--- title: "Spatial Heterogeneity Explanation(GOZH & LESH)" output: rmarkdown::html_vignette vignette: > %\VignetteIndexEntry{shegd} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- The [**GOZH**(geographically optimal zones-based heterogeneity) model](https://doi.org/10.1016/j.isprsjprs.2022.01.009) generates the optimal spatial zone based on the binary classification of the decision tree and then calculates the power of determinants. The [**LESH**(locally explained stratified heterogeneity model)](https://doi.org/10.1080/17538947.2023.2271883) based on GOZH model and combined with additive shapely theory to reasonably allocate variable interaction's power of determinants. In this vignette, we use `ndvi` data in `gdverse` package to demonstrate the *spatial heterogeneity explanation* based on **GOZH** and **LESH** model. ### Load data and package ``` r library(tidyverse) library(gdverse) data("ndvi") head(ndvi) ## # A tibble: 6 × 7 ## NDVIchange Climatezone Mining Tempchange Precipitation GDP Popdensity ## ## 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 ``` ### Univariate power of determinants detection ``` r gozh.uvi = gozh(NDVIchange ~ ., data = ndvi) gozh.uvi ## *** Geographically Optimal Zones-based Heterogeneity Model ## Factor Detector ## ## | variable | Q-statistic | P-value | ## |:-------------:|:-----------:|:--------:| ## | Precipitation | 0.87255056 | 4.52e-10 | ## | Climatezone | 0.82129550 | 2.50e-10 | ## | Tempchange | 0.33324945 | 1.12e-10 | ## | Popdensity | 0.22321863 | 3.00e-10 | ## | Mining | 0.13982859 | 6.00e-11 | ## | GDP | 0.09170153 | 3.96e-10 | plot(gozh.uvi) ``` ![](../man/figures/shegd/gozh_uni-1.png) ### Variable interaction detection ``` r gozh.bi = gozh(NDVIchange ~ ., data = ndvi, type = 'interaction') gozh.bi ## *** Geographically Optimal Zones-based Heterogeneity Model ## Interaction Detector ## ## | Interactive variable | Interaction | ## |:---------------------------:|:------------------:| ## | Climatezone ∩ Mining | Weaken, uni- | ## | Climatezone ∩ Tempchange | Weaken, uni- | ## | Climatezone ∩ Precipitation | Enhance, bi- | ## | Climatezone ∩ GDP | Enhance, bi- | ## | Climatezone ∩ Popdensity | Enhance, bi- | ## | Mining ∩ Tempchange | Enhance, bi- | ## | Mining ∩ Precipitation | Weaken, uni- | ## | Mining ∩ GDP | Enhance, bi- | ## | Mining ∩ Popdensity | Enhance, bi- | ## | Tempchange ∩ Precipitation | Enhance, bi- | ## | Tempchange ∩ GDP | Enhance, nonlinear | ## | Tempchange ∩ Popdensity | Enhance, bi- | ## | Precipitation ∩ GDP | Enhance, bi- | ## | Precipitation ∩ Popdensity | Enhance, bi- | ## | GDP ∩ Popdensity | Weaken, uni- | plot(gozh.bi) ``` ![](../man/figures/shegd/gozh_bi-1.png) ### Variable interaction contribution ``` r lesh.m = lesh(NDVIchange ~ ., data = ndvi, cores = 6) lesh.m ## *** Locally Explained Stratified Heterogeneity Model ## ## | Interactive variable | Interaction | Variable1 SPD | Variable2 SPD | ## |:---------------------------:|:------------------:|:-------------:|:-------------:| ## | Climatezone ∩ Mining | Weaken, uni- | 0.75353265 | 0.06776285 | ## | Climatezone ∩ Tempchange | Weaken, uni- | 0.64437728 | 0.17691822 | ## | Climatezone ∩ Precipitation | Enhance, bi- | 0.39405554 | 0.48986045 | ## | Climatezone ∩ GDP | Enhance, bi- | 