Title:  Ergonomic Methods for Assessing Spatial Models 

Description:  Assessing predictive models of spatial data can be challenging, both because these models are typically built for extrapolating outside the original region represented by training data and due to potential spatially structured errors, with "hot spots" of higher than expected error clustered geographically due to spatial structure in the underlying data. Methods are provided for assessing models fit to spatial data, including approaches for measuring the spatial structure of model errors, assessing model predictions at multiple spatial scales, and evaluating where predictions can be made safely. Methods are particularly useful for models fit using the 'tidymodels' framework. Methods include Moran's I ('Moran' (1950) <doi:10.2307/2332142>), Geary's C ('Geary' (1954) <doi:10.2307/2986645>), GetisOrd's G ('Ord' and 'Getis' (1995) <doi:10.1111/j.15384632.1995.tb00912.x>), agreement coefficients from 'Ji' and Gallo (2006) (<doi: 10.14358/PERS.72.7.823>), agreement metrics from 'Willmott' (1981) (<doi: 10.1080/02723646.1981.10642213>) and 'Willmott' 'et' 'al'. (2012) (<doi: 10.1002/joc.2419>), an implementation of the area of applicability methodology from 'Meyer' and 'Pebesma' (2021) (<doi:10.1111/2041210X.13650>), and an implementation of multiscale assessment as described in 'Riemann' 'et' 'al'. (2010) (<doi:10.1016/j.rse.2010.05.010>). 
Authors:  Michael Mahoney [aut, cre] , Lucas Johnson [ctb] , Virgilio GómezRubio [rev] (Virgilio reviewed the package (v. 0.2.0.9000) for rOpenSci, see <https://github.com/ropensci/softwarereview/issues/571>), Jakub Nowosad [rev] (Jakub reviewed the package (v. 0.2.0.9000) for rOpenSci, see <https://github.com/ropensci/softwarereview/issues/571>), Posit Software, PBC [cph, fnd] 
Maintainer:  Michael Mahoney <[email protected]> 
License:  MIT + file LICENSE 
Version:  0.6.0.9000 
Built:  20241007 05:50:35 UTC 
Source:  https://github.com/ropensci/waywiser 
This data and description are taken from the geodaData R package. Classic social science foundational study by AndreMichel Guerry on crime, suicide, literacy and other “moral statistics” in 1830s France. Data from the R package Guerry (Michael Friendly and Stephane Dray).
guerry
guerry
An sf data frame with 85 rows, 23 variables, and a geometry column:
Department ID: Standard numbers for the departments
Region of France ('N'='North', 'S'='South', 'E'='East', 'W'='West', 'C'='Central'). Corsica is coded as NA.
Department name: Departments are named according to usage in 1830, but without accents. A factor with levels Ain Aisne Allier ... Vosges Yonne
Population per Crime against persons.
Population per Crime against property.
Percent of military conscripts who can read and write.
Donations to the poor.
Population per illegitimate birth.
Population per suicide.
Size of principal city ('1:Sm', '2:Med', '3:Lg'), used as a surrogate for population density. Large refers to the top 10, small to the bottom 10; all the rest are classed Medium.
Per capita tax on personal property. A ranked index based on taxes on personal and movable property per inhabitant.
Commerce and Industry, measured by the rank of the number of patents / population.
Distribution of clergy, measured by the rank of the number of Catholic priests in active service population.
Crimes against parents, measured by the rank of the ratio of crimes against parents to all crimes – Average for the years 18251830.
Infanticides per capita. A ranked ratio of number of infanticides to population – Average for the years 18251830.
Donations to the clergy. A ranked ratio of the number of bequests and donations inter vivios to population – Average for the years 18151824.
Per capita wager on Royal Lottery. Ranked ratio of the proceeds bet on the royal lottery to population — Average for the years 18221826.
Military desertion, ratio of number of young soldiers accused of desertion to the force of the military contingent, minus the deficit produced by the insufficiency of available billets – Average of the years 18251827.
Instruction. Ranks recorded from Guerry's map of Instruction. Note: this is inversely related to Literacy
Number of prostitutes registered in Paris from 1816 to 1834, classified by the department of their birth
Distance to Paris (km). Distance of each department centroid to the centroid of the Seine (Paris)
Area (1000 km^2).
Population in 1831, in 1000s
Sf object, units in m. EPSG 27572: NTF (Paris) / Lambert zone II.
Angeville, A. (1836). Essai sur la Statistique de la Population française Paris: F. Doufour.
Guerry, A.M. (1833). Essai sur la statistique morale de la France Paris: Crochard. English translation: Hugh P. Whitt and Victor W. Reinking, Lewiston, N.Y. : Edwin Mellen Press, 2002.
ParentDuchatelet, A. (1836). De la prostitution dans la ville de Paris, 3rd ed, 1857, p. 32, 36
https://geodacenter.github.io/dataandlab/Guerry/
if (requireNamespace("sf", quietly = TRUE)) { library(sf) data(guerry) plot(guerry["Donatns"]) }
if (requireNamespace("sf", quietly = TRUE)) { library(sf) data(guerry) plot(guerry["Donatns"]) }
The original data is derived from the Forest Inventory and Analysis program, implemented by the US Department of Agriculture's Forest Service.
ny_trees
ny_trees
An sf object using EPSG 5070: NAD83 / Conus Albers (in meters), with 5,303 rows and 5 columns:
The year measurements were taken.
A unique identifier signifying the plot measurements were taken at.
The number of trees present on a plot.
The total aboveground biomass at the plot location, in pounds.
The centroid of the plot location.
ww_area_of_applicability
Predict from a ww_area_of_applicability
## S3 method for class 'ww_area_of_applicability' predict(object, new_data, ...)
## S3 method for class 'ww_area_of_applicability' predict(object, new_data, ...)
object 
A 
new_data 
A data frame or matrix of new samples. 
... 
Not used. 
The function computes the distance indices of the new data and whether or not they are "inside" the area of applicability.
A tibble of predictions, with two columns: di
, numeric, contains the
"dissimilarity index" of each point in new_data
, while aoa
, logical,
contains whether a row is inside (TRUE
) or outside (FALSE
) the area of
applicability.
Note that this function is often called using
terra::predict()
, in which case aoa
will be converted to numeric
implicitly; 1
values correspond to cells "inside" the area of applicability
and 0
corresponds to cells "outside" the AOA.
