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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/EE2.3.20.0170" target="_blank" >EE2.3.20.0170: Budování výzkumně-vzdělávacího týmu v oblasti modelování přírodních jevů a využití geoinformačních systémů, s vazbou na zapojení do mezinárodních sítí a programů.</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Measurement Science Review

ISSN

1335-8871

e-ISSN

—

Svazek periodika

16

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

PL - Polská republika

Počet stran výsledku

9

Strana od-do

235-243

Kód UT WoS článku

000387145900001

EID výsledku v databázi Scopus

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