# Geographically Weighted Regression Using the Poisson Distribution

From my reading so far, GWR uses the Gaussian or bisquare distribution. My dependent and explanatory variables are rates. I was reading Chapter 12 of Spatial Statistical Data Analysis for GIS Users by Krivoruchko and saw this:

"For non-Gaussian data, gwr can be used with Poisson regression when input data are counts or rates and with logistic regression when data are binary or proportions."

How do I test my data to determine if I should use Gaussian, bisquare or the Poisson for my GWR analysis? What are the key differences between them? Since I was going to use ArcGIS for the GWR, is there a way I can select the Poisson?

• are you trying to predict values based on raster inputs? – user1269942 Oct 6 '14 at 16:44
• I have a .shp file aggregated to a census geography with rates for my dept/explanatory variables. I am trying to determine how well my dept variable can be explained by my explanatory variables. Since all of these variables are rates, is using the Guassian GWR method appropriate or should I use the Poisson? Thank you. – I Heart Beats Oct 6 '14 at 19:10
• My advice would be to post your question to stats.stackexchange.com (and then remove this question). – user1269942 Oct 6 '14 at 21:53

I think this answers my question after spending some time on the web. From the text below, it seems that Gaussian is appropriate since I have some negative rates and my variables are not integers.

"Choosing the form of the regression model

Three items will control the form and output from a geographically weighted regression model:

1. The nature of the dependent variable y:

Continuous (linear or Gaussian model)

Positive integer counts (Poisson model)

Proportions or rates (logistic model)

2. The nature of the explanatory, or "x" variable or variables

Continuous

Categorical

3. The weight function(s)

Geographical weights that control how neighboring locations influence values at specific locations

Non-spatial weights to account for the reliability of data (e.g., population size for disease rate data)"