The number of rows in the tibble is guaranteed
to be the same as the number of rows in new_data
. Rows with NA
predictor
values will have NA
di
and aoa
values.
Other area of applicability functions:
ww_area_of_applicability()
library(vip) train < gen_friedman(1000, seed = 101) # ?vip::gen_friedman test < train[701:1000, ] train < train[1:700, ] pp < stats::ppr(y ~ ., data = train, nterms = 11) metric_name < ifelse( packageVersion("vip") > package_version("0.3.2"), "rsq", "rsquared" ) importance < vip::vi_permute( pp, target = "y", metric = metric_name, pred_wrapper = predict, train = train ) aoa < ww_area_of_applicability(y ~ ., train, test, importance = importance) predict(aoa, test)
library(vip) train < gen_friedman(1000, seed = 101) # ?vip::gen_friedman test < train[701:1000, ] train < train[1:700, ] pp < stats::ppr(y ~ ., data = train, nterms = 11) metric_name < ifelse( packageVersion("vip") > package_version("0.3.2"), "rsq", "rsquared" ) importance < vip::vi_permute( pp, target = "y", metric = metric_name, pred_wrapper = predict, train = train ) aoa < ww_area_of_applicability(y ~ ., train, test, importance = importance) predict(aoa, test)
This data is adapted from the CAST vignette
vignette("cast02AOAtutorial", package = "CAST")
.
The original data is derived from the Worldclim global climate variables.
worldclim_simulation
worldclim_simulation
An sf object with 10,000 rows and 6 columns:
Mean Diurnal Range (Mean of monthly (max temp  min temp))
Mean Temperature of Warmest Quarter
Precipitation of Wettest Month
Precipitation of Coldest Quarter
The location of the sampled point.
A virtual species distribution, generated using the generateSpFromPCA()
function from the virtualspecies
package.
These functions calculate the agreement coefficient and mean product difference (MPD), as well as their systematic and unsystematic components, from Ji and Gallo (2006). Agreement coefficients provides a useful measurement of agreement between two data sets which is bounded, symmetrical, and can be decomposed into systematic and unsystematic components; however, it assumes a linear relationship between the two data sets and treats both "truth" and "estimate" as being of equal quality, and as such may not be a useful metric in all scenarios.
ww_agreement_coefficient(data, ...) ## S3 method for class 'data.frame' ww_agreement_coefficient(data, truth, estimate, na_rm = TRUE, ...) ww_agreement_coefficient_vec(truth, estimate, na_rm = TRUE, ...) ww_systematic_agreement_coefficient(data, ...) ## S3 method for class 'data.frame' ww_systematic_agreement_coefficient(data, truth, estimate, na_rm = TRUE, ...) ww_systematic_agreement_coefficient_vec(truth, estimate, na_rm = TRUE, ...) ww_unsystematic_agreement_coefficient(data, ...) ## S3 method for class 'data.frame' ww_unsystematic_agreement_coefficient(data, truth, estimate, na_rm = TRUE, ...) ww_unsystematic_agreement_coefficient_vec(truth, estimate, na_rm = TRUE, ...) ww_unsystematic_mpd(data, ...) ## S3 method for class 'data.frame' ww_unsystematic_mpd(data, truth, estimate, na_rm = TRUE, ...) ww_unsystematic_mpd_vec(truth, estimate, na_rm = TRUE, ...) ww_systematic_mpd(data, ...) ## S3 method for class 'data.frame' ww_systematic_mpd(data, truth, estimate, na_rm = TRUE, ...) ww_systematic_mpd_vec(truth, estimate, na_rm = TRUE, ...) ww_unsystematic_rmpd(data, ...) ## S3 method for class 'data.frame' ww_unsystematic_rmpd(data, truth, estimate, na_rm = TRUE, ...) ww_unsystematic_rmpd_vec(truth, estimate, na_rm = TRUE, ...) ww_systematic_rmpd(data, ...) ## S3 method for class 'data.frame' ww_systematic_rmpd(data, truth, estimate, na_rm = TRUE, ...) ww_systematic_rmpd_vec(truth, estimate, na_rm = TRUE, ...)
ww_agreement_coefficient(data, ...) ## S3 method for class 'data.frame' ww_agreement_coefficient(data, truth, estimate, na_rm = TRUE, ...) ww_agreement_coefficient_vec(truth, estimate, na_rm = TRUE, ...) ww_systematic_agreement_coefficient(data, ...) ## S3 method for class 'data.frame' ww_systematic_agreement_coefficient(data, truth, estimate, na_rm = TRUE, ...) ww_systematic_agreement_coefficient_vec(truth, estimate, na_rm = TRUE, ...) ww_unsystematic_agreement_coefficient(data, ...) ## S3 method for class 'data.frame' ww_unsystematic_agreement_coefficient(data, truth, estimate, na_rm = TRUE, ...) ww_unsystematic_agreement_coefficient_vec(truth, estimate, na_rm = TRUE, ...) ww_unsystematic_mpd(data, ...) ## S3 method for class 'data.frame' ww_unsystematic_mpd(data, truth, estimate, na_rm = TRUE, ...) ww_unsystematic_mpd_vec(truth, estimate, na_rm = TRUE, ...) ww_systematic_mpd(data, ...) ## S3 method for class 'data.frame' ww_systematic_mpd(data, truth, estimate, na_rm = TRUE, ...) ww_systematic_mpd_vec(truth, estimate, na_rm = TRUE, ...) ww_unsystematic_rmpd(data, ...) ## S3 method for class 'data.frame' ww_unsystematic_rmpd(data, truth, estimate, na_rm = TRUE, ...) ww_unsystematic_rmpd_vec(truth, estimate, na_rm = TRUE, ...) ww_systematic_rmpd(data, ...) ## S3 method for class 'data.frame' ww_systematic_rmpd(data, truth, estimate, na_rm = TRUE, ...) ww_systematic_rmpd_vec(truth, estimate, na_rm = TRUE, ...)
data 
A 
... 
Not currently used. 
truth 
The column identifier for the true results
(that is 
estimate 
The column identifier for the predicted
results (that is also 
na_rm 
A 
Agreement coefficient values range from 0 to 1, with 1 indicating perfect
agreement. truth
and estimate
must be the same length. This function is
not explicitly spatial and as such can be applied to data with any number of
dimensions and any coordinate reference system.
