Realice las regresiones espaciales vistas en clase para la variable CEA a 150 cm
library(readxl)## Warning: package 'readxl' was built under R version 4.0.5library(dplyr)## Warning: package 'dplyr' was built under R version 4.0.5##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(spdep)## Warning: package 'spdep' was built under R version 4.0.5## Loading required package: sp## Warning: package 'sp' was built under R version 4.0.5## Loading required package: spData## Warning: package 'spData' was built under R version 4.0.5## To access larger datasets in this package, install the spDataLarge
## package with: `install.packages('spDataLarge',
## repos='https://nowosad.github.io/drat/', type='source')`## Loading required package: sf## Warning: package 'sf' was built under R version 4.0.5## Linking to GEOS 3.9.0, GDAL 3.2.1, PROJ 7.2.1library(ape)## Warning: package 'ape' was built under R version 4.0.5## Registered S3 method overwritten by 'ape':
## method from
## plot.mst spdeplibrary(sp)
library(MVA)## Warning: package 'MVA' was built under R version 4.0.5## Loading required package: HSAUR2## Warning: package 'HSAUR2' was built under R version 4.0.5## Loading required package: toolslibrary(Hmisc)## Warning: package 'Hmisc' was built under R version 4.0.5## Loading required package: lattice## Loading required package: survival## Loading required package: Formula## Loading required package: ggplot2## Warning: package 'ggplot2' was built under R version 4.0.5##
## Attaching package: 'Hmisc'## The following object is masked from 'package:ape':
##
## zoom## The following objects are masked from 'package:dplyr':
##
## src, summarize## The following objects are masked from 'package:base':
##
## format.pval, unitslibrary(normtest)
library(nortest)
library(dplyr)
library(spatialreg)## Warning: package 'spatialreg' was built under R version 4.0.5## Loading required package: Matrix## Registered S3 methods overwritten by 'spatialreg':
## method from
## residuals.stsls spdep
## deviance.stsls spdep
## coef.stsls spdep
## print.stsls spdep
## summary.stsls spdep
## print.summary.stsls spdep
## residuals.gmsar spdep
## deviance.gmsar spdep
## coef.gmsar spdep
## fitted.gmsar spdep
## print.gmsar spdep
## summary.gmsar spdep
## print.summary.gmsar spdep
## print.lagmess spdep
## summary.lagmess spdep
## print.summary.lagmess spdep
## residuals.lagmess spdep
## deviance.lagmess spdep
## coef.lagmess spdep
## fitted.lagmess spdep
## logLik.lagmess spdep
## fitted.SFResult spdep
## print.SFResult spdep
## fitted.ME_res spdep
## print.ME_res spdep
## print.lagImpact spdep
## plot.lagImpact spdep
## summary.lagImpact spdep
## HPDinterval.lagImpact spdep
## print.summary.lagImpact spdep
## print.sarlm spdep
## summary.sarlm spdep
## residuals.sarlm spdep
## deviance.sarlm spdep
## coef.sarlm spdep
## vcov.sarlm spdep
## fitted.sarlm spdep
## logLik.sarlm spdep
## anova.sarlm spdep
## predict.sarlm spdep
## print.summary.sarlm spdep
## print.sarlm.pred spdep
## as.data.frame.sarlm.pred spdep
## residuals.spautolm spdep
## deviance.spautolm spdep
## coef.spautolm spdep
## fitted.spautolm spdep
## print.spautolm spdep
## summary.spautolm spdep
## logLik.spautolm spdep
## print.summary.spautolm spdep
## print.WXImpact spdep
## summary.WXImpact spdep
## print.summary.WXImpact spdep
## predict.SLX spdep##
## Attaching package: 'spatialreg'## The following objects are masked from 'package:spdep':
##
## anova.sarlm, as.spam.listw, as_dgRMatrix_listw, as_dsCMatrix_I,
