Global Geary's C statistic

Calculate the global Geary's C statistic for model residuals. ww_global_geary_c() returns the statistic itself, while ww_global_geary_pvalue() returns the associated p value. These functions are meant to help assess model predictions, for instance by identifying if there are clusters of higher residuals than expected. For statistical testing and inference applications, use spdep::geary.test() instead.

Usage

ww_global_geary_c(data, ...)

ww_global_geary_c_vec(truth, estimate, wt, na_rm = FALSE, ...)

ww_global_geary_pvalue(data, ...)

ww_global_geary_pvalue_vec(truth, estimate, wt = NULL, na_rm = FALSE, ...)

Arguments

data

A data.frame containing the columns specified by the truth and estimate arguments.

...

Additional arguments passed to spdep::geary() (for ww_global_geary_c()) or spdep::geary.test() (for ww_global_geary_pvalue()).

truth

The column identifier for the true results (that is numeric). This should be an unquoted column name although this argument is passed by expression and supports quasiquotation (you can unquote column names). For _vec() functions, a numeric vector.

estimate

The column identifier for the predicted results (that is also numeric). As with truth this can be specified different ways but the primary method is to use an unquoted variable name. For _vec() functions, a numeric vector.

wt

A listw object, for instance as created with ww_build_weights(). For data.frame input, may also be a function that takes data and returns a listw object.

na_rm

A logical value indicating whether NA values should be stripped before the computation proceeds.

Value

A tibble with columns .metric, .estimator, and .estimate and 1 row of values. For grouped data frames, the number of rows returned will be the same as the number of groups. For _vec() functions, a single value (or NA).

Details

These functions can be used for geographic or projected coordinate reference systems and expect 2D data.

References

Geary, R. C. (1954). "The Contiguity Ratio and Statistical Mapping". The Incorporated Statistician. 5 (3): 115–145. doi:10.2307/2986645.

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 17.

See also

Other autocorrelation metrics: ww_global_moran_i(), ww_local_geary_c(), ww_local_getis_ord_g(), ww_local_moran_i()

Other yardstick metrics: ww_agreement_coefficient(), ww_global_moran_i(), ww_local_geary_c(), ww_local_getis_ord_g(), ww_local_moran_i(), ww_willmott_d()

Examples

guerry_model <- guerry
guerry_lm <- lm(Crm_prs ~ Litercy, guerry_model)
guerry_model$predictions <- predict(guerry_lm, guerry_model)

ww_global_geary_c(guerry_model, Crm_prs, predictions)
#> # A tibble: 1 × 3
#>   .metric        .estimator .estimate
#>   <chr>          <chr>          <dbl>
#> 1 global_geary_c standard       0.565
ww_global_geary_pvalue(guerry_model, Crm_prs, predictions)
#> # A tibble: 1 × 3
#>   .metric             .estimator .estimate
#>   <chr>               <chr>          <dbl>
#> 1 global_geary_pvalue standard    7.55e-10

wt <- ww_build_weights(guerry_model)

ww_global_geary_c_vec(
  guerry_model$Crm_prs,
  guerry_model$predictions,
  wt = wt
)
#> [1] 0.5654044
ww_global_geary_pvalue_vec(
  guerry_model$Crm_prs,
  guerry_model$predictions,
  wt = wt
)
#> [1] 7.548865e-10