---
title: "A correlation indicator based on spatial patterns"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{cisp}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---



## Install and load R packages

```r
install.packages("cisp", dep = TRUE)
```

```r
library(cisp)
```

## Spatial pattern correlation

Using the same data as [the gdverse idsa vignette](https://stscl.github.io/gdverse/articles/idsa.html):


``` r
depression = system.file('extdata/Depression.csv',package = 'gdverse') |>
  readr::read_csv() |>
  sf::st_as_sf(coords = c('X','Y'), crs = 4326)
## Rows: 1072 Columns: 13
## ── Column specification ───────────────────────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (13): X, Y, Depression_prevelence, PopulationDensity, Population65, NoHealthInsurance, Neig...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
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 [°]>
```


``` r
system.time({
  g = cisp::spc(depression,cores = 12)
})
##    user  system elapsed 
##    5.54    1.00 2024.50
g
## ***   Spatial Pattern Correlation    
## 
## |          xv           |          yv           | correlation |
## |:---------------------:|:---------------------:|:-----------:|
## |   PopulationDensity   | Depression_prevelence |   0.04614   |
## |     Population65      | Depression_prevelence |   0.04150   |
## | Neighbor_Disadvantage | Depression_prevelence |   0.03924   |
## |    DrinkingPlaces     | Depression_prevelence |   0.01485   |
## |   NoHealthInsurance   | Depression_prevelence |   0.01384   |
## |      NatureParks      | Depression_prevelence |   0.01239   |
## |   MentalHealthPati    | Depression_prevelence |   0.01042   |
## |      X.HouseRent      | Depression_prevelence |   0.00777   |
## |         Beer          | Depression_prevelence |   0.00191   |
## |        Casinos        | Depression_prevelence |  -0.00708   |
## |      X.HouseRent      |   PopulationDensity   |   0.07832   |
## |   MentalHealthPati    |   PopulationDensity   |   0.01587   |
## |    DrinkingPlaces     |   PopulationDensity   |   0.01484   |
## |     Population65      |   PopulationDensity   |   0.01037   |
## |   NoHealthInsurance   |   PopulationDensity   |   0.00619   |
## |      NatureParks      |   PopulationDensity   |   0.00528   |
## |         Beer          |   PopulationDensity   |   0.00115   |
## |        Casinos        |   PopulationDensity   |   0.00108   |
## | Neighbor_Disadvantage |   PopulationDensity   |  -0.00529   |
## | Depression_prevelence |   PopulationDensity   |  -0.07737   |
## |      X.HouseRent      |     Population65      |   0.08942   |
## | Neighbor_Disadvantage |     Population65      |   0.04196   |
## |   PopulationDensity   |     Population65      |   0.02396   |
## | Depression_prevelence |     Population65      |   0.02231   |
## |   MentalHealthPati    |     Population65      |   0.00562   |
## |    DrinkingPlaces     |     Population65      |   0.00349   |
## |   NoHealthInsurance   |     Population65      |   0.00346   |
## |         Beer          |     Population65      |  -0.00529   |
## |      NatureParks      |     Population65      |  -0.00766   |
## |        Casinos        |     Population65      |  -0.00976   |
## | Neighbor_Disadvantage |   NoHealthInsurance   |   0.11050   |
## |      X.HouseRent      |   NoHealthInsurance   |   0.06270   |
## |     Population65      |   NoHealthInsurance   |   0.02928   |
## |   PopulationDensity   |   NoHealthInsurance   |   0.02298   |
## |    DrinkingPlaces     |   NoHealthInsurance   |   0.01302   |
## |        Casinos        |   NoHealthInsurance   |   0.00775   |
## |   MentalHealthPati    |   NoHealthInsurance   |   0.00657   |
## |         Beer          |   NoHealthInsurance   |   0.00434   |
## |      NatureParks      |   NoHealthInsurance   |   0.00197   |
## | Depression_prevelence |   NoHealthInsurance   |  -0.00779   |
## |    DrinkingPlaces     | Neighbor_Disadvantage |   0.09369   |
## |   NoHealthInsurance   | Neighbor_Disadvantage |   0.06840   |
## |      X.HouseRent      | Neighbor_Disadvantage |   0.06004   |
## |      NatureParks      | Neighbor_Disadvantage |   0.01924   |
## |     Population65      | Neighbor_Disadvantage |   0.01867   |
## |   MentalHealthPati    | Neighbor_Disadvantage |   0.01157   |
## |        Casinos        | Neighbor_Disadvantage |   0.00541   |
## |   PopulationDensity   | Neighbor_Disadvantage |  -0.00357   |
## | Depression_prevelence | Neighbor_Disadvantage |  -0.00665   |
## |         Beer          | Neighbor_Disadvantage |  -0.00989   |
## |        Casinos        |         Beer          |   0.04989   |
## |     Population65      |         Beer          |   0.01780   |
## |    DrinkingPlaces     |         Beer          |   0.01469   |
## |      NatureParks      |         Beer          |   0.01295   |
## | Neighbor_Disadvantage |         Beer          |   0.00331   |
## |   PopulationDensity   |         Beer          |   0.00211   |
## |   MentalHealthPati    |         Beer          |   0.00161   |
## |      X.HouseRent      |         Beer          |  -0.00016   |
## |   NoHealthInsurance   |         Beer          |  -0.00306   |
## | Depression_prevelence |         Beer          |  -0.03499   |
## |    DrinkingPlaces     |   MentalHealthPati    |   0.07590   |
## |   PopulationDensity   |   MentalHealthPati    |   0.03785   |
## |      NatureParks      |   MentalHealthPati    |   0.03208   |
## | Neighbor_Disadvantage |   MentalHealthPati    |   0.02471   |
## |        Casinos        |   MentalHealthPati    |   0.02460   |
## |         Beer          |   MentalHealthPati    |   0.01057   |
## |     Population65      |   MentalHealthPati    |   0.00982   |
## |      X.HouseRent      |   MentalHealthPati    |   0.00799   |
## | Depression_prevelence |   MentalHealthPati    |  -0.01049   |
## |   NoHealthInsurance   |   MentalHealthPati    |  -0.01681   |
## |    DrinkingPlaces     |      NatureParks      |   0.07349   |
## |   MentalHealthPati    |      NatureParks      |   0.03486   |
## |      X.HouseRent      |      NatureParks      |   0.02807   |
## | Neighbor_Disadvantage |      NatureParks      |   0.02704   |
## |   PopulationDensity   |      NatureParks      |   0.01846   |
## |   NoHealthInsurance   |      NatureParks      |   0.01689   |
## |         Beer          |      NatureParks      |   0.01029   |
## |        Casinos        |      NatureParks      |   0.00842   |
## |     Population65      |      NatureParks      |  -0.01961   |
## | Depression_prevelence |      NatureParks      |  -0.06237   |
## |    DrinkingPlaces     |        Casinos        |   0.05319   |
## |     Population65      |        Casinos        |   0.03494   |
## |         Beer          |        Casinos        |   0.02488   |
## |      NatureParks      |        Casinos        |   0.01989   |
## |   MentalHealthPati    |        Casinos        |   0.01854   |
## | Neighbor_Disadvantage |        Casinos        |   0.00293   |
## |   NoHealthInsurance   |        Casinos        |   0.00009   |
## |   PopulationDensity   |        Casinos        |  -0.00207   |
## |      X.HouseRent      |        Casinos        |  -0.00864   |
## | Depression_prevelence |        Casinos        |  -0.01344   |
## |      NatureParks      |    DrinkingPlaces     |   0.10000   |
## |   MentalHealthPati    |    DrinkingPlaces     |   0.04482   |
## |   PopulationDensity   |    DrinkingPlaces     |   0.03366   |
## |        Casinos        |    DrinkingPlaces     |   0.02222   |
## |         Beer          |    DrinkingPlaces     |   0.01330   |
## |   NoHealthInsurance   |    DrinkingPlaces     |   0.00258   |
## |      X.HouseRent      |    DrinkingPlaces     |   0.00185   |
## | Neighbor_Disadvantage |    DrinkingPlaces     |  -0.00400   |
## | Depression_prevelence |    DrinkingPlaces     |  -0.01162   |
## |     Population65      |    DrinkingPlaces     |  -0.03072   |
## |   PopulationDensity   |      X.HouseRent      |   0.12494   |
## | Neighbor_Disadvantage |      X.HouseRent      |   0.08995   |
## |     Population65      |      X.HouseRent      |   0.04227   |
## |   NoHealthInsurance   |      X.HouseRent      |   0.01481   |
## |    DrinkingPlaces     |      X.HouseRent      |   0.00667   |
## |   MentalHealthPati    |      X.HouseRent      |  -0.00175   |
## |        Casinos        |      X.HouseRent      |  -0.00581   |
## | Depression_prevelence |      X.HouseRent      |  -0.00587   |
## |         Beer          |      X.HouseRent      |  -0.00692   |
## |      NatureParks      |      X.HouseRent      |  -0.01047   |
```

The results are visualized in a default network graph style:


``` r
plot(g)
```

![**Figure 1**. Spatial Pattern Correlation Network Visualization Results](../man/figures/cisp/plot_g1-1.png)

But the results can also be plotted using the classic correlation coefficient matrix visualization style:


``` r
plot(g,style = "matrix")
```

![**Figure 2**. Spatial Pattern Correlation Matrix Visualization Results](../man/figures/cisp/plot_g2-1.png)