## as_dsCMatrix_IrW, as_dsTMatrix_listw, bptest.sarlm, can.be.simmed,
## cheb_setup, coef.gmsar, coef.sarlm, coef.spautolm, coef.stsls,
## create_WX, deviance.gmsar, deviance.sarlm, deviance.spautolm,
## deviance.stsls, do_ldet, eigen_pre_setup, eigen_setup, eigenw,
## errorsarlm, fitted.gmsar, fitted.ME_res, fitted.sarlm,
## fitted.SFResult, fitted.spautolm, get.ClusterOption,
## get.coresOption, get.mcOption, get.VerboseOption,
## get.ZeroPolicyOption, GMargminImage, GMerrorsar, griffith_sone,
## gstsls, Hausman.test, HPDinterval.lagImpact, impacts, intImpacts,
## Jacobian_W, jacobianSetup, l_max, lagmess, lagsarlm, lextrB,
## lextrS, lextrW, lmSLX, logLik.sarlm, logLik.spautolm, LR.sarlm,
## LR1.sarlm, LR1.spautolm, LU_prepermutate_setup, LU_setup,
## Matrix_J_setup, Matrix_setup, mcdet_setup, MCMCsamp, ME, mom_calc,
## mom_calc_int2, moments_setup, powerWeights, predict.sarlm,
## predict.SLX, print.gmsar, print.ME_res, print.sarlm,
## print.sarlm.pred, print.SFResult, print.spautolm, print.stsls,
## print.summary.gmsar, print.summary.sarlm, print.summary.spautolm,
## print.summary.stsls, residuals.gmsar, residuals.sarlm,
## residuals.spautolm, residuals.stsls, sacsarlm, SE_classic_setup,
## SE_interp_setup, SE_whichMin_setup, set.ClusterOption,
## set.coresOption, set.mcOption, set.VerboseOption,
## set.ZeroPolicyOption, similar.listw, spam_setup, spam_update_setup,
## SpatialFiltering, spautolm, spBreg_err, spBreg_lag, spBreg_sac,
## stsls, subgraph_eigenw, summary.gmsar, summary.sarlm,
## summary.spautolm, summary.stsls, trW, vcov.sarlm, Wald1.sarlmdf= read_excel("BD_MODELADO.xlsx")
df_xy=df[,c(1,2)] # Coords
X= df[,-c(1,2)] # Explicativaslibrary(ape)
# Matriz de distancias
df.dists <- as.matrix(dist(cbind(df$Avg_X_MCB, df$Avg_Y_MCE)))
# Inversa de las matriz
df.dists.inv <- 1/df.dists
# Asignar ceros a la diagonal
diag(df.dists.inv) <- 0
df.dists.inv <- round(df.dists.inv,3)
We<-df.dists.inv/rowSums(df.dists.inv)contnb=dnearneigh(coordinates(df_xy),0,380000,longlat = F)
contnb## Neighbour list object:
## Number of regions: 313
## Number of nonzero links: 97656
## Percentage nonzero weights: 99.68051
## Average number of links: 312class(contnb)## [1] "nb"df_xy=as.matrix(df_xy)
dlist <- nbdists(contnb, df_xy)
dlist <- lapply(dlist, function(x) 1/x)
Wve=nb2listw(contnb,glist=dlist,style = "W")map= spautolm(Avg_CEa_07~1, data= X, listw= Wve, family="SAR")
summary(map)##
## Call: spautolm(formula = Avg_CEa_07 ~ 1, data = X, listw = Wve, family = "SAR")
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.258254 -0.650679 -0.071829 0.824652 3.063002
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 5.6941 5.5177 1.032 0.3021
##
## Lambda: 0.98811 LR test value: 162.5 p-value: < 2.22e-16
## Numerical Hessian standard error of lambda: 0.011866
##
## Log likelihood: -494.8231
## ML residual variance (sigma squared): 1.347, (sigma: 1.1606)
## Number of observations: 313
## Number of parameters estimated: 3
## AIC: 995.65residuales_map =map$fit$residuals
shapiro.test(residuales_map)##
## Shapiro-Wilk normality test
##
## data: residuales_map
## W = 0.99351, p-value = 0.1971Moran.I(residuales_map,We)## $observed
## [1] 0.1658609
##
## $expected
## [1] -0.003205128
##
## $sd
## [1] 0.004653146
##
## $p.value
## [1] 0Como el p-valor es cero, todavia hay dependencia espacial por lo que el modelo no es buno para estos datos
map2= sacsarlm(Avg_CEa_15~1, data= X, listw= Wve)## Warning in sacsarlm(Avg_CEa_15 ~ 1, data = X, listw = Wve): inversion of asymptotic covariance matrix failed for tol.solve = 2.22044604925031e-16
