GWR and Koenker (BP) Statistic

Question

OLS was performed before GWR.

However, the results(Below) from the test are statistically significant for the Koenker (BP) Statistic.

OLS Diagnostics 
Input Features: s Dependent Variable: DISTANCE 
Number of Observations: 35 Akaike's Information Criterion (AICc) [2]: 379.050298 
Multiple R-Squared [2]: 0.346008 Adjusted R-Squared [2]: 0.110571 
Joint F-Statistic [3]: 1.469641 Prob(>F), (9,25) degrees of freedom: 0.213178 
Joint Wald Statistic [4]: 19.658168 Prob(>chi-squared), (9) degrees of freedom: 0.020143*
Koenker (BP) Statistic [5]: 4.855700 Prob(>chi-squared), (9) degrees of freedom: 0.846701 
Jarque-Bera Statistic [6]: 425.511123 Prob(>chi-squared), (2) degrees of freedom: 0.000000*

I wonder whether it can be a candidates for Geographically Weighted Regression (GWR) analysis

or not.

HannesZiegler2 · Answer

In addition, it never hurts to run GWR (B) after finding a properly specified OLS (A) model using those variables from A in B. You may end up achieving a higher R2 and a lower AIC. Most relationships are not uniformly distributed in space (i.e. most variables display non-stationary relationships and so a model that can account for this is desirable).

LaurenRosenshein · Answer

Hi torock83,

This is a great question, and we've got a ton of resources that should help you moving forward!

You are absolutely right that you need to run OLS before you can move onto GWR to ensure that you've found a properly specified model.  There are actually 6 things you have to check before you can move onto GWR.  We recently published an ArcUser article that outlines these checks, Finding a Meaningful Model.  This should be very helpful.  There are also a ton of other resources at http://esriurl.com/spatialstats, including a Regression Analysis Tutorial.

As far as using the Koenker test to determine if GWR may improve your OLS model, you are absolutely right.  A statistically significant Koenker test does mean that there may be nonstationarity in your model that GWR can account for.  That being said, a statistically significant Koenker test would have an asterisk next to it, and be lower than 0.05.  In your case, your Koenker test is actually not statistically significant.  BUT...don't be discouraged.  That doesn't mean GWR wont help you.  You've actually got some work to do before you can determine if GWR will help, because you have other issues with your OLS model.  From the output you included we can see that the Jarque-Bera statistic is statistically significant (notice the asterisk*), which means that you have a biased model, and can't trust the results of your OLS analysis.  Once you go through the 6 checks described in the ArcUser article you may find that your Koenker test has changed and GWR may help after all.  It's all a matter of finding a good OLS model first!

Hope this helps!

Lauren Rosenshein
Geoprocessing Product Engineer