0.79843017 | 0.05246998 | ## | Climatezone ∩ Popdensity | Enhance, bi- | 0.74240657 | 0.11069841 | ## | Mining ∩ Tempchange | Enhance, bi- | 0.10161351 | 0.31023743 | ## | Mining ∩ Precipitation | Weaken, uni- | 0.05886173 | 0.81368883 | ## | Mining ∩ GDP | Enhance, bi- | 0.12735177 | 0.09306564 | ## | Mining ∩ Popdensity | Enhance, bi- | 0.13123771 | 0.21760488 | ## | Tempchange ∩ Precipitation | Enhance, bi- | 0.16187198 | 0.73291613 | ## | Tempchange ∩ GDP | Enhance, nonlinear | 0.35277116 | 0.08443737 | ## | Tempchange ∩ Popdensity | Enhance, bi- | 0.28786726 | 0.15633619 | ## | Precipitation ∩ GDP | Enhance, bi- | 0.84089496 | 0.04445297 | ## | Precipitation ∩ Popdensity | Enhance, bi- | 0.79267181 | 0.09507756 | ## | GDP ∩ Popdensity | Weaken, uni- | 0.06828443 | 0.15493420 | plot(lesh.m, pie = TRUE, scatter = TRUE) ``` ![](../man/figures/shegd/lesh-1.png) Compared to **GOZH Interaction Detector**, **LESH** only has a decomposition of the interactive contribution of variables, and the rest remains consistent. gdverse supports modifications to the default ploting results, such as adding subfigure annotations and adjusting the size of the text on the x-y axis: ``` r plot(lesh.m, pie = TRUE, scatter = TRUE, pielegend_x = 0.98, pielegend_y = 0.15) + patchwork::plot_annotation(tag_levels = 'a', tag_prefix = '(', tag_suffix = ')', tag_sep = '', theme = theme(plot.tag = element_text(family = "serif"))) & ggplot2::theme(axis.text.y = element_text(family = 'serif',size = 15), axis.text.x = element_text(family = 'serif',size = 15, angle = 30,vjust = 0.85,hjust = 0.75), axis.title = element_text(family = 'serif',size = 15)) ``` ![](../man/figures/shegd/lesh_own-1.png) And you can only look at the contribution part of the variable interaction: ``` r plot(lesh.m, pie = TRUE, scatter = FALSE) ``` ![](../man/figures/shegd/lesh_only-1.png) By accessing the concrete result through `lesh.m$interaction`, which returns a `tibble`. ``` r lesh.m$interaction ## # A tibble: 15 × 8 ## variable1 variable2 Interaction Variable1 Q-statisti…¹ Variable2 Q-statisti…² ## ## 1 Climatezone Mining Weaken, un… 0.821 0.140 ## 2 Climatezone Tempchan… Weaken, un… 0.821 0.333 ## 3 Climatezone Precipit… Enhance, b… 0.821 0.873 ## 4 Climatezone GDP Enhance, b… 0.821 0.0917 ## 5 Climatezone Popdensi… Enhance, b… 0.821 0.223 ## 6 Mining Tempchan… Enhance, b… 0.140 0.333 ## 7 Mining Precipit… Weaken, un… 0.140 0.873 ## 8 Mining GDP Enhance, b… 0.140 0.0917 ## 9 Mining Popdensi… Enhance, b… 0.140 0.223 ## 10 Tempchange Precipit… Enhance, b… 0.333 0.873 ## 11 Tempchange GDP Enhance, n… 0.333 0.0917 ## 12 Tempchange Popdensi… Enhance, b… 0.333 0.223 ## 13 Precipitati… GDP Enhance, b… 0.873 0.0917 ## 14 Precipitati… Popdensi… Enhance, b… 0.873 0.223 ## 15 GDP Popdensi… Weaken, un… 0.0917 0.223 ## # ℹ abbreviated names: ¹​`Variable1 Q-statistics`, ²​`Variable2 Q-statistics` ## # ℹ 3 more variables: `Variable1 and Variable2 interact Q-statistics` , ## # `Variable1 SPD` , `Variable2 SPD` ``` Use `lesh.m$spd_lesh` to access the SHAP power of determinants: ``` r lesh.m$spd_lesh ## # A tibble: 6 × 2 ## variable spd_theta ## ## 1 Precipitation 0.218 ## 2 Climatezone 0.176 ## 3 Tempchange 0.0482 ## 4 Popdensity 0.0262 ## 5 Mining 0.0158 ## 6 GDP 0.0115 ```