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Least circular distance regression for directional data

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  • Ulric Lund

Abstract

Least-squares regression is not appropriate when the response variable is circular, and can lead to erroneous results. The reason for this is that the squared difference is not an appropriate measure of distance on the circle. In this paper, a circular analog to least-squares regression is presented for predicting a circular response variable by another circular variable and a set of linear covariates. An alternative maximum-likelihood formulation yields the same regression parameter estimates. Under the maximum-likelihood model, asymptotic standard errors of the parameter estimates are obtained. As an example, the regression model is used to model data from a marine biology study.

Suggested Citation

  • Ulric Lund, 1999. "Least circular distance regression for directional data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(6), pages 723-733.
    • Handle: RePEc:taf:japsta:v:26:y:1999:i:6:p:723-733
    DOI: 10.1080/02664769922160
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    Cited by:

    1. Rodríguez, Carlos E. & Núñez-Antonio, Gabriel & Escarela, Gabriel, 2020. "A Bayesian mixture model for clustering circular data," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    2. Sungsu Kim & Ashis SenGupta, 2013. "A three-parameter generalized von Mises distribution," Statistical Papers, Springer, vol. 54(3), pages 685-693, August.
    3. Moritz N. Lang & Lisa Schlosser & Torsten Hothorn & Georg J. Mayr & Reto Stauffer & Achim Zeileis, 2020. "Circular regression trees and forests with an application to probabilistic wind direction forecasting," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1357-1374, November.
    4. McVinish, R. & Mengersen, K., 2008. "Semiparametric Bayesian circular statistics," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4722-4730, June.

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