Non-parametric regression models for compositional data

Abstract

Compositional data arise in many real-life applications and versatile methods for properly analyzing this type of data in the regression context are needed. This paper, through use of the α-transformation, extends the classical k-N N regression to what is termed α-k-N N regression, yielding a highly flexible non-parametric regression model for compositional data. 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 model without modification. Extensive simulation studies and real-life data analysis highlight the advantage of using α-k-N N regression for complex relationships between the response data and predictor variables for two cases, namely when the response data is compositional and predictor variables are continuous (or categorical) and vice versa. Both cases suggest that α-k-N N regression can lead to more accurate predictions compared to current regression models which assume a, sometimes restrictive, parametric relationship with the predictor variables.

Kernel Partial Correlation Coefficient -- a Measure of Conditional Dependence

“…Besides political science, such data are prevalent in many other fields such as sedimentology [66,1], hydrochemistry [100], economics [95], and bioinformatics [144,26,118]. Regression methods have been developed with compositional data as covariates [118,87,136], as response [1,72,66,56,140,141], or as both covariates and response [28]. But there are few variable selection methods proposed for data with compositional response and Euclidean covariates, as in our case here.…”

Dependent Bayesian nonparametric modeling of compositional data using random Bernstein polynomials

“…Other proposals use the Dirichlet distribution to model the compositional responses and link the Dirichlet parameters to covariates (see, e.g., Gueorguieva et al, 2008;Hijazi, 2003;Hijazi & Jernigan, 2009;Van der Merwe, 2019). These models can be easily extended to allow for non-parametric functional forms in the relationship between the model parameters and the predictors (see, e.g., Di Marzio et al, 2015;Tsagris et al, 2020). However, they rely on particular parametric distributional forms which limits the type of inferences that can be obtained.…”