# Spatial Association Detector(SPADE)

### Load data and package

    library(sf)
    library(tidyverse)
    library(gdverse)

    depression = system.file('extdata/Depression.csv',package = 'gdverse') %>%
      read_csv() %>%
      st_as_sf(coords = c('X','Y'), crs = 4326)
    depression
    ## Simple feature collection with 1072 features and 11 fields
    ## Geometry type: POINT
    ## Dimension:     XY
    ## Bounding box:  xmin: -83.1795 ymin: 32.11464 xmax: -78.6023 ymax: 35.17354
    ## Geodetic CRS:  WGS 84
    ## # A tibble: 1,072 × 12
    ##    Depression_prevelence PopulationDensity Population65 NoHealthInsurance Neighbor_Disadvantage
    ##  *                 <dbl>             <dbl>        <dbl>             <dbl>                 <dbl>
    ##  1                  23.1              61.5         22.5              7.98               -0.0525
    ##  2                  22.8              58.3         16.8             11.0                -0.254
    ##  3                  23.2              35.9         24.5              9.31               -0.0540
    ##  4                  21.8              76.1         21.8             13.2                 0.0731
    ##  5                  20.7              47.3         22.0             11                   0.763
    ##  6                  21.3              32.5         19.2             13.0                 0.422
    ##  7                  22                36.9         19.2             10.8                 0.113
    ##  8                  21.2              61.5         15.9              8.57               -0.154
    ##  9                  22.7              67.2         15.7             17.8                -0.320
    ## 10                  20.6             254.          11.3             12.7                 0.457
    ## # ℹ 1,062 more rows
    ## # ℹ 7 more variables: Beer <dbl>, MentalHealthPati <dbl>, NatureParks <dbl>, Casinos <dbl>,
    ## #   DrinkingPlaces <dbl>, X.HouseRent <dbl>, geometry <POINT [°]>

### Spatial Autocorrelation of Depression Prevelence

    set.seed(123456789)

    gmi = sdsfun::moran_test(depression)
    gmi
    ## ***                 global moran test

Variable | MoranI | EI | VarI | zI | pI
--- | --- | --- | --- | --- | ---
Depression_prevelence | 0.339557*** | -0.0009337 | 0.0003192 | 19.06 | 2.892e-81
PopulationDensity | 0.365364*** | -0.0009337 | 0.0003192 | 20.5 | 1.052e-93
Population65 | 0.180436*** | -0.0009337 | 0.0003192 | 10.15 | 1.641e-24
NoHealthInsurance | 0.0791199*** | -0.0009337 | 0.0003192 | 4.48 | 3.724e-06
Neighbor_Disadvantage | 0.113811*** | -0.0009337 | 0.0003192 | 6.422 | 6.723e-11
Beer | 0.0902263*** | -0.0009337 | 0.0003192 | 5.102 | 1.68e-07
MentalHealthPati | 0.19318*** | -0.0009337 | 0.0003192 | 10.86 | 8.534e-28
NatureParks | 0.0895589*** | -0.0009337 | 0.0003192 | 5.065 | 2.045e-07
Casinos | 0.243212*** | -0.0009337 | 0.0003192 | 13.66 | 8.28e-43
DrinkingPlaces | 0.239054*** | -0.0009337 | 0.0003192 | 13.43 | 1.97e-41
X.HouseRent | 0.141887*** | -0.0009337 | 0.0003192 | 7.993 | 6.562e-16

The global Moran’I Index of Depression Prevelence is `0.339557` and the P value is `2.892e-81`, which shows that Depression Prevelence has a moderate level of positive spatial autocorrelation in the global scale.

### OPGD modeling

    depression_opgd = opgd(Depression_prevelence ~ .,
                           data = depression, cores = 12)
    depression_opgd
    ## ***   Optimal Parameters-based Geographical Detector
    ##                 Factor Detector
    ##
    ## |       variable        | Q-statistic |   P-value    |
    ## |:---------------------:|:-----------:|:------------:|
    ## | Neighbor_Disadvantage | 0.13979930  | 4.960000e-10 |
    ## |   PopulationDensity   | 0.09186679  | 2.328052e-01 |
    ## |     Population65      | 0.08956911  | 1.000000e+00 |
    ## |   NoHealthInsurance   | 0.06779068  | 6.479536e-01 |
    ## |      NatureParks      | 0.05963161  | 1.000000e+00 |
    ## |    DrinkingPlaces     | 0.05411512  | 1.000000e+00 |
    ## |      X.HouseRent      | 0.03439383  | 1.000000e+00 |
    ## |         Beer          | 0.01410217  | 1.000000e+00 |
    ## |   MentalHealthPati    | 0.01295799  | 1.000000e+00 |
    ## |        Casinos        | 0.01207694  | 1.000000e+00 |