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).
Ji, L. and Gallo, K. 2006. "An Agreement Coefficient for Image Comparison." Photogrammetric Engineering & Remote Sensing 72(7), pp 823–833, doi: 10.14358/PERS.72.7.823.
Other agreement metrics:
ww_willmott_d()
Other yardstick metrics:
ww_global_geary_c()
,
ww_global_moran_i()
,
ww_local_geary_c()
,
ww_local_getis_ord_g()
,
ww_local_moran_i()
,
ww_willmott_d()
# Calculated values match Ji and Gallo 2006: x < c(6, 8, 9, 10, 11, 14) y < c(2, 3, 5, 5, 6, 8) ww_agreement_coefficient_vec(x, y) ww_systematic_agreement_coefficient_vec(x, y) ww_unsystematic_agreement_coefficient_vec(x, y) ww_systematic_mpd_vec(x, y) ww_unsystematic_mpd_vec(x, y) ww_systematic_rmpd_vec(x, y) ww_unsystematic_rmpd_vec(x, y) example_df < data.frame(x = x, y = y) ww_agreement_coefficient(example_df, x, y) ww_systematic_agreement_coefficient(example_df, x, y) ww_unsystematic_agreement_coefficient(example_df, x, y) ww_systematic_mpd(example_df, x, y) ww_unsystematic_mpd(example_df, x, y) ww_systematic_rmpd(example_df, x, y) ww_unsystematic_rmpd(example_df, x, y)
# Calculated values match Ji and Gallo 2006: x < c(6, 8, 9, 10, 11, 14) y < c(2, 3, 5, 5, 6, 8) ww_agreement_coefficient_vec(x, y) ww_systematic_agreement_coefficient_vec(x, y) ww_unsystematic_agreement_coefficient_vec(x, y) ww_systematic_mpd_vec(x, y) ww_unsystematic_mpd_vec(x, y) ww_systematic_rmpd_vec(x, y) ww_unsystematic_rmpd_vec(x, y) example_df < data.frame(x = x, y = y) ww_agreement_coefficient(example_df, x, y) ww_systematic_agreement_coefficient(example_df, x, y) ww_unsystematic_agreement_coefficient(example_df, x, y) ww_systematic_mpd(example_df, x, y) ww_unsystematic_mpd(example_df, x, y) ww_systematic_rmpd(example_df, x, y) ww_unsystematic_rmpd(example_df, x, y)
This function calculates the "area of applicability" of a model, as introduced by Meyer and Pebesma (2021). While the initial paper introducing this method focused on spatial models, there is nothing inherently spatial about the method; it can be used with any type of data (and, because it does not care about the spatial arrangement of your data, can be used with 2D or 3D spatial data, and with geographic or projected CRS).
ww_area_of_applicability(x, ...) ## S3 method for class 'data.frame' ww_area_of_applicability(x, testing = NULL, importance, ..., na_rm = FALSE) ## S3 method for class 'matrix' ww_area_of_applicability(x, testing = NULL, importance, ..., na_rm = FALSE) ## S3 method for class 'formula' ww_area_of_applicability( x, data, testing = NULL, importance, ..., na_rm = FALSE ) ## S3 method for class 'recipe' ww_area_of_applicability( x, data, testing = NULL, importance, ..., na_rm = FALSE ) ## S3 method for class 'rset' ww_area_of_applicability(x, y = NULL, importance, ..., na_rm = FALSE)
ww_area_of_applicability(x, ...) ## S3 method for class 'data.frame' ww_area_of_applicability(x, testing = NULL, importance, ..., na_rm = FALSE) ## S3 method for class 'matrix' ww_area_of_applicability(x, testing = NULL, importance, ..., na_rm = FALSE) ## S3 method for class 'formula' ww_area_of_applicability( x, data, testing = NULL, importance, ..., na_rm = FALSE ) ## S3 method for class 'recipe' ww_area_of_applicability( x, data, testing = NULL, importance, ..., na_rm = FALSE ) ## S3 method for class 'rset' ww_area_of_applicability(x, y = NULL, importance, ..., na_rm = FALSE)
x 
Either a data frame, matrix, formula
(specifying predictor terms on the righthand side), recipe
(from If 
... 
Not currently used. 
testing 
A data frame or matrix containing the data used to validate your model. This should be the same data as used to calculate all model accuracy metrics. If this argument is 
importance 
Either:
All variables in the training data ( 
na_rm 
A logical of length 1, indicating whether observations (in both
training and testing) with 
data 
The data frame representing your "training" data, when using the formula or recipe methods. 
y 
Optional: a recipe (from If 
Predictions made on points "inside" the area of applicability should be as
accurate as predictions made on the data provided to testing
.
That means that generally testing
should be your final holdout
set so that predictions on points inside the area of applicability are
accurately described by your reported model metrics.
When passing an rset
object to x
, predictions made on points "inside" the
area of applicability instead should be as accurate as predictions made on
the assessment sets during crossvalidation.
This method assumes your model was fit using dummy variables in the place of any nonnumeric predictor, and that you have one importance score per dummy variable. Having nonnumeric predictors will cause this function to fail.
A ww_area_of_applicability
object, which can be used with predict()
to
calculate the distance of new data to the original training data, and
determine if new data is within a model's area of applicability.
This implementation differs from
Meyer and Pebesma (2021) (and therefore from CAST) when using crossvalidated
data in order to minimize data leakage. Namely, in order to calculate
the dissimilarity index $DI_{k}$
, CAST:
Rescales all data used for cross validation at once, lumping assessment folds in with analysis data.
Calculates a single $\bar{d}$
as the mean distance between all points
in the rescaled data set, including between points in the same assessment
fold.
For each point $k$
that's used in an assessment fold, calculates
$d_{k}$
as the minimum distance between $k$
and any point in its
corresponding analysis fold.
Calculates $DI_{k}$
by dividing $d_{k}$
by $\bar{d}$
(which
was partially calculated as the distance between $k$
and the rest of
the rescaled data).
Because assessment data is used to calculate constants for rescaling analysis
data and $\bar{d}$
, the assessment data may appear too "similar" to
the analysis data when calculating $DI_{k}$
. As such, waywiser treats
each fold in an rset
independently:
Each analysis set is rescaled independently.
