Dear Comunity,

I'm trying to model some climate phenomena such as convection using several variables: evaporation, temperature, moisture, rainfalls, etc. My goal is get a more specific model than traditional climate projections searching the relationships between variables.

Fisrt I've done OLS analysis for see what variables have the best coefficient and what is the best global correlation to fit the phenomena that I want to predict. Then I move to GWR to see geographical variation of this data, but I have some problems with this analysis.

Now I'll explain the steps that I follow:

1. Input my data by txt files (view capture 1), and then I create a raster map using "Conversion Tools/to raster/ASCII to Raster" (capture 2). After I create a Grid of points using"Conversion Tools/From raster/Raster to point" (capture 3) and finally join my variables in an unique grid using an "Spatial Join" (capture 4).

2. Run the GWR analysis and happen this:

Somebody could help me?

I'will be so grateful

Thanks

Arnau

PS: Please you can see my captures on Facebook

http://www.facebook.com/album.php?aid=2086715&l=38d02008fd&id=1432887823

I'm trying to model some climate phenomena such as convection using several variables: evaporation, temperature, moisture, rainfalls, etc. My goal is get a more specific model than traditional climate projections searching the relationships between variables.

Fisrt I've done OLS analysis for see what variables have the best coefficient and what is the best global correlation to fit the phenomena that I want to predict. Then I move to GWR to see geographical variation of this data, but I have some problems with this analysis.

Now I'll explain the steps that I follow:

1. Input my data by txt files (view capture 1), and then I create a raster map using "Conversion Tools/to raster/ASCII to Raster" (capture 2). After I create a Grid of points using"Conversion Tools/From raster/Raster to point" (capture 3) and finally join my variables in an unique grid using an "Spatial Join" (capture 4).

2. Run the GWR analysis and happen this:

**some analysis go well (capture 5), but others appear "gaps" in my attributes table as "null values" and consequently in my map too**(capture 6). I've deduced that this only happen with moisture (it is in %, only two digits)(capture1) because the gaps appear when I use this variable, but I don't understand why.Somebody could help me?

I'will be so grateful

Thanks

Arnau

PS: Please you can see my captures on Facebook

http://www.facebook.com/album.php?aid=2086715&l=38d02008fd&id=1432887823

I'm pretty sure I answered all of your questions in an email recently, but I'm glad you posted your questions here too.

1) The coefficient surfaces are created using a weighted least squares estimator�?� the method is described on pages 52 to 54 of Geographically Weighted Regression by Fotheringham, Brunsdon and Charlton, Wiley 2002�?� the formula is labeled (2.11) and looks something like this:

β �? (i)=(X^T W(i)X)^(-1) X^T W(i)Y

Basically, GWR estimates the coefficient value at each raster cell using the same formula that it uses to estimate the coefficient values at each feature. For each raster cell, a weights matrix is constructed relating that raster cell location to every feature in the dataset�?� nearby features have a bigger weight than features that are farther away. The weighting function itself depends on what you select for Kernel Type (FIXED/ADAPTIVE) and Bandwidth Method (the distance or number of neighbors) when you run GWR. Even though the raster cell being estimated may not be associated with a specific feature (so it doesn�??t have a specific dependent variable or explanatory variables)�?� it still has weighted explanatory variables and can be associated with weighted dependent variables. In fact, the math to estimate the coefficient at a location that coincides with a feature is the same for a location that doesn�??t coincide with a feature; in both cases the coefficient is estimated using weighted X and Y variables.

Because of the weighting function, it helps me to think of the weighted least squares estimator as a type of interpolator; nearby X and Y values provide the data necessary to estimate the coefficient value at each raster cell.

2) Yes you can interpolate the predicted values from OLS and GWR if what you are modeling (your Y variable) is actually continuous (elevation, temperature, etc.). However, realize that your sampled data come from predictions (not the actual values). The result will be a prediction surface. My recommendation would be to use the actual Y values, where you have them, then obtain predicted Y values for all locations where you can obtain X values, but don�??t have the actual Y values. I hope that makes sense. Then use something like Kriging for the interpolation, if your data can be modeled using a semi-variogram.

3) OLS and GWR work fine with sampled data, so if you are missing some points, that�??s fine, you just use those points that have data. OLS and GWR do not recognize �??-999�?� or some other numeric code as missing data (they will interpret those values as REAL data values). You can use all locations with a full set of X and Y values to calibrate your model, then predict Y values for locations with a full set of X variables, but no Y values.

Your follow up email also asked about the best distance to use (scale of analysis). Please check out the supplementary spatial statistics tools available for download from the Geoprocessing Resource Center (www.bit.ly/spatialstats). The Incremental Spatial Autocorrelation tool can help you find the distance where spatial processes promoting clustering are most pronounced. These tools include full documentation.

I hope this helps.

Best wishes,

Lauren M Scott, PhD

ESRI

Geoprocessing, Spatial Statistics