I want to estimate a gravity type model for mobility flows, this means my dependent variable is an 1 x n^2 vector of flow between n^2 region pairs. I already have an nxn weight matrix which is based on the geographic distance between the n regions.
I am currently trying to build a spatial model as mentioned above. I know that for a classic spatial lag model the Weight matrix would be specified depending of the type of spatial effects .
For example for destination based effects one would form a kronecker product of an nxn idenity matrix and the nxn weight matrix, to obtain the weight matrix which can be used for the estimation.
I only want to use an SLX model, meaning i only include spatial effects for independent variables. My question now is if i can simply use the same weight matrices as i would use for the spatial lag model?
I tried to find good explanations of how the weight matrix is constructed for interaction models, but couldn’t find any.
Thank you for your Help!