Optimal Parameters-based Geographical Detector(OPGD)"
In gdverse: Analysis of Spatial Stratified Heterogeneity

Load data and package

library(gdverse)

data("ndvi")
head(ndvi)
## # A tibble: 6 × 7
##   NDVIchange Climatezone Mining Tempchange Precipitation   GDP Popdensity
##        <dbl> <chr>       <fct>       <dbl>         <dbl> <dbl>      <dbl>
## 1    0.116   Bwk         low         0.256          237. 12.6      1.45  
## 2    0.0178  Bwk         low         0.273          214.  2.69     0.801 
## 3    0.138   Bsk         low         0.302          449. 20.1     11.5   
## 4    0.00439 Bwk         low         0.383          213.  0        0.0462
## 5    0.00316 Bwk         low         0.357          205.  0        0.0748
## 6    0.00838 Bwk         low         0.338          201.  0        0.549

Determine optimal discretization parameters

Climatezone and Mining is the discrete category variables in the ndvi data, we need to discretize others. We can use gd_optunidisc() to discretize them based on geodetector q-statistic.

tictoc::tic()
g = gd_optunidisc(NDVIchange ~ .,
                  data = dplyr::select(ndvi,-c(Climatezone,Mining)),
                  discnum = 3:15, cores = 6)
tictoc::toc()
## 2.08 sec elapsed

g
## $x
## [1] "GDP"           "Popdensity"    "Precipitation" "Tempchange"   
## 
## $k
## [1] 15 15 14 14
## 
## $method
## [1] "quantile" "quantile" "natural"  "equal"   
## 
## $qstatistic
## [1] 0.1096213 0.2100134 0.8809405 0.3478433
## 
## $disc
## # A tibble: 713 × 4
##      GDP Popdensity Precipitation Tempchange
##    <int>      <int>         <int>      <int>
##  1     8          6             5          3
##  2     6          4             4          3
##  3     8         11            10          3
##  4     1          1             4          4
##  5     1          2             4          3
##  6     1          4             4          3
##  7     8          6             4          3
##  8     9          9             5          3
##  9    12         12             7          3
## 10     9         10             8          3
## # ℹ 703 more rows
new.ndvi = g$disc
new.ndvi
## # A tibble: 713 × 4
##      GDP Popdensity Precipitation Tempchange
##    <int>      <int>         <int>      <int>
##  1     8          6             5          3
##  2     6          4             4          3
##  3     8         11            10          3
##  4     1          1             4          4
##  5     1          2             4          3
##  6     1          4             4          3
##  7     8          6             4          3
##  8     9          9             5          3
##  9    12         12             7          3
## 10     9         10             8          3
## # ℹ 703 more rows

The new.ndvi is the discreted result of the optimal discretization parameter based on the Q statistic of the geographical detector (factor detector), we can combine it with other columns in ndvi tibble now.

new.ndvi = dplyr::bind_cols(dplyr::select(ndvi,NDVIchange,Climatezone,Mining),new.ndvi)
new.ndvi
## # A tibble: 713 × 7
##    NDVIchange Climatezone Mining   GDP Popdensity Precipitation Tempchange
##         <dbl> <chr>       <fct>  <int>      <int>         <int>      <int>
##  1    0.116   Bwk         low        8          6             5          3
##  2    0.0178  Bwk         low        6          4             4          3
##  3    0.138   Bsk         low        8         11            10          3
##  4    0.00439 Bwk         low        1          1             4          4
##  5    0.00316 Bwk         low        1          2             4          3
##  6    0.00838 Bwk         low        1          4             4          3
##  7    0.0335  Bwk         low        8          6             4          3
##  8    0.0387  Bwk         low        9          9             5          3
##  9    0.0882  Bsk         low       12         12             7          3
## 10    0.0690  Bsk         low        9         10             8          3
## # ℹ 703 more rows

Run geodetector

Then, we can run geodetector model by gd() function.