You can access the detailed q statistics by `depression_opgd$factor`

    depression_opgd$factor
    ## # A tibble: 10 × 3
    ##    variable              `Q-statistic` `P-value`
    ##    <chr>                         <dbl>     <dbl>
    ##  1 Neighbor_Disadvantage        0.140  4.96 e-10
    ##  2 PopulationDensity            0.0919 2.33 e- 1
    ##  3 Population65                 0.0896 1.000e+ 0
    ##  4 NoHealthInsurance            0.0678 6.48 e- 1
    ##  5 NatureParks                  0.0596 1.000e+ 0
    ##  6 DrinkingPlaces               0.0541 1.000e+ 0
    ##  7 X.HouseRent                  0.0344 1.000e+ 0
    ##  8 Beer                         0.0141 1    e+ 0
    ##  9 MentalHealthPati             0.0130 1.000e+ 0
    ## 10 Casinos                      0.0121 1    e+ 0

### Spatial Weight Matrix

SPADE explicitly considers the spatial variance by assigning the weight of the influence based on spatial distribution and also minimizes the influence of the number of levels on PD values by using the multilevel discretization and considering information loss due to discretization.

When response variable has a strong spatial dependence, maybe SPADE is a best choice.

The biggest difference between SPADE and native GD and OPGD in actual modeling is that SPADE requires a spatial weight matrix to calculate spatial variance.

I have also developed the sdsfun package to facilitate the construction of spatial weight matrices, which requires an input of an sf object.

In `spade` function, when you not provide a spatial weight matrix, it will use 1st order inverse distance weight by default, which can be created by `sdsfun::inverse_distance_swm()`.

    wt1 = sdsfun::inverse_distance_swm(depression)

You can also use gravity model weight by assigning the `power` parameter in `sdsfun::inverse_distance_swm()` function.

    wt2 = sdsfun::inverse_distance_swm(depression,power = 2)

Or using a spatial weight matrix based on geospatial contiguity.

    wt3 = sdsfun::spdep_contiguity_swm(depression, k = 8)

Or using a spatial weight matrix based on distance kernel functions.

    wt4 = sdsfun::spdep_distance_swm(depression, k = 6, kernel = 'gaussian')

The test of SPADE model significance in `gdverse` is achieved by randomization null hypothesis use a pseudo-p value, this calculation is very time-consuming. Default `gdverse` sets the `permutations` parameter to 0 and does not calculate the pseudo-p value. If you want to calculate the pseudo-p value, specify the `permutations` parameter to a number such as 99,999,9999, etc.

In the following section we will execute SPADE model using spatial weight matrix `wt1`.

### SPADE modeling

    depression_spade = spade(Depression_prevelence ~ .,
                             data = depression,
                             wt = wt1, cores = 12)
    depression_spade
    ## ***         Spatial Association Detector
    ##
    ## |       variable        | Q-statistic |      P-value      |
    ## |:---------------------:|:-----------:|:-----------------:|
    ## |   PopulationDensity   | 0.21532238  | No Pseudo-P Value |
    ## |    DrinkingPlaces     | 0.18564821  | No Pseudo-P Value |
    ## |        Casinos        | 0.17438646  | No Pseudo-P Value |
    ## | Neighbor_Disadvantage | 0.17235706  | No Pseudo-P Value |
    ## |      NatureParks      | 0.17019859  | No Pseudo-P Value |
    ## |     Population65      | 0.15592529  | No Pseudo-P Value |
    ## |         Beer          | 0.09506759  | No Pseudo-P Value |
    ## |   MentalHealthPati    | 0.07956353  | No Pseudo-P Value |
    ## |   NoHealthInsurance   | 0.07753293  | No Pseudo-P Value |
    ## |      X.HouseRent      | 0.05621546  | No Pseudo-P Value |
    plot(depression_spade, slicenum = 6)

You can also access the detailed q statistics by `depression_spade$factor`

    depression_spade$factor
    ## # A tibble: 10 × 3
    ##    variable              `Q-statistic` `P-value`
    ##    <chr>                         <dbl> <chr>
    ##  1 PopulationDensity            0.215  No Pseudo-P Value
    ##  2 DrinkingPlaces               0.186  No Pseudo-P Value
    ##  3 Casinos                      0.174  No Pseudo-P Value
    ##  4 Neighbor_Disadvantage        0.172  No Pseudo-P Value
    ##  5 NatureParks                  0.170  No Pseudo-P Value
    ##  6 Population65                 0.156  No Pseudo-P Value
    ##  7 Beer                         0.0951 No Pseudo-P Value
    ##  8 MentalHealthPati             0.0796 No Pseudo-P Value
    ##  9 NoHealthInsurance            0.0775 No Pseudo-P Value
    ## 10 X.HouseRent                  0.0562 No Pseudo-P Value