QUANTILE REGRESSION AS A COMPLEMENTARY TOOL FOR MODELLING BIOLOGICAL DATA WITH HIGH VARIABILITY

Abstract

Biological data are usually heterogeneous, fluctuating and have outliers. When these data are examined using least squares regression models, difficulties often arise in identifying the impact of regressors on specific segments of the point cloud. Traditional models cannot be applied when regression assumptions are not met. The objective of this study was to examine the robustness of quantile regression (QR) in modelling data with high presence of extreme values. Using QR and least squares methods (ordinary and non-linear), we evaluated the change in biomass contents in different organs of mahogany (Swietenia macrophylla). The results suggest that QR significantly reduces the mean absolute error and the leverage effect. It also identifies the unit impact of the regressor on a specific quantile of the distribution. One of the main novelties of this approach was that greater interpretative capacity was possible for the different sectors of the conditional distribution, especially for those points far from the mean and the median, revealing more detailed behavioural patterns of the response variable. With this information, the rate of change of one variable due to the unit change of the other is more clearly understood.