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New links for binary regression: an application to coca cultivation in Peru

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  • Artur J. Lemonte

    (Universidade Federal do Rio Grande do Norte)

  • Jorge L. Bazán

    (Universidade de São Paulo)

Abstract

Binary response data arise naturally in applications. In general, the well-known logistic and probit regression models form the basis for analyzing binary data in practice. These regression models make use of symmetric link functions (logit and probit links). However, many authors have emphasized the need of asymmetric links in modeling binary response data. In this paper, we consider a broad class of parametric link functions that contains as special cases both symmetric as well as asymmetric links. Furthermore, this class of links is quite flexible and simple, and may be an interesting alternative to the usual regression models for binary data. We consider a frequentist approach to perform inferences, and the maximum likelihood method is employed to estimate the model parameters. We also propose residuals for the link models to assess departures from model assumptions as well as to detect outlying observations. Additionally, the local influence method is discussed, and the normal curvatures for studying local influence are derived under two specific perturbation schemes. Finally, an application to the coca leaf cultivation in Peru is considered to show the usefulness of the proposed link models in practice.

Suggested Citation

  • Artur J. Lemonte & Jorge L. Bazán, 2018. "New links for binary regression: an application to coca cultivation in Peru," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 597-617, September.
    • Handle: RePEc:spr:testjl:v:27:y:2018:i:3:d:10.1007_s11749-017-0563-1
    DOI: 10.1007/s11749-017-0563-1
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    References listed on IDEAS

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    1. Sungduk Kim & Ming-Hui Chen & Dipak K. Dey, 2008. "Flexible generalized t-link models for binary response data," Biometrika, Biometrika Trust, vol. 95(1), pages 93-106.
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    5. Jorge Luis Bazán & Óscar Millones, 2008. "Una clasificación de modelos de regresión binaria asimétrica: el uso del BAYES-PUCP en una aplicación sobre la decisión del cultivo ilícito de hoja de coca," Revista Economía, Fondo Editorial - Pontificia Universidad Católica del Perú, issue 62, pages 17-32.
    6. Chib, Siddhartha & Jeliazkov, Ivan, 2006. "Inference in Semiparametric Dynamic Models for Binary Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 685-700, June.
    7. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
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    Cited by:

    1. Henry R. Scharf & Xinyi Lu & Perry J. Williams & Mevin B. Hooten, 2022. "Constructing Flexible, Identifiable and Interpretable Statistical Models for Binary Data," International Statistical Review, International Statistical Institute, vol. 90(2), pages 328-345, August.
    2. Nancy Dávila-Cárdenes & José María Pérez-Sánchez & Emilio Gómez-Déniz & José Boza-Chirino, 2021. "Skewed Binary Regression to Study Rental Cars by Tourists in the Canary Islands," JRFM, MDPI, vol. 14(11), pages 1-15, November.
    3. Chénangnon Frédéric Tovissodé & Aliou Diop & Romain Glèlè Kakaï, 2021. "Inference in skew generalized t-link models for clustered binary outcome via a parameter-expanded EM algorithm," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-31, April.
    4. Artur J. Lemonte & Germán Moreno–Arenas, 2020. "Improved Estimation for a New Class of Parametric Link Functions in Binary Regression," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 84-110, May.

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