Indice de Moran
Laura Sofia Hernandez Sanchez
09/10/2020
Calculo del indice de Moran en la dristribución de datos en un lote
library(ape)
set.seed(12345)
MO=rnorm(n=150, mean= 3, sd=0.5)
xy= expand.grid(x=seq(1,10), y =seq(1,15))
df=data.frame(MO, xy)
plot(xy, col=MO, pch=19)
mo.dists <- as.matrix(dist(cbind(xy$x, xy$y)))
mo.dists.inv <- 1/mo.dists ##(Inf) Inverso de la Matriz
### Matriz de peso, el inverso de las distancias = mas lejos va a tener menos relevancia y un menor valor
diag(mo.dists.inv) <- 0
dim(mo.dists)## [1] 150 150mo.dists.inv[1:5, 1:5]## 1 2 3 4 5
## 1 0.0000000 1.0000000 0.5 0.3333333 0.2500000
## 2 1.0000000 0.0000000 1.0 0.5000000 0.3333333
## 3 0.5000000 1.0000000 0.0 1.0000000 0.5000000
## 4 0.3333333 0.5000000 1.0 0.0000000 1.0000000
## 5 0.2500000 0.3333333 0.5 1.0000000 0.0000000Moran.I(df$MO, mo.dists.inv)## $observed
## [1] -0.009650003
##
## $expected
## [1] -0.006711409
##
## $sd
## [1] 0.007694112
##
## $p.value
## [1] 0.7025151De acuerdo al p-valor calculado en el Indice de Moran se observa que no hay dependencia espacialo (negativa) o que estan minimamente relacionados.
Ejercicio de modelación de conductividad electrica
Se modelo 18526 datos de conductiva electrica a dos profundidades diferentes: 75 cm y 150 cm. Para que el computador los procese de una mejor manera se dividieron en tres grupos, donde cada uno cuenta con aproximadamente 6000 datos. En cada caso se calculo el Indice de Moran para observar la autocorrelación espacial. Además, se representan graficamente donde se realizaron las medidas espacialmente.
library(readxl)
BD_MORAN <- read_excel("~/2020-2/Computacion estadistica/BD_MORAN.xlsx",
sheet = "Hoja1", col_types = c("numeric",
"numeric", "numeric", "numeric",
"numeric", "numeric", "numeric"))
View(BD_MORAN)
head(BD_MORAN, n=10)## # A tibble: 10 x 7
## z X_WGS84 Y_WGS84 CEa_075 CEa_150 X_MCB Y_MCE
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 194. -72.5 4.20 6.17 18.1 843499. 955943.
## 2 194. -72.5 4.20 6.21 17.7 843499. 955943.
## 3 194. -72.5 4.20 6.37 18.6 843499. 955944.
## 4 194. -72.5 4.20 6.33 18.2 843498. 955944.
## 5 194. -72.5 4.20 6.41 18.2 843498. 955944.
## 6 194. -72.5 4.20 6.37 18.8 843498. 955944.
## 7 194. -72.5 4.20 6.33 18.0 843498. 955944.
## 8 193. -72.5 4.20 6.72 18.6 843497. 955944.
## 9 193. -72.5 4.20 6.48 18.7 843497. 955944.
## 10 193. -72.5 4.20 6.60 18.4 843497. 955944.dim(BD_MORAN)## [1] 18526 7str(BD_MORAN)## tibble [18,526 x 7] (S3: tbl_df/tbl/data.frame)
