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A Generalized Logistic Link Function for Cumulative Link Models in Ordinal Regression

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Abstract

Ordinal regression is a kind of regression analysis used for predicting an ordered response variable. In these problems, the patterns are labelled by a set of ranks with an ordering among the different categories. The most common type of ordinal regression model is the cumulative link model. The cumulative link model relates an unobserved continuous latent variable with a monotone link function. Logit and probit functions are examples of link functions used in cumulative link models. In this paper, a novel generalized link function based on a generalization of the logistic distribution is proposed. The generalized link function proposed is able to reproduce other different link functions by changing two real parameters: \(\alpha \) and \(\lambda \). The generalized link function has been included in a cumulative link model where the latent function is determined by a standard neural network in order to test the performance of the proposal. For this model, a reformulation of the tunable thresholds and distribution parameters was applied to convert the constrained optimization problem into an unconstrained optimization problem. Experimental results demonstrate that our proposed approach can achieve competitive generalization performance.

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Notes

  1. The datasets and results are available at http://www.gatsby.ucl.ac.uk/~chuwei/ordinalregression.html.

  2. JCLEC url: http://jclec.sourceforge.net.

  3. JCLEC url: http://jclec.sourceforge.net.

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Acknowledgements

The author would like to thank Professor Jaime Cardoso who kindly provided us with the source code of the oNN algorithm. This work has been partially subsidised by the TIN2014-54583-C2-1-R project of the Spanish Ministry of Economy and Competitiveness (MINECO), FEDER funds and the P2011-TIC-7508 project of the “Junta de Andalucia” (Spain).

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  1. Department of Quantitative Methods, Universidad Loyola Andalucia, Seville, Spain

    F. Fernández-Navarro

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  1. F. Fernández-Navarro
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Correspondence to F. Fernández-Navarro.

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Fernández-Navarro, F. A Generalized Logistic Link Function for Cumulative Link Models in Ordinal Regression. Neural Process Lett 46, 251–269 (2017). https://doi.org/10.1007/s11063-017-9589-3

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