Trouble with Prediction Feature Class from a Geographically Weighted Regression

[EthanHowieson]

Hi all,

  Here is my situation: I am looking to use the relationship between a dependent and explanatory variable from one area to predict the same dependent variable for another area. I have done some research and found that the Prediction Feature Class from the Geographically Weighted Regression (GWR) tool should work for this.

  I was able to achieve this at a province scale using Census Subdivisions (CSDs) (modelling the relationship for an entire province then overlaying that relationship on another province and getting a proper result); however, when I reduce the size of the study area to the city-scale (and even just to half of the province), every attribute in every record in the resulting Prediction Feature Class is NULL. I thought is would be an issue with the number of features used in the calculation being reduced; however, when I switched to Dissemination Blocks (DBs) (a city of CSDs was around 17 features while a city of DBs was 13,000 features) the Prediction Feature Class still had NULL results.

I've researched this issues extensively but have had no luck finding a solution. If someone is able to help me out or point me in the right direction it would be greatly appreciate it or if there is another solution to this without using a GWR and Prediction Feature Class I am all ears.

Thanks

[DanPatterson_Retired]

Size is identified, for the first but obviously not the second

Geographically Weighted Regression (GWR)—Help | ArcGIS for Desktop

GWR should be applied to datasets with several hundred features for best results. It is not an appropriate method for small datasets. The tool does not work with multipoint data.

you are using projected data and performed an OLS first?

So what were your parameters etc in the steps outlined here?

Interpreting GWR results—Help | ArcGIS for Desktop

[DanPatterson_Retired]

Also a concern that I am sure you have addressed to avoid the MAUP when applying relationships at one organizational division to another.  There are many papers on this of course, this is one with examples

http://priede.bf.lu.lv/ftp/pub/TIS/datu_analiize/Passage/dungan_etal.pdf

[EthanHowieson]

Thanks for replying Dan.

The second data set (the one I am overlaying the relationship on to) has 13,000 DBs. I am using projected data; however I did not run an OLS. I went straight to the GWR because of the Prediction Feature Class component allowing me to overlay a relationship onto a new area while the OLS did not allow me to do so; however, that was probably a mistake.

The parameters for the GWR I used were 1 explanatory variable, an adaptive kernel type, and an AICc bandwidth (no distances or weights were used).

I haven't heard of the MUAP issue so I will take a look at that paper, thank you for that knowledge.

From your comments, a solution may come from creating a proper OLS model then running that as a GWR and then creating a Prediction Feature Class using the best model

[DanPatterson_Retired]

Keep us posted... the MAUP essentially boils down to things observed at one "scale" or level of aggregation cannot be assumed to apply to another level of aggregation.  A simple example would be voting... as you move down from the state/province ... to county/township ... to city/town  ... to neighborhood ... to street ... to individual level.... it should be very obvious that extrapolation/application of observations at one spatial aggregation cannot be applied or assume to apply to another.   In short... space is just another hassle in trying to describe patterns in space, let alone time, let alone in another space, let alone in another space in another time..... you get the drift

[EthanHowieson]

An update:

     After running the OLS on my CSD data set, I got an R^2 value of 0.78 and this data set creates a prediction feature class just fine. For my DB data set, I got an R^2 value of  0.0069 and this data set does not create a prediction feature class. This now make sense why I wasn't able to produce a prediction feature class from the DB data set because there is essentially no relationship!

     I think after I create a proper OLS model with my DB data set I should be able to generate the prediction feature class.

Thanks for you help!

[origudes]

You could have used also How Exploratory Regression works—ArcGIS Pro | ArcGIS for Desktop to test all your measures, it does account for the 6 OLS assumption, then only after move to GWR.

[EthanHowieson]

Another Update

   I have clipped out a smaller area from my DB feature class (the clipped feature class has 129 features) in order to make it easy for inputting "artificial data" (data that I have made up in order to test if creating a proper OLS will lead to generating a proper Prediction Feature Class). After running the exploratory regression, all of the assumptions were met. The model had a AICc value of 276.89, and an R^2 of 0.93.

When  I ran the GWR and the Prediction Feature class I still ended up with NULL values in the Prediction Feature Class...

[JenoraD_Acosta]

Hey Ethan!  I am sorry you are having all of this trouble!  A couple questions ...

1- What version of the software are you using?

2- Were you able to create the coefficient rasters?

3- For every prediction location, do you have explanatory variable values? Or are there some missing?

The last thing I would mention is just to double-triple-check that the order of explanatory variables for the Explanatory Variables parameter is EXACTLY the same as the order of the variables listed for the Prediction Explanatory Variables.

If you are willing to share the data for the clipped out smaller area and the settings you are using in the the tool, I am more than happy to look at it and try to figure out what's happening here.  Email me at jdacosta@esri.com

-Jenora