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Can anybody tell me please why I cannot run the GWR model in ArcGIS 10.3 with a floating explanatory variable?

When I convert the floating explanatory variable in an integer variable, then, the model runs.But, when I use floating values, I got following error message - 040038 : Results cannot be computed because of severe model design problems. And at the description of the error in help tool box is - there is a multicollinearity problem. But, I used only one explanatory variable. So, multicollinearity or redundancy problem cannot exist.

  • Please expand abbreviations like GWR the first time you use them in your questions so that they can help serve future readers as learning materials. Also can you explain why you think floating explanatory variable should work. Do you have experience of such variables working when you run such models in other software? – nmtoken Oct 9 '16 at 8:53
  • Dear @nmtoken, yes you are right. It will be Geographically Weighted Regression. I will try to change the title. This is the first time I am going to use geographically weighted regression. I am not sure why an explanatory variable, which is in floating values, does not work in GWR model. I have not also used other software. I have here mentioned about ArcGIS to make my problem more specific. I would be grateful if you can explain the matter. – Kazi Masel Oct 9 '16 at 10:41
  • Please edit the question in response to comments requesting clarification. It's not fair to the volunteers who would answer to need to mine the comments for critical information. – Vince Oct 9 '16 at 11:47
  • @Vince, thanks! I have already edited the question. – Kazi Masel Oct 9 '16 at 14:17
  • Can you also please add what is happening when you try to input your original floating values to the tool? What error message(s) are you getting by doing so? – fatih_dur Oct 10 '16 at 12:24
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If there is a high level of spatial homogeneity in your data, you can have multicolinearity within a single variable. Since GWR is, in effect, a local moving window regression, the multicolinearity issue is in regard to redundant values within a local fit and not between variables. The term multicollinearty is very misleading and not consistent with the traditional statistical usage of the term, I wish ESRI would quit using it. I imagine that the returned error is correct and is indicating that you have so much redundancy within some local scale that GWR cannot fit the model.

However, I have no idea why converting to an integer would allow the model to run, it should work the other way because floating point values would provide additional variability. This seems like a fairly serious flaw in the ESRI implementation of GWR. One possibility is that the integer values are being treated explicitly as factorial values and the code is allowing fit for very few nominal levels whereas the error check in the code is not allowing a fit of the same unique number of values when continuous.

This is a good example on why statistical analysis should not be performed in ArcGIS. You have no tools for exploratory data analysis, which should be performed before specifying a model. Are you sure that you even have nonstationarity present in the data? If not, then a GWR is not an appropriate model and you should fall back on more standard regression techniques (eg., GLM, OLS, mixed effect models).

Some summary statistics and a general idea of the spatial structure of your data would go a long way in helping us understand what may be going on here. Questions along the lines of "I received this error, why?" normally do not yield satisfactory answers. Even in this case, I am simply speculating on some possible causes. More information, hopefully to the point of a repeatable problem, is what you should be aiming for in a well formulated question.

  • Dear Jeffrey Evan, thanks a lot for your detail answer! Within few days I will come here again and will share about the data, general statistics as well as aim of the study. Wish then I will get more detail and specific feedback. Thanks! – Kazi Masel Oct 11 '16 at 16:15
  • Dear Jeffrey Evan, by the way, can you tell me how I can be sure about the non-stationarity of variables before doing GWR? In an ESRI tutorial they suggested to use Moran I spatial auto-correlation technique to see if the Standard Residuals of OLS results is spatially clustered. According to that tutorial, the significant clustered means one or two explanatory variables are missing. But, if there is randomness in spatial auto-correlation, does it also mean there exits non-stationarity? – Kazi Masel Oct 11 '16 at 19:39
  • This would only indicate global (1st order) autocorrelation, where nonstationarity is a 2nd order process. Commonly, you would use a statistic like a LISA (Local Indicators of Spatial Association), local Geary's-C or Getis-Ord G*. It is difficult to ascertain a localized autocovariance effect in residual error from a linear model. – Jeffrey Evans Oct 11 '16 at 19:48
  • Dear Jeffrey, thanks! Then, what is the explanation behind the suggestion of the tutorial that if the spatial auto-correlation test shows cluster pattern, then, one or more explanatory variables are missing? – Kazi Masel Oct 11 '16 at 20:05
  • The idea of model mispecification is a oversimplification and only really applies in very specific cases. At this point I am going to urge you to talk with somebody that is well versed in spatial statistics. I have found the ESRI help and tutorials to be misleading and often incorrect. You are getting into some complexity that just cannot be addressed on a forum. – Jeffrey Evans Oct 11 '16 at 20:25

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