GWR with anisotropic kernel (bandwidth only in one direction)

[nikosGeography]

Hello, thank you for creating the package and feel free to close the issue if you think the question is not suitable for this place.

I'm working on downscaling VIIRS nighttime lights satellite imagery. VIIRS is a whiskbroom sensor where viewing angle (VA) varies across the image swath in the cross-track direction (left to right, perpendicular to satellite motion). At higher viewing angles, the sensor observes different aspects of ground features - for example, building facades rather than rooftops when viewing straight down.

I suspect that the relationship between my covariates (land cover, population density, etc.) and observed nighttime lights should vary with viewing angle. I am about to use Geographically Weighted Regression (GWR) with a custom kernel that forms "vertical bands":

• Finite bandwidth in the cross-track direction (x-direction, where VA varies)
• Effectively infinite bandwidth in the along-track direction (y-direction, where VA is constant)
• This ensures sufficient replicates for each value of x allowing you to fit the model by pooling all along-track observations together.

Can GWmodel3 accommodate this type of directional anisotropic kernel where bandwidth is controlled in only one spatial direction (aligned with the cross-track/viewing angle direction)?

I've reviewed the GWmodel3 documentation and searched for examples of anisotropic kernels, but I haven't found any implementations of custom kernels.

Standard GWR example (isotropic kernel):

pacman::p_load(sf, GWmodel3)

data(LondonHP)

m1 <- gwr_basic(
  formula = PURCHASE ~ FLOORSZ + UNEMPLOY + PROF,
  data = LondonHP,
  bw = "AIC",
  adaptive = TRUE
)

What I need a kernel where:

Bandwidth in x-direction: finite (e.g., adaptive or fixed)
Bandwidth in y-direction: effectively infinite (all observations at similar x-positions contribute equally)
Would a custom distance matrix (dMat) be the solution, or is there another approach within GWmodel? I couldn't find a solution on how to implement a custom dMat in the package.

Session Info

R version 4.5.2 (2025-10-31 ucrt)
Platform: x86_64-w64-mingw32/x64
Running under: Windows 11 x64 (build 26200)

Matrix products: default
  LAPACK version 3.12.1

locale:
[1] LC_COLLATE=English_United States.utf8  LC_CTYPE=English_United States.utf8    LC_MONETARY=English_United States.utf8
[4] LC_NUMERIC=C                           LC_TIME=English_United States.utf8    

time zone: Europe/Budapest
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] GWmodel3_3.0-0 sf_1.1-0      

loaded via a namespace (and not attached):
 [1] compiler_4.5.2     magrittr_2.0.4     class_7.3-23       DBI_1.3.0          tools_4.5.2        otel_0.2.0        
 [7] units_1.0-0        proxy_0.4-29       rstudioapi_0.18.0  Rcpp_1.1.1         KernSmooth_2.23-26 grid_4.5.2        
[13] e1071_1.7-17       classInt_0.4-11    pacman_0.5.1

[HPDell]

Hi, I recommend the GTDR model if you are looking for an anisotropic model. In this model, you can specify a bandwidth value for each direction (x and y). Please turn to the documentation of function gtdr and this paper<https://doi.org/10.1080/13658816.2025.2466110> for more information. V best, Yigong