Separate $\bar{d}$
are calculated for each fold, as the mean distance
between all points in the analysis set for that fold.
Identically to CAST, $d_{k}$
is the minimum distance between a point
$k$
in the assessment fold and any point in the
corresponding analysis fold.
$DI_{k}$
is then found by dividing $d_{k}$
by $\bar{d}$
,
which was calculated independently from $k$
.
Predictions are made using the full training data set, rescaled once (in
the same way as CAST), and the mean $\bar{d}$
across folds, under the
assumption that the "final" model in use will be retrained using the entire
data set.
In practice, this means waywiser produces very slightly higher $\bar{d}$
values than CAST and a slightly higher area of applicability threshold than
CAST when using rset
objects.
H. Meyer and E. Pebesma. 2021. "Predicting into unknown space? Estimating the area of applicability of spatial prediction models," Methods in Ecology and Evolution 12(9), pp 1620  1633, doi: 10.1111/2041210X.13650.
Other area of applicability functions:
predict.ww_area_of_applicability()
train < vip::gen_friedman(1000, seed = 101) # ?vip::gen_friedman test < train[701:1000, ] train < train[1:700, ] pp < stats::ppr(y ~ ., data = train, nterms = 11) metric_name < ifelse( packageVersion("vip") > package_version("0.3.2"), "rsq", "rsquared" ) importance < vip::vi_permute( pp, target = "y", metric = metric_name, pred_wrapper = predict, train = train ) aoa < ww_area_of_applicability(y ~ ., train, test, importance = importance) predict(aoa, test) # Equivalent methods for calculating AOA: ww_area_of_applicability(train[2:11], test[2:11], importance) ww_area_of_applicability( as.matrix(train[2:11]), as.matrix(test[2:11]), importance )
train < vip::gen_friedman(1000, seed = 101) # ?vip::gen_friedman test < train[701:1000, ] train < train[1:700, ] pp < stats::ppr(y ~ ., data = train, nterms = 11) metric_name < ifelse( packageVersion("vip") > package_version("0.3.2"), "rsq", "rsquared" ) importance < vip::vi_permute( pp, target = "y", metric = metric_name, pred_wrapper = predict, train = train ) aoa < ww_area_of_applicability(y ~ ., train, test, importance = importance) predict(aoa, test) # Equivalent methods for calculating AOA: ww_area_of_applicability(train[2:11], test[2:11], importance) ww_area_of_applicability( as.matrix(train[2:11]), as.matrix(test[2:11]), importance )
These functions can be used for geographic or projected coordinate reference systems and expect 2D data.
ww_build_neighbors(data, nb = NULL, ..., call = rlang::caller_env())
ww_build_neighbors(data, nb = NULL, ..., call = rlang::caller_env())
data 
An sf object (of class "sf" or "sfc"). 
nb 
An object of class "nb" (in which case it will be returned
unchanged), or a function to create an object of class "nb" from 
... 
Arguments passed to the neighborcreating function. 
call 
The execution environment of a currently running
function, e.g. You only need to supply Can also be For more information about error calls, see Including function calls in error messages. 
When nb = NULL
, the method used to create neighbors from data
is
dependent on what geometry type data
is:
If nb = NULL
and data
is a point geometry
(classes "sfc_POINT" or "sfc_MULTIPOINT") the "nb" object will be created
using ww_make_point_neighbors()
.
If nb = NULL
and data
is a polygon geometry
(classes "sfc_POLYGON" or "sfc_MULTIPOLYGON") the "nb" object will be created
using ww_make_polygon_neighbors()
.
If nb = NULL
and data
is any other geometry type, the "nb" object will
be created using the centroids of the data as points, with a warning.
An object of class "nb".
ww_build_neighbors(guerry)
ww_build_neighbors(guerry)
These functions can be used for geographic or projected coordinate reference systems and expect 2D data.
ww_build_weights(x, wt = NULL, include_self = FALSE, ...)
ww_build_weights(x, wt = NULL, include_self = FALSE, ...)
x 
Either an sf object or a "nb" neighbors list object.
If an sf object, will be converted into a neighbors list via

wt 
Either a "listw" object (which will be returned unchanged),
a function for creating a "listw" object from 
include_self 
Include each region itself in its own list of neighbors? 
... 
Arguments passed to the weight constructing function. 
A listw
object.
ww_build_weights(guerry)
ww_build_weights(guerry)
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.
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, ...)
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, ...)
data 
A 
... 
Additional arguments passed to 
truth 
The column identifier for the true results
(that is 
estimate 
The column identifier for the predicted
results (that is also 
wt 
A 
na_rm 
A 
These functions can be used for geographic or projected coordinate reference systems and expect 2D data.
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).
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.
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()
guerry_model < guerry guerry_lm < lm(Crm_prs ~ Litercy, guerry_model) guerry_model$predictions < predict(guerry_lm, guerry_model) ww_global_geary_c(guerry_model, Crm_prs, predictions) ww_global_geary_pvalue(guerry_model, Crm_prs, predictions) wt < ww_build_weights(guerry_model) ww_global_geary_c_vec( guerry_model$Crm_prs, guerry_model$predictions, wt = wt ) ww_global_geary_pvalue_vec( guerry_model$Crm_prs, guerry_model$predictions, wt = wt )
guerry_model < guerry guerry_lm < lm(Crm_prs ~ Litercy, guerry_model) guerry_model$predictions < predict(guerry_lm, guerry_model) ww_global_geary_c(guerry_model, Crm_prs, predictions) ww_global_geary_pvalue(guerry_model, Crm_prs, predictions) wt < ww_build_weights(guerry_model) ww_global_geary_c_vec( guerry_model$Crm_prs, guerry_model$predictions, wt = wt ) ww_global_geary_pvalue_vec( guerry_model$Crm_prs, guerry_model$predictions, wt = wt )
Calculate the global Moran's I statistic for model residuals.
ww_global_moran_i()
returns the statistic itself, while
ww_global_moran_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::moran.test()
instead.
ww_global_moran_i(data, ...) ww_global_moran_i_vec(truth, estimate, wt = NULL, na_rm = FALSE, ...) ww_global_moran_pvalue(data, ...) ww_global_moran_pvalue_vec(truth, estimate, wt = NULL, na_rm = FALSE, ...)
ww_global_moran_i(data, ...) ww_global_moran_i_vec(truth, estimate, wt = NULL, na_rm = FALSE, ...) ww_global_moran_pvalue(data, ...) ww_global_moran_pvalue_vec(truth, estimate, wt = NULL, na_rm = FALSE, ...)
data 
A 
... 
