Apêndice B — Probit espacial

B.1 Pacotes

library(ProbitSpatial)

Loading required package: Matrix

B.2 Shapefile

# Pacotes
library(sf)

Linking to GEOS 3.10.2, GDAL 3.4.1, PROJ 8.2.1; sf_use_s2() is TRUE

library(sp)

The legacy packages maptools, rgdal, and rgeos, underpinning the sp package,
which was just loaded, will retire in October 2023.
Please refer to R-spatial evolution reports for details, especially
https://r-spatial.org/r/2023/05/15/evolution4.html.
It may be desirable to make the sf package available;
package maintainers should consider adding sf to Suggests:.
The sp package is now running under evolution status 2
     (status 2 uses the sf package in place of rgdal)

# Abra o arquivo
natregimes_montana.shp <- st_read("data/natregimes_montana.gml")

Reading layer `natregimes_montana' from data source 
  `/home/raphael/projects/ecoespacial/data/natregimes_montana.gml' 
  using driver `GML'
Simple feature collection with 55 features and 74 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: -116.0625 ymin: 44.35373 xmax: -104.0426 ymax: 49
Geodetic CRS:  WGS 84

natregimes_montana.shp <- st_make_valid(natregimes_montana.shp)
natregimes_montana.shp <- as_Spatial(natregimes_montana.shp)

# Plotar o mapa
plot(natregimes_montana.shp)

B.3 Variável de resposta

Para estes tipos de modelo, precisamos ter ou criar uma variável dicotômica para ser a variável de resposta do modelo.

natregimes_montana.shp@data$HRM <- ifelse(
  natregimes_montana.shp@data$HR90 >= mean(natregimes_montana.shp@data$HR90), TRUE, FALSE
)

B.4 Matriz de vizinhança

library(spdep)

Loading required package: spData

To access larger datasets in this package, install the spDataLarge
package with: `install.packages('spDataLarge',
repos='https://nowosad.github.io/drat/', type='source')`

library(spatialreg)

Attaching package: 'spatialreg'

The following objects are masked from 'package:spdep':

    get.ClusterOption, get.coresOption, get.mcOption,
    get.VerboseOption, get.ZeroPolicyOption, set.ClusterOption,
    set.coresOption, set.mcOption, set.VerboseOption,
    set.ZeroPolicyOption

w1 <- nb2listw(poly2nb(natregimes_montana.shp, queen = TRUE))
w1 <- as(w1, "CsparseMatrix")

B.5 Especificação

esp <- HRM ~ RD90 + UE90

B.6 Modelo SAR

mod_sar <- ProbitSpatialFit(
  formula = esp, 
  data = natregimes_montana.shp@data,
  W = w1, 
  DGP = "SAR"
)

summary(mod_sar)

-- Univariate conditional estimation of spatial probit --

Sample size =  55 
Number of covariates =  3 
DGP =  SAR 
estimation method =  conditional 
Variance covariance =  Var-Covar Matrix 
order of approx. of iW in the conditional step =  6 
Execution time =  0.1199408 

-----------------------------------------------

Unconditional standard errors with likelihood-ratio test
              Estimate   LR test      Pr(>z)
(Intercept) -1.1675986 8.6786161 0.003219654
RD90         0.2980135 0.4508751 0.501919675
UE90         0.1561540 7.5361813 0.006047208
rho          0.2835792 1.1076506 0.292593222

-----------------------------------------------
Confusion Matrix:
       pred 1 pred 0
true 1      7      4
true 0     13     31
Accuracy:    0.6909091 
Sensitivity:     0.35    Specificity:    0.8857143 
Pos Pred Value:  0.6363636   Neg Pred Value: 0.7045455 

B.7 Modelo SEM

mod_sem <- ProbitSpatialFit(
  formula = esp, 
  data = natregimes_montana.shp@data,
  W = w1, 
  DGP = "SEM"
)

summary(mod_sem)

-- Univariate conditional estimation of spatial probit --

Sample size =  55 
Number of covariates =  3 
DGP =  SEM 
estimation method =  conditional 
Variance covariance =  Var-Covar Matrix 
order of approx. of iW in the conditional step =  6 
Execution time =  0.007918835 

-----------------------------------------------

Unconditional standard errors with likelihood-ratio test
              Estimate   LR test      Pr(>z)
(Intercept) -1.2501767 8.9098968 0.002836293
RD90         0.2621078 0.3732729 0.541225647
UE90         0.1531211 7.0668738 0.007852214
rho          0.2287299 0.3990766 0.527566502

-----------------------------------------------
Confusion Matrix:
       pred 1 pred 0
true 1      7      3
true 0     13     32
Accuracy:    0.7090909 
Sensitivity:     0.35    Specificity:    0.9142857 
Pos Pred Value:  0.7     Neg Pred Value: 0.7111111 

B.8 Modelo SARAR

mod_sarar <- ProbitSpatialFit(
  formula = esp, 
  data = natregimes_montana.shp@data,
  W = w1, M = w1,
  DGP = "SARAR"
)

summary(mod_sarar)

-- Univariate conditional estimation of spatial probit --

Sample size =  55 
Number of covariates =  3 
DGP =  SARAR 
estimation method =  conditional 
Variance covariance =  Var-Covar Matrix 
order of approx. of iW in the conditional step =  6 
Execution time =  0.04153228 

-----------------------------------------------

Unconditional standard errors with likelihood-ratio test
              Estimate   LR test      Pr(>z)
(Intercept) -1.1350511 8.5202224 0.003512216
RD90         0.2981930 0.4525526 0.501125232
UE90         0.1541322 7.5865738 0.005880460
rho          0.3417969 1.6667927 0.196688677
lambda      -0.1316406 0.7036277 0.401567420

-----------------------------------------------
Confusion Matrix:
       pred 1 pred 0
true 1      7      5
true 0     13     30
Accuracy:    0.6727273 
Sensitivity:     0.35    Specificity:    0.8571429 
Pos Pred Value:  0.5833333   Neg Pred Value: 0.6976744