Creación de datos

BD_MODELADO <- read_excel("C:/Users/user/Downloads/BD_MODELADO.xlsx")
df=BD_MODELADO
df_xy=df[,c(1,2)] #Coordenadas
x=df[,-c(1,2)] #Explicativas

Diseño matriz de pesos

# 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: 312
class(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")

1. Regresión lineal no espacial

mod15=lm(df$Avg_CEa_15~df$NDVI)
summary(mod15)
## 
## Call:
## lm(formula = df$Avg_CEa_15 ~ df$NDVI)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.71991 -0.45614 -0.02841  0.38067  2.87345 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   22.227      1.179   18.85  < 2e-16 ***
## df$NDVI       -4.461      1.412   -3.16  0.00173 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7268 on 311 degrees of freedom
## Multiple R-squared:  0.0311, Adjusted R-squared:  0.02799 
## F-statistic: 9.984 on 1 and 311 DF,  p-value: 0.001735
hist(mod15$residuals)

residuales=mod15$residuals
df %>% ggplot(aes(x = Avg_X_MCB, y=Avg_Y_MCE, colour=residuales))+
   geom_point(size = 5,shape=15)+
   scale_color_continuous(type = 'viridis')

Moran.I(residuales, df.dists.inv)
## $observed
## [1] 0.1531025
## 
## $expected
## [1] -0.003205128
## 
## $sd
## [1] 0.004646164
## 
## $p.value
## [1] 0

Según el p.valor del índice de Moran (= 0), es posible afirmar que el modelo lineal no se ajusta, pues existe dependencia espacial de los residuales.

2. Modelo SAR

\[Y=\lambda W Y + \alpha 1_n +\epsilon\]

map15= spautolm(Avg_CEa_15~1, data= x, listw= Wve, family="SAR")
summary(map15)
## 
## Call: spautolm(formula = Avg_CEa_15 ~ 1, data = x, listw = Wve, family = "SAR")
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -1.453255 -0.397645 -0.042934  0.322283  2.953512 
## 
## Coefficients: 
##             Estimate Std. Error z value  Pr(>|z|)
## (Intercept)  19.3151     1.5515   12.45 < 2.2e-16
## 
## Lambda: 0.97691 LR test value: 86.774 p-value: < 2.22e-16 
## Numerical Hessian standard error of lambda: 0.023 
## 
## Log likelihood: -304.7918 
## ML residual variance (sigma squared): 0.40168, (sigma: 0.63378)
## Number of observations: 313 
## Number of parameters estimated: 3 
## AIC: 615.58
residuales_map15 =map15$fit$residuals
shapiro.test(residuales_map15)
## 
##  Shapiro-Wilk normality test
## 
## data:  residuales_map15
## W = 0.95729, p-value = 6.37e-08
Moran.I(residuales_map15,we)
## $observed
## [1] 0.09349941
## 
## $expected
## [1] -0.003205128
## 
## $sd
## [1] 0.004635041
## 
## $p.value
## [1] 0

A pesar de que Lambda es cercano a uno (0.97691), no se presenta normalidad en los residuos y el p.valor del índice de Moran es cero. Lo anterior nos indica que los residuos tienen dependencia espacial, y por ende, el modelo no explica correctamente los datos de la conductividad eletrica a 150 cm.

3. Modelo SARAR

\[Y=\lambda W Y + \alpha 1_n +u \\u=\rho Wu +\epsilon\]

map15_2= sacsarlm(Avg_CEa_15~1, data= x, listw= Wve)
summary(map15_2)
## 
## 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_map15_2 =map15_2$residuals
shapiro.test(residuales_map15_2)
## 
##  Shapiro-Wilk normality test
## 
## data:  residuales_map15_2
## W = 0.94498, p-value = 2.076e-09
Moran.I(residuales_map15_2,we)
## $observed
## [1] 0.0563745
## 
## $expected
## [1] -0.003205128
## 
## $sd
## [1] 0.004629181
## 
## $p.value
## [1] 0

A pesar de que Lambda es cercano a uno (0.95895) y rho también (0.95895), no se presenta normalidad en los residuos y el p.valor del índice de Moran es cero. Lo anterior nos indica que los residuos tienen dependencia espacial, y por ende, el modelo no explica correctamente los datos de la conductividad eletrica a 150 cm.

