Variable selection in linear-circular regression models

Date

2022-08-01

Author

Çamlı, Onur
Kalaylıoğlu Akyıldız, Zeynep Işıl
SenGupta, Ashis

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Applications of circular regression models are ubiquitous in many disciplines, particularly in meteorology, biology and geology. In circular regression models, variable selection problem continues to be a remarkable open question. In this paper, we address variable selection in linear-circular regression models where uni-variate linear dependent and a mixed set of circular and linear independent variables constitute the data set. We consider Bayesian lasso which is a popular choice for variable selection in classical linear regression models. We show that Bayesian lasso in linear-circular regression models is not able to produce robust inference as the coefficient estimates are sensitive to the choice of hyper-prior setting for the tuning parameter. To eradicate the problem, we propose a robustified Bayesian lasso that is based on an empirical Bayes (EB) type methodology to construct a hyper-prior for the tuning parameter while using Gibbs Sampling. This hyper-prior construction is computationally more feasible than the hyper-priors that are based on correlation measures. We show in a comprehensive simulation study that Bayesian lasso with EB-GS hyper-prior leads to a more robust inference. Overall, the method offers an efficient Bayesian lasso for variable selection in linear-circular regression while reducing model complexity.

Subject Keywords

Regularization, Bayesian lasso, laplace distribution, circular regression, dimension reduction, TUNING PARAMETER SELECTION, BAYESIAN-ANALYSIS, SHRINKAGE, LASSO, DISTRIBUTIONS

URI

https://hdl.handle.net/11511/100202

Journal

JOURNAL OF APPLIED STATISTICS

DOI

https://doi.org/10.1080/02664763.2022.2110860

Collections

Department of Statistics, Article

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Citation Formats

O. Çamlı, Z. I. Kalaylıoğlu Akyıldız, and A. SenGupta, “Variable selection in linear-circular regression models,” JOURNAL OF APPLIED STATISTICS, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/100202.