Tingyi’s Geob479 blog

Geographically weighted regression (GWR) is a spatial analysis technique widely used in geography and related disciplines related to spatial pattern analysis. GWR explores spatial changes and related drivers at a certain scale by establishing local regression equations at each point in the spatial range and can be used to predict future results. As it takes into account the local effects of spatial objects, its advantage is the higher accuracy. It detects the non-smoothness of spatial relations by embedding spatial structures into linear regression models. Because the method is not only simple and easy, the estimation results have a clear analytical representation, and the resulting parameter estimate can also be statistically tested, so more and more research and application.

In the spatial analysis, observational data is generally sampled as sampling units according to a given geographic location, and as the geographical location changes, the relationship or structure of the variables changes, i.e. the “space non-smoothness” referred to in GIS. This spatial non-stability is commonly found in spatial data, such as the incidence of AIDS in different provinces, the TN content of different depths of lakes, pm2.5 concentrations in urban and non-industrial areas, etc. If the traditional linear regression model is used to analyze spatial data, it is generally difficult to obtain satisfactory results, because the global model assumes that the relationship between variables is “anionic” before analysis, and the result is only some “average” in the study area. Therefore, it is necessary to adopt a new local regression method to deal with the nature of spatial data itself. Geographically weighted regression extends the traditional regression framework by allowing taking non-stationary variables into consideration (e.g., climate; demographic factors; physical environment characteristics) and models the local relationships between these predictors and an outcome of interest. In other words, GWR runs a regression for each location, instead of a sole regression for the entire study area. It is applied under the assumption that the strength and direction of the relationship between a dependent variable and its predictors may be modified by contextual factors. GWR has high utility in epidemiology, particularly for infectious disease research and evaluations of health policies or programs. The GWR model is proposed by researchers and has been practiced and verified extensively.

Limitations of GWR include problems of multicollinearity (the local regression coefficients are potentially collinear even if the underlying exogenous variables in the data generating process are uncorrelated) and the approaches to calculating goodness of fit statistics. Results and Discussion