SHAP power of determinants (SPD)

Function for calculate SHAP power of determinants \(SPD\).

Usage

spd_lesh(formula, data, cores = 1, ...)

Arguments

formula

A formula of calculate SHAP power of determinants \(SPD\).

data

A data.frame or tibble of observation data.

cores

(optional) A positive integer(default is 1). If cores > 1, a 'parallel' package cluster with that many cores is created and used. You can also supply a cluster object.

...

(optional) Other arguments passed to rpart_disc().

Value

A tibble with variable and its corresponding \(SPD\) value.

Details

The power of SHAP power of determinants formula is

\(\theta_{x_j} \left( S \right) = \sum\limits_{s \in M \setminus \{x_j\}} \frac{|S|! \left(|M| - |S| - 1\right)!}{|M|!}\left(v \left(S \cup \left\{x_j\right\} \right) - v\left(S\right)\right)\).

SHAP power of determinants (SPD) is the contribution of variable \(x_j\) to the power of determinants.

Note

The SHAP power of determinants (SPD) requires at least \(2^n-1\) calculations when has \(n\) explanatory variables. When there are more than 10 explanatory variables, carefully consider the computational burden of this model. When there are a large number of explanatory variables, the data dimensionality reduction method can be used to ensure the trade-off between analysis results and calculation speed.

References

Li, Y., Luo, P., Song, Y., Zhang, L., Qu, Y., & Hou, Z. (2023). A locally explained heterogeneity model for examining wetland disparity. International Journal of Digital Earth, 16(2), 4533–4552. https://doi.org/10.1080/17538947.2023.2271883

Author

Wenbo Lv lyu.geosocial@gmail.com

Examples

data('ndvi')
g = spd_lesh(NDVIchange ~ ., data = ndvi)
g
#> # A tibble: 6 × 2
#>   variable      spd_theta
#>   <chr>             <dbl>
#> 1 Precipitation    0.218 
#> 2 Climatezone      0.176 
#> 3 Tempchange       0.0482
#> 4 Popdensity       0.0262
#> 5 Mining           0.0158
#> 6 GDP              0.0115