Additional arguments passed to 
truth 
The column identifier for the true results
(that is 
estimate 
The column identifier for the predicted
results (that is also 
wt 
A 
na_rm 
A 
These functions can be used for geographic or projected coordinate reference systems and expect 2D data.
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).
Moran, P.A.P. (1950). "Notes on Continuous Stochastic Phenomena." Biometrika, 37(1/2), pp 17. doi: 10.2307/2332142
Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 17.
Other autocorrelation metrics:
ww_global_geary_c()
,
ww_local_geary_c()
,
ww_local_getis_ord_g()
,
ww_local_moran_i()
Other yardstick metrics:
ww_agreement_coefficient()
,
ww_global_geary_c()
,
ww_local_geary_c()
,
ww_local_getis_ord_g()
,
ww_local_moran_i()
,
ww_willmott_d()
guerry_model < guerry guerry_lm < lm(Crm_prs ~ Litercy, guerry_model) guerry_model$predictions < predict(guerry_lm, guerry_model) ww_global_moran_i(guerry_model, Crm_prs, predictions) ww_global_moran_pvalue(guerry_model, Crm_prs, predictions) wt < ww_build_weights(guerry_model) ww_global_moran_i_vec( guerry_model$Crm_prs, guerry_model$predictions, wt = wt ) ww_global_moran_pvalue_vec( guerry_model$Crm_prs, guerry_model$predictions, wt = wt )
guerry_model < guerry guerry_lm < lm(Crm_prs ~ Litercy, guerry_model) guerry_model$predictions < predict(guerry_lm, guerry_model) ww_global_moran_i(guerry_model, Crm_prs, predictions) ww_global_moran_pvalue(guerry_model, Crm_prs, predictions) wt < ww_build_weights(guerry_model) ww_global_moran_i_vec( guerry_model$Crm_prs, guerry_model$predictions, wt = wt ) ww_global_moran_pvalue_vec( guerry_model$Crm_prs, guerry_model$predictions, wt = wt )
Calculate the local Geary's C statistic for model residuals.
ww_local_geary_c()
returns the statistic itself, while
ww_local_geary_pvalue()
returns the associated p value.
These functions are meant to help assess model predictions, for instance by
identifying clusters of higher residuals than expected. For statistical
testing and inference applications, use spdep::localC_perm()
instead.
ww_local_geary_c(data, ...) ww_local_geary_c_vec(truth, estimate, wt, na_rm = FALSE, ...) ww_local_geary_pvalue(data, ...) ww_local_geary_pvalue_vec(truth, estimate, wt = NULL, na_rm = FALSE, ...)
ww_local_geary_c(data, ...) ww_local_geary_c_vec(truth, estimate, wt, na_rm = FALSE, ...) ww_local_geary_pvalue(data, ...) ww_local_geary_pvalue_vec(truth, estimate, wt = NULL, na_rm = FALSE, ...)
data 
A 
... 
Additional arguments passed to 
truth 
The column identifier for the true results
(that is 
estimate 
The column identifier for the predicted
results (that is also 
wt 
A 
na_rm 
A 
These functions can be used for geographic or projected coordinate reference systems and expect 2D data.
A tibble with columns .metric, .estimator, and .estimate and nrow(data)
rows of values.
For _vec()
functions, a numeric vector of length(truth)
(or NA).
Anselin, L. 1995. Local indicators of spatial association, Geographical Analysis, 27, pp 93–115. doi: 10.1111/j.15384632.1995.tb00338.x.
Anselin, L. 2019. A Local Indicator of Multivariate Spatial Association: Extending Geary's C. Geographical Analysis, 51, pp 133150. doi: 10.1111/gean.12164
Other autocorrelation metrics:
ww_global_geary_c()
,
ww_global_moran_i()
,
ww_local_getis_ord_g()
,
ww_local_moran_i()
Other yardstick metrics:
ww_agreement_coefficient()
,
ww_global_geary_c()
,
ww_global_moran_i()
,
ww_local_getis_ord_g()
,
ww_local_moran_i()
,
ww_willmott_d()
guerry_model < guerry guerry_lm < lm(Crm_prs ~ Litercy, guerry_model) guerry_model$predictions < predict(guerry_lm, guerry_model) ww_local_geary_c(guerry_model, Crm_prs, predictions) ww_local_geary_pvalue(guerry_model, Crm_prs, predictions) wt < ww_build_weights(guerry_model) ww_local_geary_c_vec( guerry_model$Crm_prs, guerry_model$predictions, wt = wt ) ww_local_geary_pvalue_vec( guerry_model$Crm_prs, guerry_model$predictions, wt = wt )
guerry_model < guerry guerry_lm < lm(Crm_prs ~ Litercy, guerry_model) guerry_model$predictions < predict(guerry_lm, guerry_model) ww_local_geary_c(guerry_model, Crm_prs, predictions) ww_local_geary_pvalue(guerry_model, Crm_prs, predictions) wt < ww_build_weights(guerry_model) ww_local_geary_c_vec( guerry_model$Crm_prs, guerry_model$predictions, wt = wt ) ww_local_geary_pvalue_vec( guerry_model$Crm_prs, guerry_model$predictions, wt = wt )
Calculate the local GetisOrd G and G* statistic for model residuals.
ww_local_getis_ord_g()
returns the statistic itself, while
ww_local_getis_ord_pvalue()
returns the associated p value.
These functions are meant to help assess model predictions, for instance by
identifying clusters of higher residuals than expected. For statistical
testing and inference applications, use spdep::localG_perm()
instead.
ww_local_getis_ord_g(data, ...) ww_local_getis_ord_g_vec(truth, estimate, wt, na_rm = FALSE, ...) ww_local_getis_ord_g_pvalue(data, ...) ww_local_getis_ord_g_pvalue_vec(truth, estimate, wt, na_rm = FALSE, ...)
ww_local_getis_ord_g(data, ...) ww_local_getis_ord_g_vec(truth, estimate, wt, na_rm = FALSE, ...) ww_local_getis_ord_g_pvalue(data, ...) ww_local_getis_ord_g_pvalue_vec(truth, estimate, wt, na_rm = FALSE, ...)
data 
A 
... 