## número de condición recíproco = 1.77227e-18 - using numerical Hessian.summary(map2)##
## Call:sacsarlm(formula = Avg_CEa_15 ~ 1, data = X, listw = Wve)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.364908 -0.357504 -0.063033 0.289858 2.878760
##
## Type: sac
## Coefficients: (numerical Hessian approximate standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.1253 1.1713 0.9607 0.3367
##
## Rho: 0.95895
## Approximate (numerical Hessian) standard error: 0.040792
## z-value: 23.508, p-value: < 2.22e-16
## Lambda: 0.95895
## Approximate (numerical Hessian) standard error: 0.040755
## z-value: 23.53, p-value: < 2.22e-16
##
## LR test value: 133.68, p-value: < 2.22e-16
##
## Log likelihood: -281.3411 for sac model
## ML residual variance (sigma squared): 0.34087, (sigma: 0.58384)
## Number of observations: 313
## Number of parameters estimated: 4
## AIC: 570.68, (AIC for lm: 700.36)residuales_map2 =map2$residuals
shapiro.test(residuales_map2)##
## Shapiro-Wilk normality test
##
## data: residuales_map2
## W = 0.94498, p-value = 2.076e-09Moran.I(residuales_map2,We)## $observed
## [1] 0.0563745
##
## $expected
## [1] -0.003205128
##
## $sd
## [1] 0.004629181
##
## $p.value
## [1] 0Como el p-valor del indice de moran es cero, todavia hay dependencia espacial, ademas no hay un comportamiento normal en los residuales. Por lo que el modelo no es buno para estos datos
map3= sacsarlm(formula=Avg_CEa_15~Avg_CEa_07+NDVI+DEM+SLOPE+Avg_z, data= X, listw= Wve,type="mixed")
summary(map3)##
## Call:sacsarlm(formula = Avg_CEa_15 ~ Avg_CEa_07 + NDVI + DEM + SLOPE +
## Avg_z, data = X, listw = Wve, type = "mixed")
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.259920 -0.257064 -0.024628 0.256195 1.934415
##
## Type: sacmixed
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 26.084548 36.251116 0.7196 0.47180
## Avg_CEa_07 0.362195 0.034530 10.4893 < 2.2e-16
## NDVI -0.433013 1.115198 -0.3883 0.69781
## DEM 0.025591 0.016294 1.5706 0.11628
## SLOPE 0.010971 0.013341 0.8224 0.41087
## Avg_z -0.112125 0.022705 -4.9384 7.875e-07
## lag.Avg_CEa_07 -0.486187 0.219517 -2.2148 0.02677
## lag.NDVI -29.360420 11.602286 -2.5306 0.01139
## lag.DEM -0.125137 0.091592 -1.3663 0.17186
## lag.SLOPE 0.883938 0.212106 4.1674 3.080e-05
## lag.Avg_z 0.205119 0.155215 1.3215 0.18633
##
## Rho: 0.9037
## Asymptotic standard error: 0.58886
## z-value: 1.5347, p-value: 0.12487
## Lambda: 0.94686
## Asymptotic standard error: 0.32846
## z-value: 2.8827, p-value: 0.0039429
##
## LR test value: 149.65, p-value: < 2.22e-16
##
## Log likelihood: -189.5009 for sacmixed model
## ML residual variance (sigma squared): 0.19093, (sigma: 0.43695)
## Number of observations: 313
## Number of parameters estimated: 14
## AIC: 407, (AIC for lm: 542.65)Se puede observar como el AIC disminuye notablemente con respecto a los modelos autoregresivos SAR y SARAR
residuales_map3 =map3$residuals
shapiro.test(residuales_map3)##
## Shapiro-Wilk normality test
##
## data: residuales_map3
## W = 0.97364, p-value = 1.68e-05Moran.I(residuales_map3,We)## $observed
## [1] 0.04788866
##
## $expected
## [1] -0.003205128
##
## $sd
## [1] 0.004639083
##
## $p.value
## [1] 0Como el p-valor es cero, todavia hay dependencia espacial por lo que el modelo no es buno para estos datos
Se vuelve a realizar el modelo quitando la variable NDVI ya que es la variable que menos se relaciona con la conductividad
map3b= sacsarlm(formula=Avg_CEa_15~Avg_CEa_07+DEM+SLOPE+Avg_z, data= X, listw= Wve,type="mixed")