4. Modelo GNS

\[Y= \lambda WY +\alpha 1_n + X\beta_{(1)}+ WX\beta_{(2)}+ u \\ |\lambda|<1 \\ u=\rho Wu + \epsilon \\|\rho|<1\]

map15_3= sacsarlm(formula=Avg_CEa_15~Avg_CEa_07+NDVI+DEM+SLOPE+Avg_z, data= x, listw= Wve,type="mixed")
summary(map15_3)
## 
## 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)
residuales_map15_3=map15_3$residuals
shapiro.test(residuales_map15_3)
## 
##  Shapiro-Wilk normality test
## 
## data:  residuales_map15_3
## W = 0.97364, p-value = 1.68e-05
Moran.I(residuales_map15_3,we)
## $observed
## [1] 0.04788866
## 
## $expected
## [1] -0.003205128
## 
## $sd
## [1] 0.004639083
## 
## $p.value
## [1] 0

A pesar de que Lambda es cercano a uno (0.94686) y rho también (0.9037), no se presenta normalidad en los residuos y el p.valor del índice de Moran es cero. Lo anterior nos indica que los residuos tienen dependencia espacial, y por ende, el modelo no explica correctamente los datos de la conductividad eletrica a 150 cm.

Modelo quitando DEM

map15_3b= sacsarlm(formula=Avg_CEa_15~Avg_CEa_07+NDVI+SLOPE+Avg_z, data= x, listw= Wve,type="mixed")
summary(map15_3b)
## 
## Call:sacsarlm(formula = Avg_CEa_15 ~ Avg_CEa_07 + NDVI + SLOPE + Avg_z, 
##     data = x, listw = Wve, type = "mixed")
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -1.242977 -0.273753 -0.027046  0.262976  1.942185 
## 
## Type: sacmixed 
## Coefficients: (asymptotic standard errors) 
##                  Estimate Std. Error z value  Pr(>|z|)
## (Intercept)     17.956728  33.982429  0.5284  0.597213
## Avg_CEa_07       0.373281   0.034028 10.9697 < 2.2e-16
## NDVI            -0.543373   1.116766 -0.4866  0.626571
## SLOPE            0.011352   0.013389  0.8479  0.396517
## Avg_z           -0.105276   0.022422 -4.6952 2.664e-06
## lag.Avg_CEa_07  -0.559944   0.212632 -2.6334  0.008454
## lag.NDVI       -28.742233  11.599813 -2.4778  0.013219
## lag.SLOPE        0.884282   0.203207  4.3516 1.351e-05
## lag.Avg_z        0.138273   0.128293  1.0778  0.281128
## 
## Rho: 0.90567
## Asymptotic standard error: 0.5636
##     z-value: 1.6069, p-value: 0.10807
## Lambda: 0.94735
## Asymptotic standard error: 0.31799
##     z-value: 2.9792, p-value: 0.0028904
## 
## LR test value: 147.85, p-value: < 2.22e-16
## 
## Log likelihood: -190.7997 for sacmixed model
## ML residual variance (sigma squared): 0.19248, (sigma: 0.43873)
## Number of observations: 313 
## Number of parameters estimated: 12 
## AIC: 405.6, (AIC for lm: 541.44)
residuales_map15_3b=map15_3b$residuals
shapiro.test(residuales_map15_3b)
## 
##  Shapiro-Wilk normality test
## 
## data:  residuales_map15_3b
## W = 0.97534, p-value = 3.293e-05
Moran.I(residuales_map15_3b,we)
## $observed
## [1] 0.04841028
## 
## $expected
## [1] -0.003205128
## 
## $sd
## [1] 0.004640051
## 
## $p.value
## [1] 0

A pesar de que Lambda es cercano a uno (0.94735) y rho también (0.90567), no se presenta normalidad en los residuos y el p.valor del índice de Moran es cero. Lo anterior nos indica que los residuos tienen dependencia espacial, y por ende, el modelo no explica correctamente los datos de la conductividad eletrica a 150 cm.