Additional arguments passed to 
truth 
The column identifier for the true results
(that is 
estimate 
The column identifier for the predicted
results (that is also 
wt 
A 
na_rm 
A 
These functions can be used for geographic or projected coordinate reference systems and expect 2D data.
A tibble with columns .metric, .estimator, and .estimate and nrow(data)
rows of values.
For _vec()
functions, a numeric vector of length(truth)
(or NA).
Ord, J. K. and Getis, A. 1995. Local spatial autocorrelation statistics: distributional issues and an application. Geographical Analysis, 27, 286–306. doi: 10.1111/j.15384632.1995.tb00912.x
Other autocorrelation metrics:
ww_global_geary_c()
,
ww_global_moran_i()
,
ww_local_geary_c()
,
ww_local_moran_i()
Other yardstick metrics:
ww_agreement_coefficient()
,
ww_global_geary_c()
,
ww_global_moran_i()
,
ww_local_geary_c()
,
ww_local_moran_i()
,
ww_willmott_d()
guerry_model < guerry guerry_lm < lm(Crm_prs ~ Litercy, guerry_model) guerry_model$predictions < predict(guerry_lm, guerry_model) ww_local_getis_ord_g(guerry_model, Crm_prs, predictions) ww_local_getis_ord_g_pvalue(guerry_model, Crm_prs, predictions) wt < ww_build_weights(guerry_model) ww_local_getis_ord_g_vec( guerry_model$Crm_prs, guerry_model$predictions, wt = wt ) ww_local_getis_ord_g_pvalue_vec( guerry_model$Crm_prs, guerry_model$predictions, wt = wt )
guerry_model < guerry guerry_lm < lm(Crm_prs ~ Litercy, guerry_model) guerry_model$predictions < predict(guerry_lm, guerry_model) ww_local_getis_ord_g(guerry_model, Crm_prs, predictions) ww_local_getis_ord_g_pvalue(guerry_model, Crm_prs, predictions) wt < ww_build_weights(guerry_model) ww_local_getis_ord_g_vec( guerry_model$Crm_prs, guerry_model$predictions, wt = wt ) ww_local_getis_ord_g_pvalue_vec( guerry_model$Crm_prs, guerry_model$predictions, wt = wt )
Calculate the local Moran's I statistic for model residuals.
ww_local_moran_i()
returns the statistic itself, while
ww_local_moran_pvalue()
returns the associated p value.
These functions are meant to help assess model predictions, for instance by
identifying clusters of higher residuals than expected. For statistical
testing and inference applications, use spdep::localmoran_perm()
instead.
ww_local_moran_i(data, ...) ww_local_moran_i_vec(truth, estimate, wt, na_rm = FALSE, ...) ww_local_moran_pvalue(data, ...) ww_local_moran_pvalue_vec(truth, estimate, wt = NULL, na_rm = FALSE, ...)
ww_local_moran_i(data, ...) ww_local_moran_i_vec(truth, estimate, wt, na_rm = FALSE, ...) ww_local_moran_pvalue(data, ...) ww_local_moran_pvalue_vec(truth, estimate, wt = NULL, na_rm = FALSE, ...)
data 
A 
... 
Additional arguments passed to 
truth 
The column identifier for the true results
(that is 
estimate 
The column identifier for the predicted
results (that is also 
wt 
A 
na_rm 
A 
These functions can be used for geographic or projected coordinate reference systems and expect 2D data.
A tibble with columns .metric, .estimator, and .estimate and nrow(data)
rows of values.
For _vec()
functions, a numeric vector of length(truth)
(or NA).
Anselin, L. 1995. Local indicators of spatial association, Geographical Analysis, 27, pp 93–115. doi: 10.1111/j.15384632.1995.tb00338.x.
Sokal, R. R, Oden, N. L. and Thomson, B. A. 1998. Local Spatial Autocorrelation in a Biological Model. Geographical Analysis, 30, pp 331–354. doi: 10.1111/j.15384632.1998.tb00406.x
Other autocorrelation metrics:
ww_global_geary_c()
,
ww_global_moran_i()
,
ww_local_geary_c()
,
ww_local_getis_ord_g()
Other yardstick metrics:
ww_agreement_coefficient()
,
ww_global_geary_c()
,
ww_global_moran_i()
,
ww_local_geary_c()
,
ww_local_getis_ord_g()
,
ww_willmott_d()
guerry_model < guerry guerry_lm < lm(Crm_prs ~ Litercy, guerry_model) guerry_model$predictions < predict(guerry_lm, guerry_model) ww_local_moran_i(guerry_model, Crm_prs, predictions) ww_local_moran_pvalue(guerry_model, Crm_prs, predictions) wt < ww_build_weights(guerry_model) ww_local_moran_i_vec( guerry_model$Crm_prs, guerry_model$predictions, wt = wt ) ww_local_moran_pvalue_vec( guerry_model$Crm_prs, guerry_model$predictions, wt = wt )
guerry_model < guerry guerry_lm < lm(Crm_prs ~ Litercy, guerry_model) guerry_model$predictions < predict(guerry_lm, guerry_model) ww_local_moran_i(guerry_model, Crm_prs, predictions) ww_local_moran_pvalue(guerry_model, Crm_prs, predictions) wt < ww_build_weights(guerry_model) ww_local_moran_i_vec( guerry_model$Crm_prs, guerry_model$predictions, wt = wt ) ww_local_moran_pvalue_vec( guerry_model$Crm_prs, guerry_model$predictions, wt = wt )
This function uses spdep::knearneigh()
and spdep::knn2nb()
to
create a "nb" neighbors list.
ww_make_point_neighbors(data, k = 1, sym = FALSE, ...)
ww_make_point_neighbors(data, k = 1, sym = FALSE, ...)
data 
An 
k 
How many nearest neighbors to use in 
sym 
Force the output neighbors list (from 
... 
Other arguments passed to 
These functions can be used for geographic or projected coordinate reference systems and expect 2D data.