summary(map3b)##
## Call:sacsarlm(formula = Avg_CEa_15 ~ Avg_CEa_07 + DEM + SLOPE + Avg_z,
## data = X, listw = Wve, type = "mixed")
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.270871 -0.268895 -0.043227 0.251359 2.068286
##
## Type: sacmixed
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 14.256309 35.671498 0.3997 0.689410
## Avg_CEa_07 0.376570 0.034707 10.8500 < 2.2e-16
## DEM 0.025822 0.016516 1.5635 0.117944
## SLOPE 0.012529 0.013519 0.9268 0.354028
## Avg_z -0.107267 0.022501 -4.7673 1.868e-06
## lag.Avg_CEa_07 -0.611325 0.220653 -2.7705 0.005597
## lag.DEM -0.123820 0.093118 -1.3297 0.183615
## lag.SLOPE 0.604869 0.189089 3.1989 0.001380
## lag.Avg_z 0.144362 0.158025 0.9135 0.360957
##
## Rho: 0.91887
## Asymptotic standard error: 0.59159
## z-value: 1.5532, p-value: 0.12037
## Lambda: 0.95352
## Asymptotic standard error: 0.34156
## z-value: 2.7917, p-value: 0.0052437
##
## LR test value: 140.96, p-value: < 2.22e-16
##
## Log likelihood: -194.644 for sacmixed model
## ML residual variance (sigma squared): 0.19691, (sigma: 0.44375)
## Number of observations: 313
## Number of parameters estimated: 12
## AIC: 413.29, (AIC for lm: 542.24)Se observa que el AIC aumenta por lo que el modelo empeora.
residuales_map3b =map3b$residuals
shapiro.test(residuales_map3b)##
## Shapiro-Wilk normality test
##
## data: residuales_map3b
## W = 0.96429, p-value = 5.831e-07Moran.I(residuales_map3b,We)## $observed
## [1] 0.05521322
##
## $expected
## [1] -0.003205128
##
## $sd
## [1] 0.004634968
##
## $p.value
## [1] 0Como el p-valor del indice de moran es cero, todavia hay dependencia espacial, ademas no hay un comportamiento normal en los residuales. Por lo que el modelo no es buno para estos datos
map4=lagsarlm(formula=Avg_CEa_15~Avg_CEa_07+NDVI+DEM+SLOPE+Avg_z, data= X, listw= Wve)
summary(map4)##
## Call:lagsarlm(formula = Avg_CEa_15 ~ Avg_CEa_07 + NDVI + DEM + SLOPE +
## Avg_z, data = X, listw = Wve)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.4682926 -0.3245699 0.0049751 0.3215294 1.9926400
##
## Type: lag
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 22.7597381 2.0758704 10.9639 < 2.2e-16
## Avg_CEa_07 0.2479677 0.0247839 10.0052 < 2.2e-16
## NDVI -1.2527443 1.0391615 -1.2055 0.2280
## DEM -0.0035254 0.0106002 -0.3326 0.7394
## SLOPE 0.0603502 0.0137383 4.3928 1.119e-05
## Avg_z -0.1133123 0.0145926 -7.7650 8.216e-15
##
## Rho: 0.96209, LR test value: 51.297, p-value: 7.9403e-13
## Asymptotic standard error: 0.02667
## z-value: 36.074, p-value: < 2.22e-16
## Wald statistic: 1301.3, p-value: < 2.22e-16
##
## Log likelihood: -238.6759 for lag model
## ML residual variance (sigma squared): 0.26412, (sigma: 0.51393)
## Number of observations: 313
## Number of parameters estimated: 8
## AIC: 493.35, (AIC for lm: 542.65)
## LM test for residual autocorrelation
## test value: 197.83, p-value: < 2.22e-16El AIC aumento con respecto al modelo GNS, lo que implica que el modelo SEM es peor.
residuales_map4 =map4$residuals
shapiro.test(residuales_map4)##
## Shapiro-Wilk normality test
##
## data: residuales_map4
## W = 0.98401, p-value = 0.001482Moran.I(residuales_map4,We)## $observed
## [1] 0.06272672
##
## $expected
## [1] -0.003205128
##
## $sd
## [1] 0.004645596
##
## $p.value
## [1] 0Como el p-valor del indice de moran es cero, todavia hay dependencia espacial, ademas no hay un comportamiento normal en los residuales. Por lo que el modelo no es buno para estos datos
Quitando la variable DEM que es la que parece tener menor relacion, se refina el modelo.
