Indice de Moran

knitr::opts_chunk$set(echo = TRUE)

NDICE DE MORAN

1. Ejerciccio de materia organica.

El indice de Moran (IM) es una de las medidas utilizadas para analizar la autocorrelación espacial, realizando una representación de la covarianza global. En el IM se tienen en cuenta los valores de las unidades de análisis determinadas a partir del criterio de vecindad (el valor de la unidad central no se considera para el cálculo), (R. Tobler’s et alt. 2019).

set.seed(12345)
MO <- rnorm(150, 3, 0.5)
xy <- expand.grid(x = seq(1, 10), y = seq(1, 15))
plot(xy, col = MO, pch = 15, cex = 2, 
     main = 'Distribución espacial de la materia orgánica')

Convertir los datos en una matriz

MO.dists <- as.matrix(dist(cbind(xy$x, xy$y))) 

MO.dists.inv <- 1/MO.dists 
diag(MO.dists.inv) <- 0 
MO.dists[1:5, 1:5] 

  1 2 3 4 5
1 0 1 2 3 4
2 1 0 1 2 3
3 2 1 0 1 2
4 3 2 1 0 1
5 4 3 2 1 0

xymatrix <- as.matrix(dist(cbind(xy$x, xy$y)))
xymatrix_inv <- 1/xymatrix
diag(xymatrix_inv) <- 0
xymatrix_inv[1:10, 1:10]

           1         2         3         4         5         6         7
1  0.0000000 1.0000000 0.5000000 0.3333333 0.2500000 0.2000000 0.1666667
2  1.0000000 0.0000000 1.0000000 0.5000000 0.3333333 0.2500000 0.2000000
3  0.5000000 1.0000000 0.0000000 1.0000000 0.5000000 0.3333333 0.2500000
4  0.3333333 0.5000000 1.0000000 0.0000000 1.0000000 0.5000000 0.3333333
5  0.2500000 0.3333333 0.5000000 1.0000000 0.0000000 1.0000000 0.5000000
6  0.2000000 0.2500000 0.3333333 0.5000000 1.0000000 0.0000000 1.0000000
7  0.1666667 0.2000000 0.2500000 0.3333333 0.5000000 1.0000000 0.0000000
8  0.1428571 0.1666667 0.2000000 0.2500000 0.3333333 0.5000000 1.0000000
9  0.1250000 0.1428571 0.1666667 0.2000000 0.2500000 0.3333333 0.5000000
10 0.1111111 0.1250000 0.1428571 0.1666667 0.2000000 0.2500000 0.3333333
           8         9        10
1  0.1428571 0.1250000 0.1111111
2  0.1666667 0.1428571 0.1250000
3  0.2000000 0.1666667 0.1428571
4  0.2500000 0.2000000 0.1666667
5  0.3333333 0.2500000 0.2000000
6  0.5000000 0.3333333 0.2500000
7  1.0000000 0.5000000 0.3333333
8  0.0000000 1.0000000 0.5000000
9  1.0000000 0.0000000 1.0000000
10 0.5000000 1.0000000 0.0000000

Moran.I(MO, xymatrix_inv)

$observed
[1] -0.009650003

$expected
[1] -0.006711409

$sd
[1] 0.007694112

$p.value
[1] 0.7025151

library("ape")

Moran.I(MO, MO.dists.inv)

$observed
[1] -0.009650003

$expected
[1] -0.006711409

$sd
[1] 0.007694112

$p.value
[1] 0.7025151

El p.value > 0.05, podemos decir que no existe una autocorrelación positiva entre los contenidos de materia organica (MO) del suelo.

2. Índice de Moran para datos de conductividad eléctrica aparente del suelo (CEa)

library(readxl)
BD_MORAN <- read_excel("d:/Users/Janus/Documents/Computacion estadistica/BD_MORAN.xlsx")

head(BD_MORAN, n=20)

Mapa de Conductividad Electrica Aparente (Totalidad de los puntos muestreados)

Mapa CEa a 75 cm

Mapa CEa a 150 cm

Longitud <- BD_MORAN$X_WGS84
Latitud <- BD_MORAN$Y_WGS84  
plot(Longitud,Latitud,col ="blue",cex = 0.2,main = "Puntos de muestra de Conductivica electrica aparente (CEa)")

plot(Longitud,Latitud,col=0.3*BD_MORAN$CEa_075, main = "Conductividad Electrica Aparente a 75 cm",cex.main=0.8,cex.lab=0.8,cex.axis=0.8)

plot(Longitud,Latitud,col=0.3*BD_MORAN$CEa_150, main = "Conductividad Electrica Aparente a 150 cm",cex.main=0.8,cex.lab=0.8,cex.axis=0.8)

