[R-sig-Geo] efficient code/function for rectangular SP weight Matrix and gwr

[Sam Field]

Stephane,

Thanks for the quick response.  I only just now discovered how useful 
lists are for storing non-zero spatial weights.  I have been dealing 
with the entire matrix, but with lists I can just deal with distances 
less then a specific bandwidth.  I sense that this will more or less 
deal with my problem.  Your comments about creating a new kind of "nb" 
object sound like a good idea - especially if rectangular weight 
matrices have such general usage. 

Sam




Stéphane Dray wrote:
> Hi Sam,
>
> I think that this question is quite general and could interest other 
> people, including me, with very different aims. I have developed a 
> method to look for the relationships between two data sets that have 
> been sampled on the same area but for different locations. In my 
> example, the two samples are two polygons layers. In this approach, I 
> compute a rectangular weighting matrix where each weight correspond to 
> the area of intersection between polygons of each layer. I have used 
> also the matrix form to store these weights (my data set was very 
> small compared to you). I remember that Roger was also interested by 
> these rectangular weights in another context. Here we  have different  
> problems:
> - how to compute these kind  of weights
> - how to store them.
>
> For the first point, I think that for each method/application, the 
> solution  is different. We could develop/extend classical tools for 
> square weights (one set of spatial units) to rectangular weights (two 
> sets of spatial units).
> For the second one, It would be probably interesting to define a class 
> of object in spdep. nb objects are lists, and I think that it would be 
> the solution for rectangular neighborhood.
>
> If I consider two sets of spatial units (A and B) where the number of 
> units is equal to na and nb.  We could store the neighbors in a list 
> of length 2. The first element of this list is a list of length na. In 
> this list, the j-th element is a vector of the neighbors of the j-th 
> unit of the layer A. These neighbors are spatial units of the layer 
> B.  The second element of the global list is a list of length nb where 
> each element is a vector of neighbors.
>
> I think that we have to think to a class of object that could be 
> useful for everybody dealing with this kind of rectangular weights. If 
> this class is properly defined (second point), we could then develop 
> tools to construct this kind of neighborhoods (first point). The 
> eventual extension to more than two data sets could also be taken into 
> account in this reflexion.
>
> Cheers,
>
>
> Sam Field wrote:
>> List,
>>
>> I need to create a rectangular spatial weight matrix for a set of n 
>> and m objects. I quickly run in to memory allocation problems when 
>> constructing the full matrix in a single pass. I am looking for a 
>> more efficient way of doing this. There appears to be efficient 
>> procedures in spdep for constructing SQUARE spatial weight matrices 
>> (e.g. dnearneigh()). Are there analogous procedures for constructing 
>> distance based weights between two different point patterns? I am 
>> doing this in preparation for implementing an approximate 
>> geographically weighted logistic regression procedure. I was thinking 
>> about using re sampling procedure as an inferential frame- perhaps I 
>> might get some feedback. This is what I was going to do.
>>
>> I have a point pattern of 30,000 diabetic people based on where they 
>> lived during a 2 year period. During that period, approximately 4% of 
>> them developed diabetes. I am interested in isolating the impact of 
>> ecological factors on the geographic variation" of the disease, so it 
>> is necessary to control for the spatial clustering of individual 
>> level risk factors associated with the disease (diabetes).
>>
>> Step 1: Estimate a logistic regression using the full sample and 
>> predict incidence diabetes using individual level covariates (i.e. 
>> who developed diabetes over the two year period).
>>
>> Step 2. Estimate a weighted logit model at each location (grid). The 
>> observations would be the people (not the geographic units) and the 
>> weights would be kernel weights based on distance. The model would 
>> only contain a single freely estimated parameter, the intercept, but 
>> it would also contain an offset term. For each patient, the offset 
>> term would simply be an evaluation of the linear predictor of the 
>> global model estimated above (based on the observed covariate 
>> values), but without the intercept. This would effectively fix the 
>> estimates of the patient level coefficients to their global values, 
>> requiring only a local estimate of the intercept. My hope is that I 
>> could interpret geographic variability in the intercept as evidence 
>> for a "location effect" net of the patient composition or "risk 
>> profile" at a particular location. It would probably make sense to 
>> center the X variables so that the intercept was interpretable and 
>> estimated in a region of the response plane where their is plenty of 
>> data. I would let the other covariates vary as well, but I doubt the 
>> model could be estimated in large portions of the study area because 
>> of sparse data.
>>
>> Step 3. If I were going to do inference on the location specific 
>> intercepts, I would generate a sampling distribution at each location 
>> by re sampling from the global model, and repeat Step 2 for each 
>> randomly drawn sample. This would give me a local sampling 
>> distribution of intercept estimates at each location and I could 
>> compare it to the the single one generated from the observed data. 
>> The global model represents a kind of null because the intercept is 
>> fixed to its global value and geographic variability is driven 
>> entirely by the spatial clustering of patient level factors.
>>
>>
>> thanks!
>>
>> Sam
>>
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