Modelo quitando DEM y NDVI

map15_3c= sacsarlm(formula=Avg_CEa_15~Avg_CEa_07+SLOPE+Avg_z, data= x, listw= Wve,type="mixed")
summary(map15_3c)
## 
## Call:sacsarlm(formula = Avg_CEa_15 ~ Avg_CEa_07 + SLOPE + Avg_z, data = x, 
##     listw = Wve, type = "mixed")
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -1.253068 -0.278077 -0.027132  0.246479  2.075108 
## 
## Type: sacmixed 
## Coefficients: (asymptotic standard errors) 
##                 Estimate Std. Error z value  Pr(>|z|)
## (Intercept)     6.265194  33.583259  0.1866 0.8520079
## Avg_CEa_07      0.388032   0.034184 11.3514 < 2.2e-16
## SLOPE           0.012949   0.013568  0.9543 0.3399067
## Avg_z          -0.100612   0.022265 -4.5189 6.216e-06
## lag.Avg_CEa_07 -0.686182   0.213268 -3.2175 0.0012933
## lag.SLOPE       0.605897   0.179713  3.3715 0.0007477
## lag.Avg_z       0.080770   0.130640  0.6183 0.5363998
## 
## Rho: 0.92017
## Asymptotic standard error: 0.57014
##     z-value: 1.6139, p-value: 0.10654
## Lambda: 0.95375
## Asymptotic standard error: 0.33291
##     z-value: 2.8649, p-value: 0.0041718
## 
## LR test value: 139.01, p-value: < 2.22e-16
## 
## Log likelihood: -195.9188 for sacmixed model
## ML residual variance (sigma squared): 0.1985, (sigma: 0.44553)
## Number of observations: 313 
## Number of parameters estimated: 10 
## AIC: 411.84, (AIC for lm: 540.85)
residuales_map15_3c=map15_3c$residuals
shapiro.test(residuales_map15_3c)
## 
##  Shapiro-Wilk normality test
## 
## data:  residuales_map15_3c
## W = 0.96658, p-value = 1.265e-06
Moran.I(residuales_map15_3c,we)
## $observed
## [1] 0.05566855
## 
## $expected
## [1] -0.003205128
## 
## $sd
## [1] 0.004635825
## 
## $p.value
## [1] 0

A pesar de que Lambda es cercano a uno (0.95375) y rho también (0.92017), no se presenta normalidad en los residuos y el p.valor del índice de Moran es cero. Lo anterior nos indica que los residuos tienen dependencia espacial, y por ende, el modelo no explica correctamente los datos de la conductividad eletrica a 150 cm.

5. Modelo SEM

\[Y= \alpha 1_n + X\beta+u \\ u=\rho Wu + \epsilon \]

map15_4=lagsarlm(formula=Avg_CEa_15~Avg_CEa_07+NDVI+DEM+SLOPE+Avg_z, data= x, listw= Wve)
summary(map15_4)
## 
## 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-16
residuales_map15_4 =map15_4$residuals
shapiro.test(residuales_map15_4)
## 
##  Shapiro-Wilk normality test
## 
## data:  residuales_map15_4
## W = 0.98401, p-value = 0.001482
Moran.I(residuales_map15_4,we)
## $observed
## [1] 0.06272672
## 
## $expected
## [1] -0.003205128
## 
## $sd
## [1] 0.004645596
## 
## $p.value
## [1] 0

A pesar de que Rho es cercano a uno (0.96209), no se presenta normalidad en los residuos y el p.valor del índice de Moran es cero. Lo anterior nos indica que los residuos tienen dependencia espacial, y por ende, el modelo no explica correctamente los datos de la conductividad eletrica a 150 cm.