## $ z : num [1:18526] 194 194 194 194 194 ...
## $ X_WGS84: num [1:18526] -72.5 -72.5 -72.5 -72.5 -72.5 ...
## $ Y_WGS84: num [1:18526] 4.2 4.2 4.2 4.2 4.2 ...
## $ CEa_075: num [1:18526] 6.17 6.21 6.37 6.33 6.41 ...
## $ CEa_150: num [1:18526] 18.1 17.7 18.6 18.2 18.2 ...
## $ X_MCB : num [1:18526] 843499 843499 843499 843498 843498 ...
## $ Y_MCE : num [1:18526] 955943 955943 955944 955944 955944 ...plot(BD_MORAN$Y_WGS84, BD_MORAN$X_WGS84, cex=0.01*BD_MORAN$CEa_075, col="red", pch=19)
### Profundidad de 75 cm
plot(BD_MORAN$Y_WGS84, BD_MORAN$X_WGS84, cex=1, col=0.3*BD_MORAN$CEa_075, pch=19)
### Profundidad de 150 cm
plot(BD_MORAN$Y_WGS84, BD_MORAN$X_WGS84, cex=1, col=0.3*BD_MORAN$CEa_150, pch=19)
Datos de conductividad electrica, parte 1
library(ape)
library(readxl)
BD_MORAN_1 <- read_excel("~/2020-2/Computacion estadistica/BD_MORAN - Copia.xlsx",
sheet = "Hoja1", col_types = c("numeric",
"numeric", "numeric", "numeric",
"numeric", "numeric", "numeric"))
View(BD_MORAN_1)
head(BD_MORAN_1 , n=10)## # A tibble: 10 x 7
## z X_WGS84 Y_WGS84 CEa_075 CEa_150 X_MCB Y_MCE
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 194. -72.5 4.20 6.17 18.1 843499. 955943.
## 2 194. -72.5 4.20 6.21 17.7 843499. 955943.
## 3 194. -72.5 4.20 6.37 18.6 843499. 955944.
## 4 194. -72.5 4.20 6.33 18.2 843498. 955944.
## 5 194. -72.5 4.20 6.41 18.2 843498. 955944.
## 6 194. -72.5 4.20 6.37 18.8 843498. 955944.
## 7 194. -72.5 4.20 6.33 18.0 843498. 955944.
## 8 193. -72.5 4.20 6.72 18.6 843497. 955944.
## 9 193. -72.5 4.20 6.48 18.7 843497. 955944.
## 10 193. -72.5 4.20 6.60 18.4 843497. 955944.dim(BD_MORAN_1 )## [1] 5999 7str(BD_MORAN_1 )## tibble [5,999 x 7] (S3: tbl_df/tbl/data.frame)
## $ z : num [1:5999] 194 194 194 194 194 ...
## $ X_WGS84: num [1:5999] -72.5 -72.5 -72.5 -72.5 -72.5 ...
## $ Y_WGS84: num [1:5999] 4.2 4.2 4.2 4.2 4.2 ...
## $ CEa_075: num [1:5999] 6.17 6.21 6.37 6.33 6.41 ...
## $ CEa_150: num [1:5999] 18.1 17.7 18.6 18.2 18.2 ...
## $ X_MCB : num [1:5999] 843499 843499 843499 843498 843498 ...
## $ Y_MCE : num [1:5999] 955943 955943 955944 955944 955944 ...### Profundidad de 75 cm
plot(BD_MORAN_1$X_WGS84, BD_MORAN_1$Y_WGS84, cex=0.01*BD_MORAN_1$CEa_075, col="red", pch=19)
### Profundidad de 150 cm
plot(BD_MORAN_1$X_WGS84, BD_MORAN_1$Y_WGS84, cex=0.01*BD_MORAN_1$CEa_150, col="red", pch=19)
ce.dists1<-as.matrix(dist(cbind(BD_MORAN_1$X_WGS84, BD_MORAN_1$Y_WGS84)))
dim(ce.dists1)## [1] 5999 5999ce.dists.inv1 <-1/ce.dists1
ce.dists.inv1[is.infinite(ce.dists.inv1)] <- 0
diag(ce.dists.inv1)<-0
ce.dists.inv1[1:6, 1:6]## 1 2 3 4 5 6
## 1 0.00 406473.8 183582.7 136552.7 99512.0 80767.51
## 2 406473.84 0.0 334028.1 205286.9 131603.4 100690.59
## 3 183582.68 334028.1 0.0 532631.2 217163.1 144140.71
## 4 136552.66 205286.9 532631.2 0.0 366652.3 197620.35
## 5 99512.00 131603.4 217163.1 366652.3 0.0 428663.73
## 6 80767.51 100690.6 144140.7 197620.4 428663.7 0.00## Indice de Moran de conductividad electrica a 75 cm de profundidad
I.Moran1_75<-Moran.I(BD_MORAN_1$CEa_075, ce.dists.inv1); I.Moran1_75## $observed
## [1] 0.5138156
##
## $expected
## [1] -0.0001667222
##
## $sd
## [1] 0.001570002
##
## $p.value
## [1] 0## Indice de Moran de conductividad electrica a 150 cm de profundidad
I.Moran1_150<-Moran.I(BD_MORAN_1$CEa_150, ce.dists.inv1); I.Moran1_150## $observed
## [1] 0.3309809
##
## $expected
## [1] -0.0001667222
##
## $sd
## [1] 0.001569744
##
## $p.value
## [1] 0Datos de conductividad electrica, parte 2
BD_MORAN_2 <- read_excel("~/2020-2/Computacion estadistica/BD_MORAN - Copia.xlsx",
sheet = "Hoja2", col_types = c("numeric",
"numeric", "numeric", "numeric",
"numeric", "numeric", "numeric"))
View(BD_MORAN_2)
head(BD_MORAN_2 , n=10)## # A tibble: 10 x 7
## z X_WGS84 Y_WGS84 CEa_075 CEa_150 X_MCB Y_MCE
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 201. -72.5 4.20 10.5 19.7 843507. 956121.
