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Regression modelling for size-and-shape data based on a Gaussian model for landmarks

Dryden, Ian L., Kume, Alfred, Paine, Phillip J., Wood, Andrew T. A. (2020) Regression modelling for size-and-shape data based on a Gaussian model for landmarks. Journal of the American Statistical Association, . ISSN 0162-1459. (doi:10.1080/01621459.2020.1724115) (KAR id:79862)

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Official URL:
https://doi.org/10.1080/01621459.2020.1724115

Abstract

In this paper we propose a regression model for size-and-shape response data. So far as we are aware, few such models have been explored in the literature to date. We assume a Gaussian model for labelled landmarks; these landmarks are used to represent the random objects under study. The regression structure, assumed in this paper to be linear in the ambient space, enters through the landmark means. Two approaches to parameter estimation are considered. The first approach is based directly on the marginal likelihood for the landmark-based shapes. In the second approach we treat the orientations of the landmarks as missing data, and we set up a model-consistent estimation procedure for the parameters using the EM algorithm. Both approaches raise challenging computational issues which we explain how to deal with. The usefulness of this regression modelling framework is demonstrated through real-data examples.

Item Type: Article
DOI/Identification number: 10.1080/01621459.2020.1724115
Uncontrolled keywords: EM algorithm, size-and-shape analysis, offset-normal shape distributions, mean shape, shape of the mean
Subjects: Q Science
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Alfred Kume
Date Deposited: 29 Jan 2020 09:43 UTC
Last Modified: 03 Mar 2021 14:50 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/79862 (The current URI for this page, for reference purposes)
Kume, Alfred: https://orcid.org/0000-0001-7683-1693
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