawara

摘要

For communality estimation in factor analysis, a method called anti-ridge (AR) regression using a negative ridge parameter is presented to improve the squared multiple correlation coefficient (SMC) for a lower bound of the communality. The optimal improved SMC called the ARSMC is obtained when the anti-ridge parameter (the absolute value of the negative ridge parameter) is the smallest uniqueness in a correlation matrix. When the one-factor model holds, a method to have the smallest uniqueness is provided, which gives the exact communalities. For the multi-factor model, a communality estimator using the Moore–Penrose generalized inverse in the ARSMC is provided.