Abstract
Regression analysis is used to model the relationship between a response variable and one or more explanatory variables (covariates). In the compositional case, the proper choice of logratio coordinates matters, both due to the interpretation of the regression parameters and because of the properties of the regression models. And again, orthonormal coordinates, particularly in their pivot version, are preferable. Moreover, in case of regression with compositional response and real covariates, ilr coordinates enable to decompose the multivariate regression model into single multiple regressions. The coordinate representation of compositions is essential also for statistical inference like hypotheses testing, which is frequently of interest in the regression context. In this chapter, all basic regression cases are contained: the mentioned regression with compositional response and real covariates, the case of real response and compositional explanatory variables, regression between two compositions, and finally also regression between the parts within one composition. A further important task is considered: variable selection of relevant covariates by forward and backward selection. Robustness issues are also of particular importance in the regression context—outliers in the response or in the covariates will have limited effect for robust regression estimates.
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Filzmoser, P., Hron, K., Templ, M. (2018). Regression Analysis. In: Applied Compositional Data Analysis. Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-96422-5_10
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