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Exploratory extended redundancy analysis using sparse estimation and oblique rotation of parameter matrices

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Abstract

Extended redundancy analysis (ERA) is a multivariate analysis procedure that regresses dependent variable(s) on the component scores, defined as weighted sums of independent variables. ERA requires information on the group structure of the independent variables, which is not available in many cases. The research proposes a new exploratory variant of ERA called exploratory ERA (ExERA), which does not require the group structure but estimates it using the dataset. ExERA is further classified into the following two procedures: ExERA-Sp and ExERA-R. ExERA-Sp estimates the group structure of independent variables by sparsely estimating the weight matrix, while ExERA-R approximates a similar structure obtained using ExERA-Sp and obliquely rotating the weight matrix. The performance of the two procedures was investigated using numerical simulation and a real data example. The results showed that the proposed methods were effective for exploratory data analysis.

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Funding

This research was supported by JSPS KAKENHI Grant Number 23K16854.

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  1. Department of Sociology, Kansai University, 3-3-35, Yamate-cho, Suita, Osaka, 564-8680, Japan

    Naoto Yamashita

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  1. Naoto Yamashita
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Correspondence to Naoto Yamashita.

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Communicated by Kei Hirose.

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Yamashita, N. Exploratory extended redundancy analysis using sparse estimation and oblique rotation of parameter matrices. Behaviormetrika 50, 679–697 (2023). https://doi.org/10.1007/s41237-023-00200-7

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  • DOI: https://doi.org/10.1007/s41237-023-00200-7

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