Hat matrix in ggwr models with adaptative kernel

Hi to all,

I have some questions about the ggwr logistic GWR function of spgwr 
package. I'm trying to get the hat matrix to calculate the AIC for a 
comparison of different models, but I get a message that the option 
"hat matrix=TRUE" is disabled in ggwr. How can I get the effective 
number of parameters as GWR book (pg.55) for a logistic model based on 
an adaptative gaussian kernel to make this calculation? Is not possible 
to use AIC instead of CV as the criteria for adaptative selection 
(ggwr.sel function)?

Beyond this questions I have a few others on ggwr function.


Is this model considered experimental? How can I get more information 
about the implemented algorithm? It will change soon?

I`m using pgirmess package spatial correlograms of Moran`s I to check 
for autocorrelation of residuals of global logistic and logistic gwr 
models (response residuals). It`s correct or does it have another 
approach to check spatial autocorrelation issues on global and local 
logistic regression models?

My code is below and the measure to compare between models that I`m 
using is C (area under curve) in Hmisc package. Thanks in advance for 
all comments and suggestions.


Marcos Freitas

PhD Student INPE-Brasil

library(spdep)
library(spgwr)

library(Hmisc)

fit = readShapePoints("C://Documents and Settings/Marcos Freitas/Meus documentos/Doutorado/Area_Lages_trabalho/TESE_ESDA_LAGES/LOGISTICA/samples_floresta_01.shp", proj4string=CRS("+proj=utm +zone=-22 +datum=WGS84"), verbose = FALSE, repair=FALSE)

head(fit)

bw = ggwr.sel(DEP_VAR ~ declividad + rug_norm + dist_riv + PTH_AR_MN + PTH_AR_SD + NP + LPI + MESH + GEOM_DC1, data=fit, coords=cbind(dados$Eastings, dados$Northings), adapt=TRUE, gweight=gwr.Gauss, family=binomial(link="logit"), verbose=TRUE, longlat=NULL, RMSE=FALSE, tol=.Machine$double.eps^0.25)

gwr.deg = ggwr(DEP_VAR ~ declividad + rug_norm + dist_riv + PTH_AR_MN + PTH_AR_SD + NP + LPI + MESH + GEOM_DC1, data=fit, coords=cbind(fit$POINT_X, fit$POINT_Y), gweight=gwr.Gauss, adapt=bw, family=binomial(link="logit"), longlat=NULL, type=c("response"))

write.table (gwr.deg$SDF, file=paste("C://Documents and Settings/Marcos Freitas/Meusdocumentos/Doutorado/Area_Lages_trabalho/TESE_ESDA_LAGES/LOGISTICA/lgwr_floresta_fit_reduzido", ".txt", sep=""))

pred_prob = fit$DEP_VAR - gwr.deg$SDF$response_resids

auc = somers2(pred_prob, fit$DEP_VAR, weights=NULL, normwt=FALSE, na.rm=TRUE)

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Hi Prof. Bivand,

Thanks for the explanation of the problems founded in the implementation of
GWR in R. My objective is to use logistic GWR in the generation of land use
classes probabilities maps in my PhD thesis, an exploratory use as well. The
objective of having a hat matrix for me is to compute AIC`s to perform a
comparison of models with different included independent variables. So, I`ll
be delighted if you or other colleagues would provide me some references
about those statistical issues on GWR and where I can found more information
about the spgwr implementation of ggwr function. Certainly, I`ll be asked
about those issues if I don`t clearly understand and explain such
implementation. Thanks in advance.

Best regards,

Marcos Freitas

2011/9/20 Roger Bivand <Roger.Bivand at nhh.no>

On Tue, 20 Sep 2011, Marcos Freitas wrote:

Hi to all,

I have some questions about the ggwr logistic GWR function of spgwr
package. I'm trying to get the hat matrix to calculate the AIC for a
comparison of different models, but I get a message that the option "hat
matrix=TRUE" is disabled in ggwr. How can I get the effective number of
parameters as GWR book (pg.55) for a logistic model based on an adaptative
gaussian kernel to make this calculation? Is not possible to use AIC instead
of CV as the criteria for adaptative selection (ggwr.sel function)?

Beyond this questions I have a few others on ggwr function.


Is this model considered experimental? How can I get more information
about the implemented algorithm? It will change soon?

The spgwr package began as an attempt to document what GWR3 does. We found
numerous discrepancies, including multiple definitions of AIC, and the
unnecessary use of an approximation in the df calculations for the linear
model case. The glm case is highly experimental, and given strong doubts
about GWR as an approach, is there only for exploring data, not as a
statistical model. No hat matrix will be attempted by me, and if anyone
contributes one, I'll include it requiring the user to set an argument
agreeing to the sentence: "I am aware that GWR has not been shown to be an
adequate method beyond exploratory data analysis".


 I`m using pgirmess package spatial correlograms of Moran`s I to check for

autocorrelation of residuals of global logistic and logistic gwr models
(response residuals). It`s correct or does it have another approach to check
spatial autocorrelation issues on global and local logistic regression
models?

This is a different question.

Roger

My code is below and the measure to compare between models that I`m using
is C (area under curve) in Hmisc package. Thanks in advance for all comments
and suggestions.


Marcos Freitas

PhD Student INPE-Brasil

library(spdep)
library(spgwr)

library(Hmisc)

fit = readShapePoints("C://Documents and Settings/Marcos Freitas/Meus
documentos/Doutorado/Area_**Lages_trabalho/TESE_ESDA_**
LAGES/LOGISTICA/samples_**floresta_01.shp", proj4string=CRS("+proj=utm
+zone=-22 +datum=WGS84"), verbose = FALSE, repair=FALSE)

head(fit)

bw = ggwr.sel(DEP_VAR ~ declividad + rug_norm + dist_riv + PTH_AR_MN +
PTH_AR_SD + NP + LPI + MESH + GEOM_DC1, data=fit,
coords=cbind(dados$Eastings, dados$Northings), adapt=TRUE,
gweight=gwr.Gauss, family=binomial(link="logit"), verbose=TRUE,
longlat=NULL, RMSE=FALSE, tol=.Machine$double.eps^0.25)

gwr.deg = ggwr(DEP_VAR ~ declividad + rug_norm + dist_riv + PTH_AR_MN +
PTH_AR_SD + NP + LPI + MESH + GEOM_DC1, data=fit, coords=cbind(fit$POINT_X,
fit$POINT_Y), gweight=gwr.Gauss, adapt=bw, family=binomial(link="logit"),
longlat=NULL, type=c("response"))

write.table (gwr.deg$SDF, file=paste("C://Documents and Settings/Marcos
Freitas/Meusdocumentos/**Doutorado/Area_Lages_trabalho/**
TESE_ESDA_LAGES/LOGISTICA/**lgwr_floresta_fit_reduzido", ".txt",
sep=""))

pred_prob = fit$DEP_VAR - gwr.deg$SDF$response_resids

auc = somers2(pred_prob, fit$DEP_VAR, weights=NULL, normwt=FALSE,
na.rm=TRUE)

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--
Roger Bivand
Department of Economics, NHH Norwegian School of Economics,
Helleveien 30, N-5045 Bergen, Norway.
voice: +47 55 95 93 55; fax +47 55 95 95 43
e-mail: Roger.Bivand at nhh.no