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Multinomial Principal Component Logistic Regression on Shape Data

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Abstract

This paper proposes a linear model that uses the principal component scores in shape data and fits the nominal responses in the tangent space of shapes. Multinomial logistic regression for multivariate data and logistic regression for binary responses are considered in this regard. Principal components in the tangent space are employed to improve the estimation of logistic model parameters under multicollinearity and to reduce the dimension of the input data. This paper improves the classification of shape data according to their different nominal groups. Furthermore, we assess the effectiveness of the proposed method using a comprehensive simulation and highlight the benefits of the new method using five real-world data sets.

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Data Availability

The real data sets analyzed during the current study are available in R software package shapes, [https://cran.r-project.org/web/packages/shape/index.html]. Also, the R codes for simulation study are available from the corresponding author upon request.

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Acknowledgements

We would also like to thank the editor, and two referees for their constructive and thoughtful comments which helped us tremendously in improving the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematics and Computer Science, Kharazmi University, KhU, No. 43. South Mofatteh Ave., Tehran, Iran

    Meisam Moghimbeygi

  2. Department of Statistics, Computer Science, Applications “Giuseppe Parenti”, University of Florence, Viale Morgagni 59, 50134, Florence, Italy

    Anahita Nodehi

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  1. Meisam Moghimbeygi
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Correspondence to Meisam Moghimbeygi.

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Moghimbeygi, M., Nodehi, A. Multinomial Principal Component Logistic Regression on Shape Data. J Classif 39, 578–599 (2022). https://doi.org/10.1007/s00357-022-09423-x

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Mathematics Subject Classification (2010)

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