Modelo quitando NDVI

map15_4b=lagsarlm(formula=Avg_CEa_15~Avg_CEa_07+DEM+SLOPE+Avg_z, data= x, listw= Wve)
summary(map15_4b)
## 
## Call:lagsarlm(formula = Avg_CEa_15 ~ Avg_CEa_07 + DEM + SLOPE + Avg_z, 
##     data = x, listw = Wve)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -1.4816823 -0.3104710 -0.0029262  0.3123820  2.0086327 
## 
## Type: lag 
## Coefficients: (asymptotic standard errors) 
##               Estimate Std. Error z value  Pr(>|z|)
## (Intercept) 22.2840690  2.0415406 10.9153 < 2.2e-16
## Avg_CEa_07   0.2511915  0.0246965 10.1712 < 2.2e-16
## DEM         -0.0023501  0.0105797 -0.2221    0.8242
## SLOPE        0.0590076  0.0137250  4.2993 1.713e-05
## Avg_z       -0.1174587  0.0142130 -8.2642 2.220e-16
## 
## Rho: 0.96224, LR test value: 51.442, p-value: 7.3763e-13
## Asymptotic standard error: 0.026571
##     z-value: 36.214, p-value: < 2.22e-16
## Wald statistic: 1311.5, p-value: < 2.22e-16
## 
## Log likelihood: -239.4008 for lag model
## ML residual variance (sigma squared): 0.26534, (sigma: 0.51511)
## Number of observations: 313 
## Number of parameters estimated: 7 
## AIC: 492.8, (AIC for lm: 542.24)
## LM test for residual autocorrelation
## test value: 204.24, p-value: < 2.22e-16
residuales_map15_4b =map15_4b$residuals
shapiro.test(residuales_map15_4b)
## 
##  Shapiro-Wilk normality test
## 
## data:  residuales_map15_4b
## W = 0.98402, p-value = 0.001489
Moran.I(residuales_map15_4b,we)
## $observed
## [1] 0.06381437
## 
## $expected
## [1] -0.003205128
## 
## $sd
## [1] 0.004645202
## 
## $p.value
## [1] 0

A pesar de que Rho es cercano a uno (0.96224), no se presenta normalidad en los residuos y el p.valor del índice de Moran es cero. Lo anterior nos indica que los residuos tienen dependencia espacial, y por ende, el modelo no explica correctamente los datos de la conductividad eletrica a 150 cm.

Modelo quitando DEM y NDVI

map15_4c=lagsarlm(formula=Avg_CEa_15~Avg_CEa_07+SLOPE+Avg_z, data= x, listw= Wve)
summary(map15_4c)
## 
## Call:lagsarlm(formula = Avg_CEa_15 ~ Avg_CEa_07 + SLOPE + Avg_z, data = x, 
##     listw = Wve)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -1.4784823 -0.3104058 -0.0036333  0.3134775  2.0108734 
## 
## Type: lag 
## Coefficients: (asymptotic standard errors) 
##              Estimate Std. Error  z value  Pr(>|z|)
## (Intercept) 22.244004   2.033354  10.9396 < 2.2e-16
## Avg_CEa_07   0.250818   0.024640  10.1794 < 2.2e-16
## SLOPE        0.059387   0.013617   4.3611 1.294e-05
## Avg_z       -0.119649   0.010216 -11.7118 < 2.2e-16
## 
## Rho: 0.96243, LR test value: 51.997, p-value: 5.56e-13
## Asymptotic standard error: 0.026429
##     z-value: 36.416, p-value: < 2.22e-16
## Wald statistic: 1326.1, p-value: < 2.22e-16
## 
## Log likelihood: -239.4255 for lag model
## ML residual variance (sigma squared): 0.26537, (sigma: 0.51514)
## Number of observations: 313 
## Number of parameters estimated: 6 
## AIC: 490.85, (AIC for lm: 540.85)
## LM test for residual autocorrelation
## test value: 204.57, p-value: < 2.22e-16
residuales_map15_4c=map15_4c$residuals
shapiro.test(residuales_map15_4c)
## 
##  Shapiro-Wilk normality test
## 
## data:  residuales_map15_4c
## W = 0.98381, p-value = 0.001347
Moran.I(residuales_map15_4c,we)
## $observed
## [1] 0.06388428
## 
## $expected
## [1] -0.003205128
## 
## $sd
## [1] 0.004645126
## 
## $p.value
## [1] 0

A pesar de que Rho es cercano a uno (0.96243), no se presenta normalidad en los residuos y el p.valor del índice de Moran es cero. Lo anterior nos indica que los residuos tienen dependencia espacial, y por ende, el modelo no explica correctamente los datos de la conductividad eletrica a 150 cm.

