Compositional observations and their role in regression

Spracklen, Callum

Compositional observations and their role in regression

Master Thesis

2018

Publisher

University of Cape Town

Department

Division of Actuarial Science

Faculty

Faculty of Commerce

Abstract

This dissertation examines the properties and some of the uses of compositional data. It gives a brief history of the distinction between 'normal' data and compositions, as well as the various methods of analysing compositional data. It is mainly concerned with performing regression analysis including compositions. In order to model a composition it is necessary to understand the nature of compositions and how to use standard statistical tools with them. This dissertation describes the simplex and several functions which can be performed in it, as well as introducing several useful covariate structures for compositional samples after transformation. It also introduces the transformations between the simplex and unconstrained real space. The dissertation concludes with four examples of regression analyses involving compositions.

Keywords

Actuarial Science

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