map4b=lagsarlm(formula=Avg_CEa_15~Avg_CEa_07+NDVI+SLOPE+Avg_z, data= X, listw= Wve)
summary(map4b)##
## Call:lagsarlm(formula = Avg_CEa_15 ~ Avg_CEa_07 + NDVI + SLOPE + Avg_z,
## data = X, listw = Wve)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.463873 -0.328326 0.012762 0.317752 1.996379
##
## Type: lag
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 22.687995 2.064129 10.9916 < 2.2e-16
## Avg_CEa_07 0.247494 0.024746 10.0015 < 2.2e-16
## NDVI -1.220936 1.034918 -1.1797 0.2381
## SLOPE 0.060880 0.013646 4.4614 8.141e-06
## Avg_z -0.116676 0.010501 -11.1105 < 2.2e-16
##
## Rho: 0.9624, LR test value: 51.982, p-value: 5.6e-13
## Asymptotic standard error: 0.026456
## z-value: 36.377, p-value: < 2.22e-16
## Wald statistic: 1323.3, p-value: < 2.22e-16
##
## Log likelihood: -238.7312 for lag model
## ML residual variance (sigma squared): 0.2642, (sigma: 0.514)
## Number of observations: 313
## Number of parameters estimated: 7
## AIC: 491.46, (AIC for lm: 541.44)
## LM test for residual autocorrelation
## test value: 198.54, p-value: < 2.22e-16Se observa que al refinar el modelo, el AIC mejora un poco, pero sigue estando por detras del modelo GNS
residuales_map4b =map4b$residuals
shapiro.test(residuales_map4b)##
## Shapiro-Wilk normality test
##
## data: residuales_map4b
## W = 0.98375, p-value = 0.001306Moran.I(residuales_map4b,We)## $observed
## [1] 0.06286341
##
## $expected
## [1] -0.003205128
##
## $sd
## [1] 0.00464547
##
## $p.value
## [1] 0Como el p-valor del indice de moran es cero, todavia hay dependencia espacial, ademas no hay un comportamiento normal en los residuales. Por lo que el modelo no es buno para estos datos
map5=errorsarlm(formula=Avg_CEa_15~Avg_CEa_07+NDVI+DEM+SLOPE+Avg_z, data= X, listw= Wve)
summary(map5)##
## Call:errorsarlm(formula = Avg_CEa_15 ~ Avg_CEa_07 + NDVI + DEM + SLOPE +
## Avg_z, data = X, listw = Wve)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.46790 -0.32241 -0.02153 0.36060 1.99578
##
## Type: error
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 45.5088603 2.7607166 16.4844 < 2.2e-16
## Avg_CEa_07 0.2959247 0.0286368 10.3337 < 2.2e-16
## NDVI -1.1627276 1.1220178 -1.0363 0.3000703
## DEM -0.0093728 0.0123588 -0.7584 0.4482181
## SLOPE 0.0518339 0.0144655 3.5833 0.0003393
## Avg_z -0.1327355 0.0171932 -7.7202 1.155e-14
##
## Lambda: 0.96877, LR test value: 49.814, p-value: 1.69e-12
## Asymptotic standard error: 0.022011
## z-value: 44.013, p-value: < 2.22e-16
## Wald statistic: 1937.2, p-value: < 2.22e-16
##
## Log likelihood: -239.4171 for error model
## ML residual variance (sigma squared): 0.26504, (sigma: 0.51482)
## Number of observations: 313
## Number of parameters estimated: 8
## AIC: 494.83, (AIC for lm: 542.65)El modelo GNS sigue siendo el mejor, ya que el modelo SML tiene un AIC mayor
residuales_map5 =map5$residuals
shapiro.test(residuales_map5)##
## Shapiro-Wilk normality test
##
## data: residuales_map5
## W = 0.98846, p-value = 0.01377Moran.I(residuales_map5,We)## $observed
## [1] 0.07550844
##
## $expected
## [1] -0.003205128
##
## $sd
## [1] 0.004647281
##
## $p.value
## [1] 0Como el p-valor es cero, todavia hay dependencia espacial por lo que el modelo no es buno para estos datos
Quitando la variable DEM
map5b=errorsarlm(formula=Avg_CEa_15~Avg_CEa_07+NDVI+SLOPE+Avg_z, data= X, listw= Wve)
summary(map5b)##