6. Modelo SLM

\[Y=\lambda W Y + \alpha 1_n + X\beta+\epsilon \]

map15_5=errorsarlm(formula=Avg_CEa_15~Avg_CEa_07+NDVI+DEM+SLOPE+Avg_z, data= x, listw= Wve)
summary(map15_5)
## 
## 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)
residuales_map15_5 =map15_5$residuals
shapiro.test(residuales_map15_5)
## 
##  Shapiro-Wilk normality test
## 
## data:  residuales_map15_5
## W = 0.98846, p-value = 0.01377
Moran.I(residuales_map15_5,we)
## $observed
## [1] 0.07550844
## 
## $expected
## [1] -0.003205128
## 
## $sd
## [1] 0.004647281
## 
## $p.value
## [1] 0

A pesar de que Lambda es cercano a uno (0.96877), no se presenta normalidad en los residuos y el p.valor del índice de Moran es cero. Lo anterior nos indica que los residuos tienen dependencia espacial, y por ende, el modelo no explica correctamente los datos de la conductividad eletrica a 150 cm.

Modelo quitando el NDVI

map15_5b=errorsarlm(formula=Avg_CEa_15~Avg_CEa_07+DEM+SLOPE+Avg_z, data= x, listw= Wve)
summary(map15_5b)
## 
## Call:errorsarlm(formula = Avg_CEa_15 ~ Avg_CEa_07 + DEM + SLOPE + 
##     Avg_z, data = x, listw = Wve)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -1.477728 -0.316994 -0.014091  0.367283  2.009859 
## 
## Type: error 
## Coefficients: (asymptotic standard errors) 
##              Estimate Std. Error z value  Pr(>|z|)
## (Intercept) 45.035550   2.729375 16.5003 < 2.2e-16
## Avg_CEa_07   0.299387   0.028492 10.5079 < 2.2e-16
## DEM         -0.008240   0.012332 -0.6682 0.5040078
## SLOPE        0.051310   0.014481  3.5432 0.0003953
## Avg_z       -0.136386   0.016857 -8.0910 6.661e-16
## 
## Lambda: 0.96901, LR test value: 50.337, p-value: 1.2949e-12
## Asymptotic standard error: 0.021843
##     z-value: 44.363, p-value: < 2.22e-16
## Wald statistic: 1968.1, p-value: < 2.22e-16
## 
## Log likelihood: -239.9531 for error model
## ML residual variance (sigma squared): 0.26594, (sigma: 0.51569)
## Number of observations: 313 
## Number of parameters estimated: 7 
## AIC: 493.91, (AIC for lm: 542.24)
residuales_map15_5b =map15_5b$residuals
shapiro.test(residuales_map15_5b)
## 
##  Shapiro-Wilk normality test
## 
## data:  residuales_map15_5b
## W = 0.98823, p-value = 0.01217
Moran.I(residuales_map15_5b,we)
## $observed
## [1] 0.07620439
## 
## $expected
## [1] -0.003205128
## 
## $sd
## [1] 0.004646962
## 
## $p.value
## [1] 0

A pesar de que Lambda es cercano a uno (0.96901), no se presenta normalidad en los residuos y el p.valor del índice de Moran es cero. Lo anterior nos indica que los residuos tienen dependencia espacial, y por ende, el modelo no explica correctamente los datos de la conductividad eletrica a 150 cm.

Modelo quitando DEM y NDVI

map15_5c=errorsarlm(formula=Avg_CEa_15~Avg_CEa_07+SLOPE+Avg_z, data= x, listw= Wve)
summary(map15_5c) 
## 
## Call:errorsarlm(formula = Avg_CEa_15 ~ Avg_CEa_07 + SLOPE + Avg_z, 
##     data = x, listw = Wve)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -1.470171 -0.318709 -0.014481  0.355224  2.014963 
## 
## Type: error 
## Coefficients: (asymptotic standard errors) 
##              Estimate Std. Error  z value  Pr(>|z|)
## (Intercept) 44.749718   2.699784  16.5753 < 2.2e-16
## Avg_CEa_07   0.297488   0.028368  10.4868 < 2.2e-16
## SLOPE        0.052248   0.014422   3.6227 0.0002915
## Avg_z       -0.143289   0.013322 -10.7558 < 2.2e-16
## 
## Lambda: 0.96928, LR test value: 50.495, p-value: 1.1945e-12
## Asymptotic standard error: 0.021655
##     z-value: 44.761, p-value: < 2.22e-16
## Wald statistic: 2003.5, p-value: < 2.22e-16
## 
## Log likelihood: -240.1762 for error model
## ML residual variance (sigma squared): 0.2663, (sigma: 0.51604)
## Number of observations: 313 
## Number of parameters estimated: 6 
## AIC: 492.35, (AIC for lm: 540.85)
residuales_map15_5c =map15_5c$residuals
shapiro.test(residuales_map15_5c)
## 
##  Shapiro-Wilk normality test
## 
## data:  residuales_map15_5c
## W = 0.98814, p-value = 0.01166
Moran.I(residuales_map15_5c,we)
## $observed
## [1] 0.0767392
## 
## $expected
## [1] -0.003205128
## 
## $sd
## [1] 0.004646816
## 
## $p.value
## [1] 0

