Practical aspects of log-ratio coordinate representations in regression with compositional response

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F16%3A33159862" target="_blank" >RIV/61989592:15310/16:33159862 - isvavai.cz</a>
Result on the web
<a href="https://www.degruyter.com/downloadpdf/j/msr.2016.16.issue-5/msr-2016-0029/msr-2016-0029.xml" target="_blank" >https://www.degruyter.com/downloadpdf/j/msr.2016.16.issue-5/msr-2016-0029/msr-2016-0029.xml</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/msr-2016-0029" target="_blank" >10.1515/msr-2016-0029</a>

Result language
angličtina
Original language name
Practical aspects of log-ratio coordinate representations in regression with compositional response
Original language description
Regression analysis with compositional response, observations carrying relative information, is an appropriate tool for statistical modelling in many scientific areas (e.g. medicine, geochemistry, geology, economics). Even though this technique has been recently intensively studied, there are still some practical aspects that deserve to be further analysed. Here we discuss the issue related to the coordinate representation of compositional data. It is shown that linear relation between particular orthonormal coordinates and centred log-ratio coordinates can be utilized to simplify the computation concerning regression parameters estimation and hypothesis testing. To enhance interpretation of regression parameters, the orthogonal coordinates and their relation with orthonormal and centred log-ratio coordinates are presented. Further we discuss the quality of prediction in different coordinate system. It is shown that the mean squared error (MSE) for orthonormal coordinates is less or equal to the MSE for log-transformed data. Finally, an illustrative real-world example from geology is presented.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/EE2.3.20.0170" target="_blank" >EE2.3.20.0170: Building of Research Team in the Field of Environmental Modeling and the Use of Geoinformation Systems with the Consequence in Participation in International Networks and Programs</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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