Índice de Moran - CE a 75cm [primeras 5000 muestras]

Longitud <- BD_MORAN$X_WGS84[1:5000]
Latitud <- BD_MORAN$Y_WGS84[1:5000]
Ce_dist <- as.matrix(dist(cbind(Longitud, Latitud)))
dim(Ce_dist)

[1] 5000 5000

Ce_dist_inv <- 1/Ce_dist
Ce_dist_inv[is.infinite(Ce_dist_inv)] <- 0
diag(Ce_dist_inv) <- 0
CEa_075_1 <- BD_MORAN$CEa_075[1:5000]
Ce_dist_inv[1:10,1:10]

           1         2         3         4         5         6         7
1       0.00 406473.84 183582.68 136552.66  99512.00  80767.51  66276.45
2  406473.84      0.00 334028.09 205286.88 131603.44 100690.59  79119.77
3  183582.68 334028.09      0.00 532631.20 217163.07 144140.71 103677.22
4  136552.66 205286.88 532631.20      0.00 366652.29 197620.35 128735.53
5   99512.00 131603.44 217163.07 366652.29      0.00 428663.73 198393.56
6   80767.51 100690.59 144140.71 197620.35 428663.73      0.00 369323.16
7   66276.45  79119.77 103677.22 128735.53 198393.56 369323.16      0.00
8   57404.68  66798.00  83495.12  99016.99 135648.88 198443.56 428837.13
9   49363.96  56156.93  67505.83  77303.00  97952.59 126960.00 193437.71
10  44785.68  50307.49  59227.30  66636.81  81434.82 100529.27 138109.95
           8         9        10
1   57404.68  49363.96  44785.68
2   66798.00  56156.93  50307.49
3   83495.12  67505.83  59227.30
4   99016.99  77303.00  66636.81
5  135648.88  97952.59  81434.82
6  198443.56 126960.00 100529.27
7  428837.13 193437.71 138109.95
8       0.00 352381.47 203715.00
9  352381.47      0.00 482860.83
10 203715.00 482860.83      0.00

Moran.I(CEa_075_1,Ce_dist_inv)

$observed
[1] 0.5843435

$expected
[1] -0.00020004

$sd
[1] 0.001784892

$p.value
[1] 0

Índice de Moran - CE a 75cm [de la muestra 5001 a la 10000]

Longitud <- BD_MORAN$X_WGS84[5001:10000]
Latitud <- BD_MORAN$Y_WGS84[5001:10000]
Ce_dist <- as.matrix(dist(cbind(Longitud, Latitud)))
dim(Ce_dist)

[1] 5000 5000

Ce_dist_inv <- 1/Ce_dist
Ce_dist_inv[is.infinite(Ce_dist_inv)] <- 0
diag(Ce_dist_inv) <- 0
CEa_075_1 <- BD_MORAN$CEa_075[5001:10000]
Ce_dist_inv[1:10,1:10]

           1         2         3         4         5         6         7
1       0.00 211114.28 105557.14  67146.52  50907.07  38565.37  32827.27
2  211114.28      0.00 211114.28  98463.65  67083.19  47184.82  38871.55
3  105557.14 211114.28      0.00 184526.97  98327.51  60766.16  47643.88
4   67146.52  98463.65 184526.97      0.00 210489.47  90601.53  64226.45
5   50907.07  67083.19  98327.51 210489.47      0.00 159066.16  92427.56
6   38565.37  47184.82  60766.16  90601.53 159066.16      0.00 220624.26
7   32827.27  38871.55  47643.88  64226.45  92427.56 220624.26      0.00
8   27536.92  31667.42  37255.68  46679.98  59981.23  96290.96 170864.05
9   24166.24  27290.06  31341.34  37753.41  46004.28  64723.18  91593.34
10  21364.07  23769.39  26785.02  31332.98  36812.50  47897.33  61179.29
           8         9        10
1   27536.92  24166.24  21364.07
2   31667.42  27290.06  23769.39
3   37255.68  31341.34  26785.02
4   46679.98  37753.41  31332.98
5   59981.23  46004.28  36812.50
6   96290.96  64723.18  47897.33
7  170864.05  91593.34  61179.29
8       0.00 197424.61  95303.43
9  197424.61      0.00 184244.25
10  95303.43 184244.25      0.00

Moran.I(CEa_075_1,Ce_dist_inv)

