Flexible non-parametric regression models for compositional response data with zeros

Compositional data arise in many real-life applications and versatile methods for properly analyzing this type of data in the regression context are needed. When parametric assumptions do not hold or are difficult to verify, non-parametric regression models can provide a convenient alternative method for prediction. To this end, we consider an extension to the classical k-Nearest Neighbours (k-N N) regression, that yields a highly flexible non-parametric regression model for compositional data. A similar extension of kernel regression is proposed by adopting the Nadaraya-Watson estimator. Both extensions involve a power transformation termed the alpha-transformation. Unlike many of the recommended regression models for compositional data, zeros values (which commonly occur in practice) are not problematic and they can be incorporated into the proposed models without modification. Extensive simulation studies and real-life data analyses highlight the advantage of using these non-parametric regressions for complex relationships between compositional response data and Euclidean predictor variables. Both the extended K-N N and kernel regressions can lead to more accurate predictions compared to current regression models which assume a, sometimes restrictive, parametric relationship with the predictor variables. In addition, the extended k-N N regression, in contrast to current regression techniques, enjoys a high computational efficiency rendering it highly attractive for use with large sample data sets.