Scaled von Mises-Fisher distributions and regression models for paleomagnetic directional data

Scealy, J. L.; Wood, Andrew T. A.

Abstract

We propose a new distribution for analysing paleomagnetic directional data that is a novel transformation of the von Mises-Fisher distribution. The new distribution has ellipse-like symmetry, as does the Kent distribution; however, unlike the Kent distribution the normalising constant in the new density is easy to compute and estimation of the shape parameters is straightforward. To accommodate outliers, the model also incorporates an additional shape parameter which controls the tail-weight of the distribution. We also develop a general regression model framework that allows both the mean direction and the shape parameters of the error distribution to depend on covariates. The proposed regression procedure is shown to be equivariant with respect to the choice of coordinate system for the directional response. To illustrate, we analyse paleomagnetic directional data from the GEOMAGIA50.v3 database (Brown et al. 2015). We predict the mean direction at various geological 1 time points and show that there is significant heteroscedasticity present. It is envisaged that the regression structures and error distribution proposed here will also prove useful when covariate information is available with (i) other types of directional response data; and (ii) square-root transformed compositional data of general dimension.

Citation

Scealy, J. L., & Wood, A. T. A. (2019). Scaled von Mises-Fisher distributions and regression models for paleomagnetic directional data. Journal of the American Statistical Association, 114(528), 1547-1560. https://doi.org/10.1080/01621459.2019.1585249

• Journal Article Type: Article
• Acceptance Date: Feb 10, 2019
• Online Publication Date: Feb 27, 2019
• Publication Date: Feb 27, 2019
• Deposit Date: Mar 11, 2019
• Publicly Available Date: Feb 28, 2020
• Journal: Journal of the American Statistical Association
• Print ISSN: 0162-1459
• Electronic ISSN: 1537-274X
• Publisher: Taylor & Francis Open
• Peer Reviewed: Peer Reviewed
• Volume: 114
• Issue: 528
• Pages: 1547-1560
• DOI: https://doi.org/10.1080/01621459.2019.1585249
• Keywords: Heteroscedasticity; Regression; Spherical data; t-distribution
• Public URL: https://nottingham-repository.worktribe.com/output/1626796
• Publisher URL: https://amstat.tandfonline.com/doi/full/10.1080/01621459.2019.1585249#.XIi68-RvJ9A
• Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 27.02.2019 available online: http://10.1080/01621459.2019.1585249