…

________________________________ From: Nikolaos Tziokas ***@***.***> Sent: 28 February 2026 17:24 To: GWmodel-Lab/GWmodel3 ***@***.***> Cc: Subscribed ***@***.***> Subject: [GWmodel-Lab/GWmodel3] GWR with anisotropic kernel (bandwidth only in one direction) (Issue #39) [https://avatars.githubusercontent.com/u/45749751?s=20&v=4]nikosGeography created an issue (GWmodel-Lab/GWmodel3#39)<#39> Hello, thank you for creating the package and feel free to close the issue if you think the question is not suitable for this place. I'm working on downscaling VIIRS nighttime lights satellite imagery. VIIRS is a whiskbroom sensor where viewing angle (VA) varies across the image swath in the cross-track direction (left to right, perpendicular to satellite motion). At higher viewing angles, the sensor observes different aspects of ground features - for example, building facades rather than rooftops when viewing straight down. I suspect that the relationship between my covariates (land cover, population density, etc.) and observed nighttime lights should vary with viewing angle. I am about to use Geographically Weighted Regression (GWR) with a custom kernel that forms "vertical bands": * Finite bandwidth in the cross-track direction (x-direction, where VA varies) * Effectively infinite bandwidth in the along-track direction (y-direction, where VA is constant) * This ensures sufficient replicates for each value of x allowing you to fit the model by pooling all along-track observations together. Can GWmodel3 accommodate this type of directional anisotropic kernel where bandwidth is controlled in only one spatial direction (aligned with the cross-track/viewing angle direction)? I've reviewed the GWmodel3 documentation and searched for examples of anisotropic kernels, but I haven't found any implementations of custom kernels. Standard GWR example (isotropic kernel): pacman::p_load(sf, GWmodel3) data(LondonHP) m1 <- gwr_basic( formula = PURCHASE ~ FLOORSZ + UNEMPLOY + PROF, data = LondonHP, bw = "AIC", adaptive = TRUE ) What I need a kernel where: Bandwidth in x-direction: finite (e.g., adaptive or fixed) Bandwidth in y-direction: effectively infinite (all observations at similar x-positions contribute equally) Would a custom distance matrix (dMat) be the solution, or is there another approach within GWmodel? I couldn't find a solution on how to implement a custom dMat in the package. Session Info R version 4.5.2 (2025-10-31 ucrt) Platform: x86_64-w64-mingw32/x64 Running under: Windows 11 x64 (build 26200) Matrix products: default LAPACK version 3.12.1 locale: [1] LC_COLLATE=English_United States.utf8 LC_CTYPE=English_United States.utf8 LC_MONETARY=English_United States.utf8 [4] LC_NUMERIC=C LC_TIME=English_United States.utf8 time zone: Europe/Budapest tzcode source: internal attached base packages: [1] stats graphics grDevices utils datasets methods base other attached packages: [1] GWmodel3_3.0-0 sf_1.1-0 loaded via a namespace (and not attached): [1] compiler_4.5.2 magrittr_2.0.4 class_7.3-23 DBI_1.3.0 tools_4.5.2 otel_0.2.0 [7] units_1.0-0 proxy_0.4-29 rstudioapi_0.18.0 Rcpp_1.1.1 KernSmooth_2.23-26 grid_4.5.2 [13] e1071_1.7-17 classInt_0.4-11 pacman_0.5.1 — Reply to this email directly, view it on GitHub<#39>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/AEIEACLXTOHDXH43ZFM2ZWL4OFNENAVCNFSM6AAAAACWCQO6AKVHI2DSMVQWIX3LMV43ASLTON2WKOZUGAYDIMRZGM2DEMQ>. You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[nikosGeography]

Thank you for the recommendation! I've reviewed the GTDR paper and code, and it looks very promising for handling anisotropic relationships.
However, I have a question about prediction to unseen locations. My goal is to downscale satellite imagery, which requires:

1. Building the GTDR model at coarse spatial resolution.
2. Applying the fitted model to predict at finer spatial resolution (i.e., unseen locations).

Looking at the provided code (named GWDR.R), I can only see the gwdr() function that calibrates the model at the observed locations. Moreover, I checked the tutorial on this page (vignettes/tutorial-03-gtdr.Rmd), but I think I didn't see a predict() function as well. Is there a predict() function (or similar functionality) that allows applying the fitted GTDR model to new, unseen coordinate locations?

If this functionality doesn't currently exist, would it be possible to implement it, or could you provide guidance on how to extend the code to support prediction at new locations?

Thank you for your help!

[HPDell]

Sorry, but we haven't implemented the predict method for GTDR because the related mathematical theory hasn't been developed. But implement one may be not too complicated. Just follow how GWR does: 1. Compute the weighting matrix W in the GTDR way. 2. Estimate the regression coefficients β = (X^T W X)^{-1} (X^T W y) to predict the model in one of the new locations. 3. Get the linear combination of independent variables X by β at that location. Again, this is not formally proved. If you are interested, you can get in touch with Binbin Lu (email: ***@***.***) and discuss this idea with him. V best, Yigong.

…

________________________________ From: Nikolaos Tziokas ***@***.***> Sent: 28 February 2026 19:42 To: GWmodel-Lab/GWmodel3 ***@***.***> Cc: Yigong Hu ***@***.***>; Comment ***@***.***> Subject: Re: [GWmodel-Lab/GWmodel3] GWR with anisotropic kernel (bandwidth only in one direction) (Issue #39) [https://avatars.githubusercontent.com/u/45749751?s=20&v=4]nikosGeography left a comment (GWmodel-Lab/GWmodel3#39)<#39 (comment)> Thank you for the recommendation! I've reviewed the GTDR paper and code, and it looks very promising for handling anisotropic relationships. However, I have a question about prediction to unseen locations. My goal is to downscale satellite imagery, which requires: 1. Building the GTDR model at coarse spatial resolution. 2. Applying the fitted model to predict at finer spatial resolution (i.e., unseen locations). Looking at the provided code (named GWDR.R), I can only see the gwdr() function that calibrates the model at the observed locations. Moreover, I checked the tutorial on this page (vignettes/tutorial-03-gtdr.Rmd), but I think I didn't see a predict() function as well. Is there a predict() function (or similar functionality) that allows applying the fitted GTDR model to new, unseen coordinate locations? If this functionality doesn't currently exist, would it be possible to implement it, or could you provide guidance on how to extend the code to support prediction at new locations? Thank you for your help! — Reply to this email directly, view it on GitHub<#39 (comment)>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/AEIEACPY3R2XI6VPV65JCHD4OF5JRAVCNFSM6AAAAACWCQO6AKVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZTSNZXGA2DQOJSGU>. You are receiving this because you commented.Message ID: ***@***.***>