Analysis of Spatio-Temporal Data for Forest Fire Control
This project aims to establish the relationship of forest fire with ecological/environmental factors, such as forest structure and weather. We analyze records of forest fires during the fire season (May to August) in 1992 from the Forest Fire Management Branch of Ontario Ministry of Natural Resource (OMNR). We start with a preliminary analysis of the data, which includes a descriptive summary and an ordinary linear regression analysis with fire duration as the response. The preliminary analysis indicates that the fire weather index (FWI) used by Natural Resource of Canada is the most relevant together with fire location and starting time. We apply semi-variogram and Moran's I, the conventional methods for exploring spatial patterns, and extend them to investigate spatial-temporal patterns with the fire data. Evaluations of the extended Moran's I statistic reveals strong spatial-temporal correlation in the residuals of the linear regression analysis. It motivates two sets of partially linear regression models to accommodate possible nonlinear spatial/temporal patterns of the forest fires. We integrate univariate and bivariate kernel smoothing procedures with the least squares procedure for estimating the model parameters. Residual analysis indicates satisfactory fittings in both sets of regression analysis. The partially linear regression analyses find that the association of fire duration with FWI varies across different fire management zones, and depends on the fire starting time.
Keywords: Kernel Smoothing; Local Constant/Linear Regression; Moran’s I; Partially Linear Models