## 2 201. -72.5 4.20 10.5 19.5 843507. 956121.
## 3 201. -72.5 4.20 10.6 20.1 843508. 956122.
## 4 201. -72.5 4.20 10.5 19.9 843508. 956122.
## 5 201. -72.5 4.20 10.2 19.9 843508. 956122.
## 6 201. -72.5 4.20 10.2 19.9 843509. 956122.
## 7 201. -72.5 4.20 10.6 20.1 843509. 956123.
## 8 201. -72.5 4.20 10.4 19.6 843509. 956123.
## 9 201. -72.5 4.20 10.4 19.2 843510. 956123.
## 10 201. -72.5 4.20 10.5 19.7 843510. 956124.dim(BD_MORAN_2)## [1] 6000 7str(BD_MORAN_2)## tibble [6,000 x 7] (S3: tbl_df/tbl/data.frame)
## $ z : num [1:6000] 201 201 201 201 201 ...
## $ X_WGS84: num [1:6000] -72.5 -72.5 -72.5 -72.5 -72.5 ...
## $ Y_WGS84: num [1:6000] 4.2 4.2 4.2 4.2 4.2 ...
## $ CEa_075: num [1:6000] 10.5 10.5 10.6 10.5 10.2 ...
## $ CEa_150: num [1:6000] 19.7 19.5 20.1 19.9 19.9 ...
## $ X_MCB : num [1:6000] 843507 843507 843508 843508 843508 ...
## $ Y_MCE : num [1:6000] 956121 956121 956122 956122 956122 ...### Profundidad de 75 cm
plot(BD_MORAN_2$X_WGS84, BD_MORAN_2$Y_WGS84, cex=0.01*BD_MORAN_2$CEa_075, col="red", pch=19)
### Profundidad de 150 cm
plot(BD_MORAN_2$X_WGS84, BD_MORAN_2$Y_WGS84, cex=0.01*BD_MORAN_2$CEa_150, col="red", pch=19)
ce.dists2<-as.matrix(dist(cbind(BD_MORAN_2$X_WGS84, BD_MORAN_2$Y_WGS84)))
dim(ce.dists2)## [1] 6000 6000ce.dists.inv2 <-1/ce.dists2
ce.dists.inv2[is.infinite(ce.dists.inv2)] <- 0
diag(ce.dists.inv2)<-0
ce.dists.inv2[1:6, 1:6]## 1 2 3 4 5 6
## 1 0.00 310158.42 129663.3 91605.67 70889.74 54871.26
## 2 310158.42 0.00 222810.0 130001.76 91892.63 66665.19
## 3 129663.30 222810.01 0.0 312102.51 156393.25 95127.50
## 4 91605.67 130001.76 312102.5 0.00 313473.46 136833.86
## 5 70889.74 91892.63 156393.2 313473.46 0.00 242832.20
## 6 54871.26 66665.19 95127.5 136833.86 242832.20 0.00## Indice de Moran de conductividad electrica a 75 cm de profundidad
I.Moran2_75<-Moran.I(BD_MORAN_2$CEa_075, ce.dists.inv2); I.Moran2_75## $observed
## [1] 0.6147608
##
## $expected
## [1] -0.0001666944
##
## $sd
## [1] 0.001342329
##
## $p.value
## [1] 0## Indice de Moran de conductividad electrica a 150 cm de profundidad
I.Moran2_150<-Moran.I(BD_MORAN_2$CEa_150, ce.dists.inv2); I.Moran2_150## $observed
## [1] 0.3012973
##
## $expected
## [1] -0.0001666944
##
## $sd
## [1] 0.001342245
##
## $p.value
## [1] 0Datos de conductividad electrica, parte 3
BD_MORAN_3 <- read_excel("~/2020-2/Computacion estadistica/BD_MORAN - Copia.xlsx",
sheet = "Hoja3", col_types = c("numeric",
"numeric", "numeric", "numeric",
"numeric", "numeric", "numeric"))
View(BD_MORAN_3)
head(BD_MORAN_3 , n=10)## # A tibble: 10 x 7
## z X_WGS84 Y_WGS84 CEa_075 CEa_150 X_MCB Y_MCE
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 208. -72.5 4.20 11.2 18.0 843648. 956381.
