Hi again 🙂
Eric will likely have suggestions as well, but here are some of the guidelines I follow for my own projects.
While no empirical workflow (step by step recipe) can guarantee you've found a fully specified GWR/MGWR model, completing the following checks will greatly improve your chances:
1) Ask yourself if you are modeling processes that would behave differently in different locations. You should be able to explain why it is plausible that the relationship between water demand and the square area of a particular land use would vary across space. Local models like GWR or MGWR are only appropriate if you have reason to believe the *spatial* processes influencing the relationships are different in different locations. GWR/MGWR isn't appropriate if all your variable relationships are purely deterministic. Hmmm... for your analysis, it might be that the people in some neighborhoods are more dedicated to water conservation than people in other areas ?
2) Ask yourself if your data is appropriate for GWR/MGWR model calibration.
a. Do you have enough observations? (Usually, 100 or more features is sufficient).
b. Do the data cover the study area consistently? You shouldn't have isolated clusters of features or other strong spatial discontinuities.
c. Have you consulted the literature, theory, related/relevant applications, community advocates, and common sense to ensure you're starting with a comprehensive and appropriate list of candidate explanatory variables? Can you articulate the expected relationship for each one?
d. Are local relationships between Y and every candidate X variable linear? (see my earlier notes about modeling linear relationships).
3) Are you starting with a good, robust, defensible global model (see Fotheringham, 2022, citation below)? Finding a properly specified OLS model might be a good way to ensure you're including at least some of the key explanatory variables in your model. The Exploratory Regression tool in ArcGIS Pro can be very helpful here.
If you can't find a properly specified OLS model before moving to GWR/MGWR you will need to come up with some other way to ensure your model includes all key explanatory variables (see 2c and number 4).
4) Does your final GWR/MGWR model pass these additional tests?
a. The data are scaled (especially for MGWR).
b. Residuals from your GWR/MGWR model are free from statistically significant spatial autocorrelation (this can be checked with the Global Moran's I tool).
c. There is no evidence of local multicollinearity (all Condition Numbers are less than 30, as a rule of thumb).
d. Every model explanatory variable is significant for at least some portion of the study area and the coefficient patterns are plausible (the significant coefficients should have the expected sign).
e. GWR/MGWR produces better results than OLS: a larger AdjR2 value and smaller AICc value. If not, OLS is the better model.
f. You're modeling linear relations only (see Sachdeva, Fotheringham, Li, and Yu 2022 for details about how to check this from the model output ... or ask me to send you instructions for creating the charts they recommend).
g. None of the scaled coefficients for the intercept are statistically significant (any variation in coefficient values reflects noise only). For MGWR, ideally the spatial scale for the intercept is global. Failing this check suggests variables may have been omitted from the model (Fotheringham, 2022).
References:
Fotheringham, S., Yang, W., & Kang, W. 2022. Multiscale Geographically Weighted Regression (MGWR). Annals of the American Association of Geographers, 1-19. https://doi.org/10.1080/24694452.2017.1352480
Fotheringham, A. S. 2022. A Comment on “A Route Map for Successful Applications of Geographically Weighted Regression”: The Alternative Expressway to Defensible Regression-Based Local Modeling. Geographical Analysis. https://doi.org/10.1111/gean.12347
Sachdeva, M., Fotheringham, A. S., Li, Z., & Yu, H. (2022). Are We Modelling Spatially Varying Processes or Non-linear Relationships? Geographical Analysis, 54(4), 715-738. https://doi.org/10.1111/gean.12297
Your call, but you might want to try MGWR since it automatically reports GWR results as well. Then you can decide if GWR or MGWR is the better model (if results are very similar, I might go with GWR because it's the simpler model). GWR allows coefficients to vary across the study area for a fixed spatial scale. MGWR does this also, but in addition, it allows each explanatory variable to have its own fixed spatial scale.
Other tips: Unless I have a good justification for using number of neighbors vs distance band, I try both to see which provides the best result. Same for Bisquare vs Gaussian for the Local Weighting Scheme (I try both and go with the best result).
I hope this is helpful!
Best wishes on your project! Keep us posted 🙂
Lauren