A pesar de que Lambda es cercano a uno (0.96928), no se presenta normalidad en los residuos y el p.valor del índice de Moran es cero. Lo anterior nos indica que los residuos tienen dependencia espacial, y por ende, el modelo no explica correctamente los datos de la conductividad eletrica a 150 cm.

7. Modelo SDE

\[Y= \alpha 1_n + X\beta+ WX\beta_{(2)}+ u \\ u=\rho Wu + \epsilon \]

map15_6=lagsarlm(formula=Avg_CEa_15~Avg_CEa_07+NDVI+DEM+SLOPE+Avg_z, data= x, listw= Wve,type="mixed")
summary(map15_6)
## 
## 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: (numerical Hessian approximate standard errors) 
##                  Estimate Std. Error z value  Pr(>|z|)
## (Intercept)     28.265444  12.265241  2.3045  0.021194
## Avg_CEa_07       0.318816   0.032741  9.7376 < 2.2e-16
## NDVI            -0.463244   1.198688 -0.3865  0.699157
## DEM              0.026816   0.015544  1.7252  0.084488
## SLOPE            0.010237   0.014217  0.7200  0.471503
## Avg_z           -0.127758   0.019283 -6.6254 3.462e-11
## lag.Avg_CEa_07  -0.148588   0.184740 -0.8043  0.421220
## lag.NDVI       -33.518708  10.042695 -3.3376  0.000845
## lag.DEM         -0.135244   0.071200 -1.8995  0.057501
## lag.SLOPE        1.004251   0.157735  6.3667 1.931e-10
## lag.Avg_z        0.216661   0.078053  2.7758  0.005506
## 
## Rho: 0.91953, LR test value: 20.527, p-value: 5.8806e-06
## Approximate (numerical Hessian) standard error: 0.078987
##     z-value: 11.642, p-value: < 2.22e-16
## Wald statistic: 135.53, 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)
residuales_map15_6=map15_6$residuals
shapiro.test(residuales_map15_6)
## 
##  Shapiro-Wilk normality test
## 
## data:  residuales_map15_6
## W = 0.97531, p-value = 3.25e-05
Moran.I(residuales_map15_6,we)
## $observed
## [1] 0.04750286
## 
## $expected
## [1] -0.003205128
## 
## $sd
## [1] 0.004640154
## 
## $p.value
## [1] 0

A pesar de que Rho es cercano a uno (0.91953), no se presenta normalidad en los residuos y el p.valor del índice de Moran es cero. Lo anterior nos indica que los residuos tienen dependencia espacial, y por ende, el modelo no explica correctamente los datos de la conductividad eletrica a 150 cm.