## 2 208. -72.5 4.20 11.1 18.1 843648. 956382.
## 3 208. -72.5 4.20 11.1 18.0 843649. 956382.
## 4 208. -72.5 4.20 11.2 18.2 843649. 956382.
## 5 208. -72.5 4.20 11.3 18.2 843650. 956383.
## 6 208. -72.5 4.20 10.8 18.0 843650. 956383.
## 7 208. -72.5 4.20 11.1 18.4 843651. 956384.
## 8 208. -72.5 4.20 11.2 18.0 843651. 956384.
## 9 208. -72.5 4.20 11.6 18.3 843652. 956384.
## 10 208. -72.5 4.20 11.7 18.6 843652. 956385.dim(BD_MORAN_3)## [1] 6527 7str(BD_MORAN_3)## tibble [6,527 x 7] (S3: tbl_df/tbl/data.frame)
## $ z : num [1:6527] 208 208 208 208 208 ...
## $ X_WGS84: num [1:6527] -72.5 -72.5 -72.5 -72.5 -72.5 ...
## $ Y_WGS84: num [1:6527] 4.2 4.2 4.2 4.2 4.2 ...
## $ CEa_075: num [1:6527] 11.2 11.1 11.1 11.2 11.3 ...
## $ CEa_150: num [1:6527] 18 18.1 18 18.2 18.2 ...
## $ X_MCB : num [1:6527] 843648 843648 843649 843649 843650 ...
## $ Y_MCE : num [1:6527] 956381 956382 956382 956382 956383 ...### Profundidad de 75 cm
plot(BD_MORAN_3$X_WGS84, BD_MORAN_3$Y_WGS84, cex=0.01*BD_MORAN_3$CEa_075, col="red", pch=19)
### Profundidad de 150 cm
plot(BD_MORAN_3$X_WGS84, BD_MORAN_3$Y_WGS84, cex=0.01*BD_MORAN_3$CEa_150, col="red", pch=19)
ce.dists3<-as.matrix(dist(cbind(BD_MORAN_3$X_WGS84, BD_MORAN_3$Y_WGS84)))
dim(ce.dists3)## [1] 6527 6527ce.dists.inv3 <-1/ce.dists3
ce.dists.inv3[is.infinite(ce.dists.inv3)] <- 0
diag(ce.dists.inv3)<-0
ce.dists.inv3[1:6, 1:6]## 1 2 3 4 5 6
## 1 0.00 153846.15 81143.90 60735.31 42442.36 36671.26
## 2 153846.15 0.00 171709.56 100349.37 58608.55 48145.03
## 3 81143.90 171709.56 0.00 241412.12 88965.96 66895.51
## 4 60735.31 100349.37 241412.12 0.00 140885.18 92537.63
## 5 42442.36 58608.55 88965.96 140885.18 0.00 269655.43
## 6 36671.26 48145.03 66895.51 92537.63 269655.43 0.00## Indice de Moran de conductividad electrica a 75 cm de profundidad
I.Moran3_75<-Moran.I(BD_MORAN_3$CEa_075, ce.dists.inv3); I.Moran3_75## $observed
## [1] 0.4490286
##
## $expected
## [1] -0.0001532332
##
## $sd
## [1] 0.001302786
##
## $p.value
## [1] 0## Indice de Moran de conductividad electrica a 150 cm de profundidad
I.Moran3_150<-Moran.I(BD_MORAN_3$CEa_150, ce.dists.inv3); I.Moran3_150## $observed
## [1] 0.4800518
##
## $expected
## [1] -0.0001532332
##
## $sd
## [1] 0.00130293
##
## $p.value
## [1] 0library(dplyr)
bind_rows(I.Moran1_75, I.Moran2_75, I.Moran3_75, id=NULL)## # A tibble: 3 x 4
## observed expected sd p.value
## <dbl> <dbl> <dbl> <dbl>
## 1 0.514 -0.000167 0.00157 0
## 2 0.615 -0.000167 0.00134 0
## 3 0.449 -0.000153 0.00130 0bind_rows(I.Moran1_150, I.Moran2_150, I.Moran3_150, id=NULL)## # A tibble: 3 x 4
## observed expected sd p.value
## <dbl> <dbl> <dbl> <dbl>
## 1 0.331 -0.000167 0.00157 0
## 2 0.301 -0.000167 0.00134 0
## 3 0.480 -0.000153 0.00130 0De acuerdo al Indice de Moran se observa que en las tres partes del p-valor fue de 0.