$observed
[1] 0.6230116

$expected
[1] -0.00020004

$sd
[1] 0.001710357

$p.value
[1] 0

Índice de Moran - CE a 75cm [de la muestra 10001 a la 18526]

Longitud <- BD_MORAN$X_WGS84[10001:18526]
Latitud <- BD_MORAN$Y_WGS84[10001:18526]
Ce_dist <- as.matrix(dist(cbind(Longitud, Latitud)))
dim(Ce_dist)

[1] 8526 8526

Ce_dist_inv <- 1/Ce_dist
Ce_dist_inv[is.infinite(Ce_dist_inv)] <- 0
diag(Ce_dist_inv) <- 0
CEa_075_1 <- BD_MORAN$CEa_075[10001:18526]
Ce_dist_inv[1:10,1:10]

          1         2         3         4         5         6         7
1      0.00  96784.06  60123.33  49109.46  38403.86  32791.83  27656.57
2  96784.06      0.00 158725.16  99696.88  63666.71  49595.41  38721.36
3  60123.33 158725.16      0.00 268081.10 106308.11  72134.49  51215.40
4  49109.46  99696.88 268081.10      0.00 176167.77  98689.57  63310.51
5  38403.86  63666.71 106308.11 176167.77      0.00 224397.51  98826.34
6  32791.83  49595.41  72134.49  98689.57 224397.51      0.00 176604.04
7  27656.57  38721.36  51215.40  63310.51  98826.34 176604.04      0.00
8  24230.57  32322.75  40588.04  47829.52  65654.77  92809.07 195601.85
9  21273.47  27266.74  32922.26  37531.37  47691.77  60563.48  92172.36
10 17129.70  20813.31  23954.27  26304.66  30921.66  35863.50  45001.75
           8         9       10
1   24230.57  21273.47 17129.70
2   32322.75  27266.74 20813.31
3   40588.04  32922.26 23954.27
4   47829.52  37531.37 26304.66
5   65654.77  47691.77 30921.66
6   92809.07  60563.48 35863.50
7  195601.85  92172.36 45001.75
8       0.00 174312.08 58448.07
9  174312.08      0.00 87930.51
10  58448.07  87930.51     0.00

Moran.I(CEa_075_1,Ce_dist_inv)

$observed
[1] 0.4493558

$expected
[1] -0.0001173021

$sd
[1] 0.001024234

$p.value
[1] 0

Índice de Moran - CE a 150cm [primeras 5000 muestras]

Longitud <- BD_MORAN$X_WGS84[1:5000]
Latitud <- BD_MORAN$Y_WGS84[1:5000]
Ce_dist <- as.matrix(dist(cbind(Longitud, Latitud)))
dim(Ce_dist)

[1] 5000 5000

Ce_dist_inv <- 1/Ce_dist
Ce_dist_inv[is.infinite(Ce_dist_inv)] <- 0
diag(Ce_dist_inv) <- 0
CEa_150_1 <- BD_MORAN$CEa_150[1:5000]
Ce_dist_inv[1:10,1:10]

           1         2         3         4         5         6         7
1       0.00 406473.84 183582.68 136552.66  99512.00  80767.51  66276.45
2  406473.84      0.00 334028.09 205286.88 131603.44 100690.59  79119.77
3  183582.68 334028.09      0.00 532631.20 217163.07 144140.71 103677.22
4  136552.66 205286.88 532631.20      0.00 366652.29 197620.35 128735.53
5   99512.00 131603.44 217163.07 366652.29      0.00 428663.73 198393.56
6   80767.51 100690.59 144140.71 197620.35 428663.73      0.00 369323.16
7   66276.45  79119.77 103677.22 128735.53 198393.56 369323.16      0.00
8   57404.68  66798.00  83495.12  99016.99 135648.88 198443.56 428837.13
9   49363.96  56156.93  67505.83  77303.00  97952.59 126960.00 193437.71
10  44785.68  50307.49  59227.30  66636.81  81434.82 100529.27 138109.95
           8         9        10
1   57404.68  49363.96  44785.68
2   66798.00  56156.93  50307.49
3   83495.12  67505.83  59227.30
4   99016.99  77303.00  66636.81
5  135648.88  97952.59  81434.82
6  198443.56 126960.00 100529.27
7  428837.13 193437.71 138109.95
8       0.00 352381.47 203715.00
9  352381.47      0.00 482860.83
10 203715.00 482860.83      0.00

Moran.I(CEa_150_1,Ce_dist_inv)