gd(NDVIchange ~ .,data = new.ndvi,type = 'factor')
##                 Factor Detector            
## 
## |   variable    | Q-statistic | P-value  |
## |:-------------:|:-----------:|:--------:|
## | Precipitation |  0.8809405  | 9.18e-10 |
## |  Climatezone  |  0.8218335  | 7.34e-10 |
## |  Tempchange   |  0.3478433  | 2.41e-10 |
## |  Popdensity   |  0.2100134  | 1.61e-10 |
## |    Mining     |  0.1411154  | 6.73e-10 |
## |      GDP      |  0.1096213  | 4.18e-10 |
gd(NDVIchange ~ .,data = new.ndvi,type = 'interaction')
##                 Interaction Detector         
## 
## |    Interactive variable     |    Interaction     |
## |:---------------------------:|:------------------:|
## |    Climatezone ∩ Mining     |    Enhance, bi-    |
## |      Climatezone ∩ GDP      |    Enhance, bi-    |
## |  Climatezone ∩ Popdensity   |    Enhance, bi-    |
## | Climatezone ∩ Precipitation |    Enhance, bi-    |
## |  Climatezone ∩ Tempchange   |    Enhance, bi-    |
## |        Mining ∩ GDP         | Enhance, nonlinear |
## |     Mining ∩ Popdensity     | Enhance, nonlinear |
## |   Mining ∩ Precipitation    |    Enhance, bi-    |
## |     Mining ∩ Tempchange     |    Enhance, bi-    |
## |      GDP ∩ Popdensity       |    Enhance, bi-    |
## |     GDP ∩ Precipitation     |    Enhance, bi-    |
## |      GDP ∩ Tempchange       | Enhance, nonlinear |
## | Popdensity ∩ Precipitation  |    Enhance, bi-    |
## |   Popdensity ∩ Tempchange   |    Enhance, bi-    |
## | Precipitation ∩ Tempchange  |    Enhance, bi-    |

You can also use `opgd()` in one time to get result above.

ndvi_opgd = opgd(NDVIchange ~ ., data = ndvi, discnum = 3:15,
                 discvar = names(dplyr::select(ndvi,-c(NDVIchange,Climatezone,Mining))),
                 cores = 6, type = c('factor','interaction'))
ndvi_opgd
## ***   Optimal Parameters-based Geographical Detector     
##                 Factor Detector            
## 
## |   variable    | Q-statistic | P-value  |
## |:-------------:|:-----------:|:--------:|
## | Precipitation |  0.8809405  | 9.18e-10 |
## |  Climatezone  |  0.8218335  | 7.34e-10 |
## |  Tempchange   |  0.3478433  | 2.41e-10 |
## |  Popdensity   |  0.2100134  | 1.61e-10 |
## |    Mining     |  0.1411154  | 6.73e-10 |
## |      GDP      |  0.1096213  | 4.18e-10 |
## 
##                 Interaction Detector         
## 
## |    Interactive variable     |    Interaction     |
## |:---------------------------:|:------------------:|
## |    Climatezone ∩ Mining     |    Enhance, bi-    |
## |      Climatezone ∩ GDP      |    Enhance, bi-    |
## |  Climatezone ∩ Popdensity   |    Enhance, bi-    |
## | Climatezone ∩ Precipitation |    Enhance, bi-    |
## |  Climatezone ∩ Tempchange   |    Enhance, bi-    |
## |        Mining ∩ GDP         | Enhance, nonlinear |
## |     Mining ∩ Popdensity     | Enhance, nonlinear |
## |   Mining ∩ Precipitation    |    Enhance, bi-    |
## |     Mining ∩ Tempchange     |    Enhance, bi-    |
## |      GDP ∩ Popdensity       |    Enhance, bi-    |
## |     GDP ∩ Precipitation     |    Enhance, bi-    |
## |      GDP ∩ Tempchange       | Enhance, nonlinear |
## | Popdensity ∩ Precipitation  |    Enhance, bi-    |
## |   Popdensity ∩ Tempchange   |    Enhance, bi-    |
## | Precipitation ∩ Tempchange  |    Enhance, bi-    |

You can use plot() to visualize the result.

plot(ndvi_opgd)

Use $opt_param to get the optimal discretization parameter in OPGD model:

ndvi_opgd$opt_param
## # A tibble: 4 × 3
##   varibale      discnum method  
##   <chr>           <int> <chr>   
## 1 GDP                15 quantile
## 2 Popdensity         15 quantile
## 3 Precipitation      14 natural 
## 4 Tempchange         14 equal