I do understand that GWR is performed to take into consideration the heteroskedastic nature of variable in terms of its geographical location, however the application for spatial analysis is unclear.
As far as I can conceptualise the basic difference between the two set of techniques is the way they consider space. While the spatial case is local with regard to attribute space. That is spatial attributes (lat and long) as an attribute, as a variable. However, the GW case considers space with regard to it's geographic character. That is, all the variables are marked as per the spatial attribute (lat and long). I think one more difference is- GW is a first level spatial technique, while the spatial case is a second level. Hope it helps you.
My pleasure. Btw spatial case cannot be represented on maps since they give a global summary only, unlike the GW case.
Here is the link to my article: https://www.mdpi.com/2220-9964/7/2/64
Let me know if you have any questions
SAR: Statistical spatial dependence comes from the assumption that location i's DV value is directly influenced by location j's DV value.
SEM: Spatial dependence comes from unobserved variables that cannot be included in the set of independent variables and therefore the spatial dependence is only through the error terms.
SAR/SEM: no spatial heterogeneity. The relationship between X and Y is the same for all spaces. Spatial autoregressive models have theoretical assumptions of spatial interdependence or contagion.
GWR: spatial heterogeneity. non-stationary effect of space. It assumes that the relationship between X and Y is different depending on the location. It is about the location where a No assumptions about interdependence or contagion.
Soomi Lee sorry, just to clarify based on your answers on Aug 2 & Jul 30 - Isn't spatial lag model (ie, spatial error model) also autoregressive? that is, in both spatial lag and GWR, the i's DV value is affected by j's DV value? The key difference seems to be just spatial heterogeneity (or not) as per your answer on Aug 2.
Chan-Hoong Leong Yes, spatial lag models (SEM & SAR) are by definition spatial autoregressive models. The W matrix measures the relationship between units' proximity to each other regardless of however the proximity is defined. So DV of i's unit depends on DV of j, which demonstrates the interdependence of the two units. In GWR, there is no interdependence across units. It is about non-stationary variables such as climate, etc., and how the coefficient of X and Y differs depending on location. In short, the key difference is that (1) spatial lag models are about the interdependence of the units and (2) GWR is about locational effects (not interdependence).
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