$observed
[1] 0.3531011

$expected
[1] -0.00020004

$sd
[1] 0.001784437

$p.value
[1] 0

Índice de Moran - CE a 150cm [de la muestra 5001 a la 10000]

Longitud <- BD_MORAN$X_WGS84[5001:10000]
Latitud <- BD_MORAN$Y_WGS84[5001:10000]
Ce_dist <- as.matrix(dist(cbind(Longitud, Latitud)))
dim(Ce_dist)

[1] 5000 5000

Ce_dist_inv <- 1/Ce_dist
Ce_dist_inv[is.infinite(Ce_dist_inv)] <- 0
diag(Ce_dist_inv) <- 0
CEa_150_1 <- BD_MORAN$CEa_150[5001:10000]
Ce_dist_inv[1:10,1:10]

           1         2         3         4         5         6         7
1       0.00 211114.28 105557.14  67146.52  50907.07  38565.37  32827.27
2  211114.28      0.00 211114.28  98463.65  67083.19  47184.82  38871.55
3  105557.14 211114.28      0.00 184526.97  98327.51  60766.16  47643.88
4   67146.52  98463.65 184526.97      0.00 210489.47  90601.53  64226.45
5   50907.07  67083.19  98327.51 210489.47      0.00 159066.16  92427.56
6   38565.37  47184.82  60766.16  90601.53 159066.16      0.00 220624.26
7   32827.27  38871.55  47643.88  64226.45  92427.56 220624.26      0.00
8   27536.92  31667.42  37255.68  46679.98  59981.23  96290.96 170864.05
9   24166.24  27290.06  31341.34  37753.41  46004.28  64723.18  91593.34
10  21364.07  23769.39  26785.02  31332.98  36812.50  47897.33  61179.29
           8         9        10
1   27536.92  24166.24  21364.07
2   31667.42  27290.06  23769.39
3   37255.68  31341.34  26785.02
4   46679.98  37753.41  31332.98
5   59981.23  46004.28  36812.50
6   96290.96  64723.18  47897.33
7  170864.05  91593.34  61179.29
8       0.00 197424.61  95303.43
9  197424.61      0.00 184244.25
10  95303.43 184244.25      0.00

Moran.I(CEa_150_1,Ce_dist_inv)

$observed
[1] 0.3476675

$expected
[1] -0.00020004

$sd
[1] 0.001710253

$p.value
[1] 0

Índice de Moran - CE a 150cm [de la muestra 10001 a la 18526]

Longitud <- BD_MORAN$X_WGS84[10001:18526]
Latitud <- BD_MORAN$Y_WGS84[10001:18526]
Ce_dist <- as.matrix(dist(cbind(Longitud, Latitud)))
dim(Ce_dist)

[1] 8526 8526

Ce_dist_inv <- 1/Ce_dist
Ce_dist_inv[is.infinite(Ce_dist_inv)] <- 0
diag(Ce_dist_inv) <- 0
CEa_150_1 <- BD_MORAN$CEa_150[10001:18526]
Ce_dist_inv[1:10,1:10]

          1         2         3         4         5         6         7
1      0.00  96784.06  60123.33  49109.46  38403.86  32791.83  27656.57
2  96784.06      0.00 158725.16  99696.88  63666.71  49595.41  38721.36
3  60123.33 158725.16      0.00 268081.10 106308.11  72134.49  51215.40
4  49109.46  99696.88 268081.10      0.00 176167.77  98689.57  63310.51
5  38403.86  63666.71 106308.11 176167.77      0.00 224397.51  98826.34
6  32791.83  49595.41  72134.49  98689.57 224397.51      0.00 176604.04
7  27656.57  38721.36  51215.40  63310.51  98826.34 176604.04      0.00
8  24230.57  32322.75  40588.04  47829.52  65654.77  92809.07 195601.85
9  21273.47  27266.74  32922.26  37531.37  47691.77  60563.48  92172.36
10 17129.70  20813.31  23954.27  26304.66  30921.66  35863.50  45001.75
           8         9       10
1   24230.57  21273.47 17129.70
2   32322.75  27266.74 20813.31
3   40588.04  32922.26 23954.27
4   47829.52  37531.37 26304.66
5   65654.77  47691.77 30921.66
6   92809.07  60563.48 35863.50
7  195601.85  92172.36 45001.75
8       0.00 174312.08 58448.07
9  174312.08      0.00 87930.51
10  58448.07  87930.51     0.00

Moran.I(CEa_150_1,Ce_dist_inv)

$observed
[1] 0.4248239

$expected
[1] -0.0001173021

$sd
[1] 0.001024294

$p.value
[1] 0