Geographically Weighted Polynomial Regression:Selection of the Optimal Bandwidth and the Optimal Polynomial Degrees and Its Application to Water Quality Index Modelling

Fatmawati, Toha Saifudin, Nur Chamidah

2018

Abstract

In this paper we introduce geographically weighted polynomial regression (GWPolR) model as a generalization of GWR model. It is an alternative solution to overcome the existence of nonlinear relationships between response variable and one or more explanatory variables involved in spatial modelling. This study aims to provide a procedure for finding the optimal bandwidth and polynomial degrees in the GWPolR technique. This procedure is applied to Water Quality Index (WQI) modelling based on several factors. Because GWR method does not account for nonlinearity relationships of the spatial data type, we hypothesize that a GWPolR model will help us better understand how the factors are related to WQI patterns. Both types of models were applied to examine the relationship between WQI and various explanatory variables in 33 provinces of Indonesia. The goal was to determine which approach yielded a better predictive model. Based on three explanatory variables, i.e. percentage of untreated waste, population density, and number of micro industries, the GWR produced a spatial precision, i.e. R2, of 35.28%. GWPolR efforts increased the value explained by explanatory variables with better spatial precision (R2 = 50.12%). The results of GWPolR approach provide more complete understanding of how each explanatory variable is related to WQI, which should allow improved planning of explanatory management strategies.

Paper Citation

in Harvard Style

Saifudin T., Fatmawati. and Chamidah N. (2018). Geographically Weighted Polynomial Regression:Selection of the Optimal Bandwidth and the Optimal Polynomial Degrees and Its Application to Water Quality Index Modelling.In Proceedings of the International Conference on Mathematics and Islam - Volume 1: ICMIs, ISBN 978-989-758-407-7, pages 93-100. DOI: 10.5220/0008517700930100

in Bibtex Style

@conference{icmis18,
author={Toha Saifudin and Fatmawati and Nur Chamidah},
title={Geographically Weighted Polynomial Regression:Selection of the Optimal Bandwidth and the Optimal Polynomial Degrees and Its Application to Water Quality Index Modelling},
booktitle={Proceedings of the International Conference on Mathematics and Islam - Volume 1: ICMIs,},
year={2018},
pages={93-100},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0008517700930100},
isbn={978-989-758-407-7},
}

in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Mathematics and Islam - Volume 1: ICMIs,
TI - Geographically Weighted Polynomial Regression:Selection of the Optimal Bandwidth and the Optimal Polynomial Degrees and Its Application to Water Quality Index Modelling
SN - 978-989-758-407-7
AU - Saifudin T.
AU - Fatmawati.
AU - Chamidah N.
PY - 2018
SP - 93
EP - 100
DO - 10.5220/0008517700930100