Modelo quitando el DEM

map15_6b=lagsarlm(formula=Avg_CEa_15~Avg_CEa_07+NDVI+SLOPE+Avg_z, data= x, listw= Wve,type="mixed")
summary(map15_6b)
## 
## Call:lagsarlm(formula = Avg_CEa_15 ~ Avg_CEa_07 + NDVI + SLOPE + Avg_z, 
##     data = x, listw = Wve, type = "mixed")
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -1.333622 -0.275363 -0.029168  0.282362  1.964752 
## 
## Type: mixed 
## Coefficients: (numerical Hessian approximate standard errors) 
##                  Estimate Std. Error z value  Pr(>|z|)
## (Intercept)     19.647922  11.671165  1.6835  0.092286
## Avg_CEa_07       0.330155   0.032126 10.2768 < 2.2e-16
## NDVI            -0.589440   1.162183 -0.5072  0.612026
## SLOPE            0.010556   0.014130  0.7470  0.455040
## Avg_z           -0.121066   0.019364 -6.2522 4.048e-10
## lag.Avg_CEa_07  -0.223421   0.181059 -1.2340  0.217216
## lag.NDVI       -32.761470  10.059924 -3.2566  0.001127
## lag.SLOPE        1.008515   0.155767  6.4745 9.512e-11
## lag.Avg_z        0.143016   0.075228  1.9011  0.057288
## 
## Rho: 0.92005, LR test value: 20.705, p-value: 5.3568e-06
## Approximate (numerical Hessian) standard error: 0.078739
##     z-value: 11.685, p-value: < 2.22e-16
## Wald statistic: 136.53, p-value: < 2.22e-16
## 
## Log likelihood: -204.0637 for mixed model
## ML residual variance (sigma squared): 0.21275, (sigma: 0.46124)
## Number of observations: 313 
## Number of parameters estimated: 11 
## AIC: 430.13, (AIC for lm: 448.83)
residuales_map15_6b=map15_6b$residuals
shapiro.test(residuales_map15_6b)
## 
##  Shapiro-Wilk normality test
## 
## data:  residuales_map15_6b
## W = 0.97702, p-value = 6.545e-05
Moran.I(residuales_map15_6b,we)
## $observed
## [1] 0.04829465
## 
## $expected
## [1] -0.003205128
## 
## $sd
## [1] 0.004641113
## 
## $p.value
## [1] 0

A pesar de que Rho es cercano a uno (0.92005), no se presenta normalidad en los residuos y el p.valor del índice de Moran es cero. Lo anterior nos indica que los residuos tienen dependencia espacial, y por ende, el modelo no explica correctamente los datos de la conductividad eletrica a 150 cm.

Modelo quitando NDVI y DEM

map15_6c=lagsarlm(formula=Avg_CEa_15~Avg_CEa_07+SLOPE+Avg_z, data= x, listw= Wve,type="mixed")
summary(map15_6c)
## 
## Call:lagsarlm(formula = Avg_CEa_15 ~ Avg_CEa_07 + SLOPE + Avg_z, data = x, 
##     listw = Wve, type = "mixed")
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -1.356185 -0.291875 -0.027334  0.266255  2.154409 
## 
## Type: mixed 
## Coefficients: (numerical Hessian approximate standard errors) 
##                 Estimate Std. Error z value  Pr(>|z|)
## (Intercept)     7.568151  11.577432  0.6537   0.51331
## Avg_CEa_07      0.349842   0.032747 10.6832 < 2.2e-16
## SLOPE           0.014569   0.014404  1.0114   0.31181
## Avg_z          -0.112156   0.020166 -5.5617 2.672e-08
## lag.Avg_CEa_07 -0.405714   0.183619 -2.2095   0.02714
## lag.SLOPE       0.634660   0.128471  4.9401 7.808e-07
## lag.Avg_z       0.070200   0.077591  0.9048   0.36560
## 
## Rho: 0.93603, LR test value: 26.717, p-value: 2.3559e-07
## Approximate (numerical Hessian) standard error: 0.063387
##     z-value: 14.767, p-value: < 2.22e-16
## Wald statistic: 218.06, p-value: < 2.22e-16
## 
## Log likelihood: -212.4981 for mixed model
## ML residual variance (sigma squared): 0.2242, (sigma: 0.4735)
## Number of observations: 313 
## Number of parameters estimated: 9 
## AIC: 443, (AIC for lm: 467.71)
residuales_map15_6c=map15_6c$residuals
shapiro.test(residuales_map15_6c)
## 
##  Shapiro-Wilk normality test
## 
## data:  residuales_map15_6c
## W = 0.96734, p-value = 1.649e-06
Moran.I(residuales_map15_6c,we)
## $observed
## [1] 0.06194672
## 
## $expected
## [1] -0.003205128
## 
## $sd
## [1] 0.00463645
## 
## $p.value
## [1] 0

A pesar de que Rho es cercano a uno (0.93603), no se presenta normalidad en los residuos y el p.valor del índice de Moran es cero. Lo anterior nos indica que los residuos tienen dependencia espacial, y por ende, el modelo no explica correctamente los datos de la conductividad eletrica a 150 cm.

En conclusión, ninguno de los modelos explica los datos de conductividad electrica a 150 cm, sin embargo, al observar el AIC, el modelo que obtuvo el valor más bajo fue 4. Modelo GNS, con AIC: 405.6, es decir, fue el que estuvo más cerca.