Algorithm Description

Geographically Weighted Regression (GWR) is a spatial regression technique used to evaluate a local model of the variable or process by fitting a regression equation to every feature in the dataset. Generally, it is a local form of linear regression used to model spatially varying relationships.

Input Layer

Select the input layer containing all the fields used to build local regression model.

Input Parameters

Select only one dependent variable and one or multiple explanatory variables (a.k.a. independent variables).

1. Dependent Variable: The field containing values dependent on explanatory variable(s) in regression model
2. Explanatory Variable: The field(s) representing independent explanatory variable(s) in regression model.

Spatial Kernel Type

Select the kernel type, either fixed or adaptive, usually depending on how observations distribute in the region of interest.

1. Fixed: The spatial context used to solve each local regression analysis is a fixed distance. Fixed kernel type is suggested when observations distribute evenly in the research region.
2. Adaptive: The spatial context is a specified number of nearest neighbors. Where feature distribution is dense, the spatial context is smaller, while where feature distribution is sparse, the spatial context is larger.

Spatial Kernel Function

Select one kernel function to calculate weight matrix for each observation.

1. Gaussian
2. Exponential
3. Bisquare

Note: A potential issue with the Gaussian and Exponential kernel functions is that all observations retain non-zero weight, regardless of their distance from the calibration location. This means that even faraway observations can remain influential for moderate-to-large bandwidth parameters.

To avoid the issue above, the default kernel function is set to bi-square kernel. Moreover, bi-square kernel has a much more intuitive interpretation, where the bandwidth parameter is the distance or number of nearest neighbors away in space so that the remaining observations will not affect in searching optimal bandwidth parameters.

Bandwidth Searching

Specify which method to use in order to search for an optimal bandwidth.

1. Golden Section Search Method: The golden section search is a technique for finding an extremum (minimum or maximum) of a function inside a specified interval. In GWR this method helps searching for the optimal bandwidth.

2. Equal Interval Method: The equal interval is an intuitive method to search for the optimal bandwidth since it simply checks each bandwidth between the predefined minimum and maximum bandwidth based on a fixed user-input interval. Therefore, if user chooses to use equal interval method, it is mandatory to fill the three optional fields:

   1. Bandwidth Min: Bandwidth searching will start from this number.
   2. Bandwidth Max: Bandwidth searching will end before this number.
   3. Interval: Interval increment used in bandwidth search.

   Important Note: Pay attention to the units of bandwidth, meters for fixed kernel type, number of nearest neighbors for adaptvie one.

Bandwidth Searching Criterion

Specify how the extent of the kernel should be determined.

1. CV: Cross validation criterion compares the model residuals based on different bandwidths and chooses the optimal solution.
2. AIC: Akaike information criterion estimates the quality of each model, relative to each of the other models.
3. AICc: Corrected Akaike information criterion is an improved version of AIC, as well as the mostly suggested one, since it penalizes smaller bandwidths that result in more complex models that consume more degrees of freedom.
4. BIC: Bayesian information criterion shares the same methodology with AIC, but performs better at model selection.

Plugin Authors: Gao & Song

Algorithm Version: 1.2