Regression for non-Euclidean data using distance matrices

Julian J. Faraway

Journal of Applied Statistics, 2014, vol. 41, issue 11, 2342-2357

Abstract: Regression methods for common data types such as measured, count and categorical variables are well understood but increasingly statisticians need ways to model relationships between variable types such as shapes, curves, trees, correlation matrices and images that do not fit into the standard framework. Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which requires only the specification of a distance function. A low-dimensional representation of such distance matrices can be obtained using methods such as multidimensional scaling. Once these variables have been represented as scores, an internal model linking the predictors and the responses can be developed using standard methods. We call scoring as the transformation from a new observation to a score, whereas backscoring is a method to represent a score as an observation in the data space. Both methods are essential for prediction and explanation. We illustrate the methodology for shape data, unregistered curve data and correlation matrices using motion capture data from an experiment to study the motion of children with cleft lip.

Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/02664763.2014.909794 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:japsta:v:41:y:2014:i:11:p:2342-2357

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/CJAS20

DOI: 10.1080/02664763.2014.909794

Access Statistics for this article

Journal of Applied Statistics is currently edited by Robert Aykroyd

More articles in Journal of Applied Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().