Performance of Bayesian quantile regression and its application to eutrophication modelling in Sutami Reservoir, East Java, Indonesia

Abstract

Phytoplankton has an important role in aquatic ecosystem as the primary natural feed for another aquatic biota. However, the density of phytoplankton must be controlled at desirable level in order to prevent eutrophication. Because eutrophication can damage the ecosystem and as the consequence will led to mass mortalities of fish. There are several factors that affecting phytoplankton density such as light availability, temperature, pH, and nutrient content. Nutrient content is composed by nitrate and phosphate. The relationship between nutrient content and phytoplankton density commonly performed by using simple linear regression. But, this method cannot give an overall description of the data since it is worked at conditional mean. Moreover, simple linear regression has several limitation like highly influence by outlier and need the fulfillment of classical assumption. Thus, the aims of this research are to offer an alternative method namely Bayesian quantile regression and provide its performance compared to simple linear regression under various data condition. Also to apply such model to the relationship between nutrients content and phytoplankton density in Sutami Reservoir. The results indicate that Bayesian quantile regression performs better than simple linear regression when the outlier exists. Unfortunately, the data of phytoplankton density and nutrients content in Sutami Reservoir contains outlier according to Cook's distance criteria. It means that Bayesian quantile regression should be used. The obtained model showed that the parameter values of regression model between nutrients content and phytoplankton density vary, which are depended on the analyzed quantile.