An object of class "nb"
ww_make_point_neighbors(ny_trees)
ww_make_point_neighbors(ny_trees)
This function is an extremely thin wrapper around spdep::poly2nb()
,
renamed to use the waywiser "ww" prefix.
ww_make_polygon_neighbors(data, ...)
ww_make_polygon_neighbors(data, ...)
data 
An 
... 
Additional arguments passed to 
These functions can be used for geographic or projected coordinate reference systems and expect 2D data.
An object of class "nb"
ww_make_polygon_neighbors(guerry)
ww_make_polygon_neighbors(guerry)
Evaluate metrics at multiple scales of aggregation
ww_multi_scale( data = NULL, truth, estimate, metrics = list(yardstick::rmse, yardstick::mae), grids = NULL, ..., na_rm = TRUE, aggregation_function = "mean", autoexpand_grid = TRUE, progress = TRUE )
ww_multi_scale( data = NULL, truth, estimate, metrics = list(yardstick::rmse, yardstick::mae), grids = NULL, ..., na_rm = TRUE, aggregation_function = "mean", autoexpand_grid = TRUE, progress = TRUE )
data 
Either: a point geometry 
truth , estimate

If 
metrics 
Either a 
grids 
Optionally, a list of precomputed 
... 
Arguments passed to 
na_rm 
Boolean: Should polygons with NA values be removed before
calculating metrics? Note that this does not impact how values are
aggregated to polygons: if you want to remove NA values before aggregating,
provide a function to 
aggregation_function 
The function to use to aggregate predictions and
true values at various scales, by default 
autoexpand_grid 
Boolean: if 
progress 
Boolean: if 
A tibble with six columns: .metric
, with the name
of the metric that the row describes; .estimator
, with the name of the
estimator used, .estimate
, with the output of the metric function;
.grid_args
, with the arguments passed to sf::st_make_grid()
via ...
(if any), .grid
, containing the grids used to aggregate predictions,
as well as the aggregated values of truth
and estimate
as well as the
count of nonNA values for each, and .notes
, which (if data
is an sf
object) will indicate any observations which were not used in a given
assessment.
If data
is NULL
, then truth
and estimate
should both be SpatRaster
objects, as created via terra::rast()
. These rasters will then be
aggregated to each grid using exactextractr::exact_extract()
. If data
is a SpatRaster
object, then truth
and estimate
should be indices to
select the appropriate layers of the raster via terra::subset()
.
Grids are calculated using the bounding box of truth
, under the assumption
that you may have extrapolated into regions which do not have matching "true"
values. This function does not check that truth
and estimate
overlap at
all, or that they are at all contained within the grid.
The grid blocks can be controlled by passing arguments to
sf::st_make_grid()
via ...
. Some particularly useful arguments include:
cellsize
: Target cellsize, expressed as the "diameter" (shortest
straightline distance between opposing sides; two times the apothem)
of each block, in map units.
n
: The number of grid blocks in the x and y direction (columns, rows).
square
: A logical value indicating whether to create square (TRUE
) or
hexagonal (FALSE
) cells.
If both cellsize
and n
are provided, then the number of blocks requested
by n
of sizes specified by cellsize
will be returned, likely not
lining up with the bounding box of data
. If only cellsize
is provided, this function will return as many blocks of size
cellsize
as fit inside the bounding box of data
. If only n
is provided,
then cellsize
will be automatically adjusted to create the requested
number of cells.
Grids are created by mapping over each argument passed via ...
simultaneously, in a similar manner to mapply()
or purrr::pmap()
. This
means that, for example, passing n = list(c(1, 2))
will create a single
1x2 grid, while passing n = c(1, 2)
will create a 1x1 grid and a 2x2
grid. It also means that arguments will be recycled using R's standard
vector recycling rules, so that passing n = c(1, 2)
and square = FALSE
will create two separate grids of hexagons.
This function can be used for geographic or projected coordinate reference systems and expects 2D data.
Riemann, R., Wilson, B. T., Lister, A., and Parks, S. (2010). "An effective assessment protocol for continuous geospatial datasets of forest characteristics using USFS Forest Inventory and Analysis (FIA) data." Remote Sensing of Environment 114(10), pp 23372352, doi: 10.1016/j.rse.2010.05.010 .
data(ames, package = "modeldata") ames_sf < sf::st_as_sf(ames, coords = c("Longitude", "Latitude"), crs = 4326) ames_model < lm(Sale_Price ~ Lot_Area, data = ames_sf) ames_sf$predictions < predict(ames_model, ames_sf) ww_multi_scale( ames_sf, Sale_Price, predictions, n = list( c(10, 10), c(1, 1) ), square = FALSE ) # or, mostly equivalently # (there will be a slight difference due to `autoexpand_grid = TRUE`) grids < list( sf::st_make_grid(ames_sf, n = c(10, 10), square = FALSE), sf::st_make_grid(ames_sf, n = c(1, 1), square = FALSE) ) ww_multi_scale(ames_sf, Sale_Price, predictions, grids = grids)
data(ames, package = "modeldata") ames_sf < sf::st_as_sf(ames, coords = c("Longitude", "Latitude"), crs = 4326) ames_model < lm(Sale_Price ~ Lot_Area, data = ames_sf) ames_sf$predictions < predict(ames_model, ames_sf) ww_multi_scale( ames_sf, Sale_Price, predictions, n = list( c(10, 10), c(1, 1) ), square = FALSE ) # or, mostly equivalently # (there will be a slight difference due to `autoexpand_grid = TRUE`) grids < list( sf::st_make_grid(ames_sf, n = c(10, 10), square = FALSE), sf::st_make_grid(ames_sf, n = c(1, 1), square = FALSE) ) ww_multi_scale(ames_sf, Sale_Price, predictions, grids = grids)
These functions calculate Willmott's d value, a proposed replacement for R2 which better differentiates between types and magnitudes of possible covariations. Additional functions calculate systematic and unsystematic components of MSE and RMSE; the sum of the systematic and unsystematic components of MSE equal total MSE (though the same is not true for RMSE).