## Call:errorsarlm(formula = Avg_CEa_15 ~ Avg_CEa_07 + NDVI + SLOPE +
## Avg_z, data = X, listw = Wve)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.4600071 -0.3276113 -0.0094465 0.3499612 2.0024552
##
## Type: error
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 45.155600 2.726282 16.5631 < 2.2e-16
## Avg_CEa_07 0.294005 0.028549 10.2982 < 2.2e-16
## NDVI -1.087459 1.118645 -0.9721 0.3309900
## SLOPE 0.052858 0.014414 3.6670 0.0002454
## Avg_z -0.140762 0.013554 -10.3854 < 2.2e-16
##
## Lambda: 0.9691, LR test value: 50.036, p-value: 1.5097e-12
## Asymptotic standard error: 0.021782
## z-value: 44.49, p-value: < 2.22e-16
## Wald statistic: 1979.4, p-value: < 2.22e-16
##
## Log likelihood: -239.7044 for error model
## ML residual variance (sigma squared): 0.26551, (sigma: 0.51528)
## Number of observations: 313
## Number of parameters estimated: 7
## AIC: 493.41, (AIC for lm: 541.44)El AIC mejora muy poco
residuales_map5b =map5b$residuals
shapiro.test(residuales_map5b)##
## Shapiro-Wilk normality test
##
## data: residuales_map5b
## W = 0.98839, p-value = 0.01325Moran.I(residuales_map5b,We)## $observed
## [1] 0.07616883
##
## $expected
## [1] -0.003205128
##
## $sd
## [1] 0.004647095
##
## $p.value
## [1] 0Como el p-valor es cero, todavia hay dependencia espacial por lo que el modelo no es buno para estos datos
map6=lagsarlm(formula=Avg_CEa_15~Avg_CEa_07+NDVI+DEM+SLOPE+Avg_z, data= X, listw= Wve,type="mixed")
summary(map6)##
## Call:lagsarlm(formula = Avg_CEa_15 ~ Avg_CEa_07 + NDVI + DEM + SLOPE +
## Avg_z, data = X, listw = Wve, type = "mixed")
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.356577 -0.269279 -0.016311 0.269347 1.954889
##
## Type: mixed
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 28.265444 13.304190 2.1246 0.033624
## Avg_CEa_07 0.318816 0.033502 9.5163 < 2.2e-16
## NDVI -0.463244 1.170570 -0.3957 0.692295
## DEM 0.026816 0.016575 1.6179 0.105686
## SLOPE 0.010237 0.014082 0.7269 0.467260
## Avg_z -0.127758 0.021328 -5.9901 2.098e-09
## lag.Avg_CEa_07 -0.148588 0.197032 -0.7541 0.450771
## lag.NDVI -33.518708 10.304158 -3.2529 0.001142
## lag.DEM -0.135244 0.080945 -1.6708 0.094759
## lag.SLOPE 1.004251 0.157352 6.3822 1.746e-10
## lag.Avg_z 0.216661 0.099651 2.1742 0.029690
##
## Rho: 0.91953, LR test value: 20.527, p-value: 5.8806e-06
## Asymptotic standard error: 0.056295
## z-value: 16.334, p-value: < 2.22e-16
## Wald statistic: 266.81, p-value: < 2.22e-16
##
## Log likelihood: -202.5621 for mixed model
## ML residual variance (sigma squared): 0.21072, (sigma: 0.45905)
## Number of observations: 313
## Number of parameters estimated: 13
## AIC: 431.12, (AIC for lm: 449.65)
## LM test for residual autocorrelation
## test value: 128.64, p-value: < 2.22e-16Este modelo es el que presenta un valor de AIC menor, lo que indica que es el mejor modelo
residuales_map6 =map6$residuals
shapiro.test(residuales_map6)##
## Shapiro-Wilk normality test
##
## data: residuales_map6
## W = 0.97531, p-value = 3.25e-05Moran.I(residuales_map6,We)## $observed
## [1] 0.04750286
##
## $expected
## [1] -0.003205128
##
## $sd
## [1] 0.004640154
##
## $p.value
## [1] 0Como el p-valor del indice de moran es cero, todavia hay dependencia espacial, ademas no hay un comportamiento normal en los residuales. Por lo que el modelo no es buno para estos datos