ww_willmott_d(data, ...) ## S3 method for class 'data.frame' ww_willmott_d(data, truth, estimate, na_rm = TRUE, ...) ww_willmott_d_vec(truth, estimate, na_rm = TRUE, ...) ww_willmott_d1(data, ...) ## S3 method for class 'data.frame' ww_willmott_d1(data, truth, estimate, na_rm = TRUE, ...) ww_willmott_d1_vec(truth, estimate, na_rm = TRUE, ...) ww_willmott_dr(data, ...) ## S3 method for class 'data.frame' ww_willmott_dr(data, truth, estimate, na_rm = TRUE, ...) ww_willmott_dr_vec(truth, estimate, na_rm = TRUE, ...) ww_systematic_mse(data, ...) ## S3 method for class 'data.frame' ww_systematic_mse(data, truth, estimate, na_rm = TRUE, ...) ww_systematic_mse_vec(truth, estimate, na_rm = TRUE, ...) ww_unsystematic_mse(data, ...) ## S3 method for class 'data.frame' ww_unsystematic_mse(data, truth, estimate, na_rm = TRUE, ...) ww_unsystematic_mse_vec(truth, estimate, na_rm = TRUE, ...) ww_systematic_rmse(data, ...) ## S3 method for class 'data.frame' ww_systematic_rmse(data, truth, estimate, na_rm = TRUE, ...) ww_systematic_rmse_vec(truth, estimate, na_rm = TRUE, ...) ww_unsystematic_rmse(data, ...) ## S3 method for class 'data.frame' ww_unsystematic_rmse(data, truth, estimate, na_rm = TRUE, ...) ww_unsystematic_rmse_vec(truth, estimate, na_rm = TRUE, ...)
ww_willmott_d(data, ...) ## S3 method for class 'data.frame' ww_willmott_d(data, truth, estimate, na_rm = TRUE, ...) ww_willmott_d_vec(truth, estimate, na_rm = TRUE, ...) ww_willmott_d1(data, ...) ## S3 method for class 'data.frame' ww_willmott_d1(data, truth, estimate, na_rm = TRUE, ...) ww_willmott_d1_vec(truth, estimate, na_rm = TRUE, ...) ww_willmott_dr(data, ...) ## S3 method for class 'data.frame' ww_willmott_dr(data, truth, estimate, na_rm = TRUE, ...) ww_willmott_dr_vec(truth, estimate, na_rm = TRUE, ...) ww_systematic_mse(data, ...) ## S3 method for class 'data.frame' ww_systematic_mse(data, truth, estimate, na_rm = TRUE, ...) ww_systematic_mse_vec(truth, estimate, na_rm = TRUE, ...) ww_unsystematic_mse(data, ...) ## S3 method for class 'data.frame' ww_unsystematic_mse(data, truth, estimate, na_rm = TRUE, ...) ww_unsystematic_mse_vec(truth, estimate, na_rm = TRUE, ...) ww_systematic_rmse(data, ...) ## S3 method for class 'data.frame' ww_systematic_rmse(data, truth, estimate, na_rm = TRUE, ...) ww_systematic_rmse_vec(truth, estimate, na_rm = TRUE, ...) ww_unsystematic_rmse(data, ...) ## S3 method for class 'data.frame' ww_unsystematic_rmse(data, truth, estimate, na_rm = TRUE, ...) ww_unsystematic_rmse_vec(truth, estimate, na_rm = TRUE, ...)
data 
A 
... 
Not currently used. 
truth 
The column identifier for the true results
(that is 
estimate 
The column identifier for the predicted
results (that is also 
na_rm 
A 
Values of d and d1 range from 0 to 1, with 1 indicating perfect agreement.
Values of
dr range from 1 to 1, with 1 similarly indicating perfect agreement. Values
of RMSE are in the same units as truth
and estimate
, while values of MSE
are in squared units. truth
and estimate
must be the same length. This
function is not explicitly spatial and as such can be applied to data with
any number of dimensions and any coordinate reference system.
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).
Willmott, C. J. 1981. "On the Validation of Models". Physical Geography 2(2), pp 184194, doi: 10.1080/02723646.1981.10642213.
Willmott, C. J. 1982. "Some Comments on the Evaluation of Model Performance". Bulletin of the American Meteorological Society 63(11), pp 13091313, doi: 10.1175/15200477(1982)063<1309:SCOTEO>2.0.CO;2.
Willmott C. J., Ackleson S. G., Davis R. E., Feddema J. J., Klink K. M., Legates D. R., O’Donnell J., Rowe C. M. 1985. "Statistics for the evaluation of model performance." Journal of Geophysical Research 90(C5): 8995–9005, doi: 10.1029/jc090ic05p08995
Willmott, C. J., Robeson, S. M., and Matsuura, K. "A refined index of model performance". International Journal of Climatology 32, pp 20882094, doi: 10.1002/joc.2419.
Other agreement metrics:
ww_agreement_coefficient()
Other yardstick metrics:
ww_agreement_coefficient()
,
ww_global_geary_c()
,
ww_global_moran_i()
,
ww_local_geary_c()
,
ww_local_getis_ord_g()
,
ww_local_moran_i()
x < c(6, 8, 9, 10, 11, 14) y < c(2, 3, 5, 5, 6, 8) ww_willmott_d_vec(x, y) ww_willmott_d1_vec(x, y) ww_willmott_dr_vec(x, y) ww_systematic_mse_vec(x, y) ww_unsystematic_mse_vec(x, y) ww_systematic_rmse_vec(x, y) ww_unsystematic_rmse_vec(x, y) example_df < data.frame(x = x, y = y) ww_willmott_d(example_df, x, y) ww_willmott_d1(example_df, x, y) ww_willmott_dr(example_df, x, y) ww_systematic_mse(example_df, x, y) ww_unsystematic_mse(example_df, x, y) ww_systematic_rmse(example_df, x, y) ww_unsystematic_rmse(example_df, x, y)
x < c(6, 8, 9, 10, 11, 14) y < c(2, 3, 5, 5, 6, 8) ww_willmott_d_vec(x, y) ww_willmott_d1_vec(x, y) ww_willmott_dr_vec(x, y) ww_systematic_mse_vec(x, y) ww_unsystematic_mse_vec(x, y) ww_systematic_rmse_vec(x, y) ww_unsystematic_rmse_vec(x, y) example_df < data.frame(x = x, y = y) ww_willmott_d(example_df, x, y) ww_willmott_d1(example_df, x, y) ww_willmott_dr(example_df, x, y) ww_systematic_mse(example_df, x, y) ww_unsystematic_mse(example_df, x, y) ww_systematic_rmse(example_df, x, y) ww_unsystematic_rmse(example_df, x, y)