GEE (Generalized Estimating Equations)

Description

GEE provides GEE-based methods from the packages gee and geepack to account for spatial autocorrelation in multiple linear regressions

Usage

GEE(
  formula,
  family,
  data,
  coord,
  corstr = "fixed",
  cluster = 3,
  moran.params = list(),
  plot = FALSE,
  scale.fix = FALSE,
  customize_plot = NULL
)

## S3 method for class 'GEE'
plot(x, ...)

## S3 method for class 'GEE'
predict(object, newdata, ...)

## S3 method for class 'GEE'
summary(object, ..., printAutoCorPars = TRUE)

Arguments

Details

GEE can be used to fit linear models for response variables with different distributions: gaussian, binomial, or poisson. As a spatial model, it is a generalized linear model in which the residuals may be autocorrelated. It accounts for spatial (2-dimensional) autocorrelation of the residuals in cases of regular gridded datasets and returns corrected parameter estimates. The grid cells are assumed to be square. Furthermore, this function requires that all predictor variables be continuous.

Value

An object of class GEE. This consists of a list with the following elements:

call

Call

formula

Model formula

family

Family

coord

Coordinates used for the model

corstr

User-selected correlation structure

b

Estimate of regression parameters

s.e.

Standard errors of the estimates

z

Depending on the family, either a z or t value

p

p-values for each parameter estimate

scale

Scale parameter (dispersion parameter) of the distribution's variance

scale.fix

Logical indicating whether scale has fixed value

cluster

User-specified cluster size for clustered models

fitted

Fitted values from the model

resid

Normalized Pearson residuals

w.ac

Working autocorrelation parameters

Mat.ac

Working autocorrelation matrix

QIC

Quasi Information Criterion. See qic.calc for further details

QLik

Quasi-likelihood. See qic.calc for further details

plot

Logical value indicating whether autocorrelation should be plotted

moran.params

Parameters for calculating Moran's I

v2

Parameter variance of the GEE model

var.naive

Parameter variance of the independence model

ac.glm

Autocorrelation of GLM residuals

ac.gee

Autocorrelation of GEE residuals

plot

An object of class ggplot containing information on the autocorrelation of residuals from the fitted GEE and a GLM

Elements can be viewed using the summary.GEE methods included in the package.

Note

When using corstr = "fixed" on large data sets, the function may return an error, as the resulting variance-covariance matrix is too large for R to handle. If this happens, one will have to use one of the cluster models (i.e quadratic, exchangeable).

Author(s)

Gudrun Carl, Sam Levin

References

Carl G & Kuehn I, 2007. Analyzing Spatial Autocorrelation in Species Distributions using Gaussian and Logit Models, Ecol. Model. 207, 159 - 170

Carey, V. J., 2006. Ported to R by Thomas Lumley (versions 3.13, 4.4, version 4.13)., B. R. gee: Generalized Estimation Equation solver. R package version 4.13-11.

Yan, J., 2004. geepack: Generalized Estimating Equation Package. R package version 0.2.10.

See Also

qic.calc, summary.GEE, gee

Examples

data(musdata)
coords<- musdata[,4:5]

## Not run: 
mgee <- GEE(musculus ~ pollution + exposure,
            family = "poisson",
            data =  musdata,
            coord = coords,
            corstr = "fixed",
            scale.fix = FALSE)

summary(mgee, printAutoCorPars = TRUE)

pred <- predict(mgee, newdata = musdata)

library(ggplot2)

plot(mgee)

my_gee_plot <- mgee$plot

# move the legend to a new position
print(my_gee_plot + ggplot2::theme(legend.position = 'top'))


## End(Not run)

Wavelet-revised models (WRMs)

Description

A wavelet-based method to remove spatial autocorrelation in multiple linear regressions. Wavelet transforms are implemented using waveslim (Whitcher, 2005).

Usage

WRM(
  formula,
  family,
  data,
  coord,
  level = 1,
  wavelet = "haar",
  wtrafo = "dwt",
  b.ini = NULL,
  pad = list(),
  control = list(),
  moran.params = list(),
  plot = FALSE,
  customize_plot = NULL
)

## S3 method for class 'WRM'
plot(x, ...)

## S3 method for class 'WRM'
summary(object, ...)

## S3 method for class 'WRM'
predict(object, newdata, sm = FALSE, newcoord = NA, ...)

Arguments

Details

WRM can be used to fit linear models for response vectors of different distributions: gaussian, binomial, or poisson. As a spatial model, it is a generalized linear model in which the residuals may be autocorrelated. It corrects for 2-dimensional residual autocorrelation for regular gridded data sets using the wavelet decomposition technique. The grid cells are assumed to be square. Furthermore, this function requires that all predictor variables be continuous.

Value

An object of class WRM. This consists of a list with the following elements:

call

Call

formula

Model formula

family

Family

coord

Coordinates used in the model

b

Estimate of regression parameters

s.e.

Standard errors

z

Depending on the family, either a z or t value

p

p-values

fitted

Fitted values from the model

resid

Pearson residuals

b.sm

Parameter estimates of neglected smooth part

fitted.sm

Fitted values of neglected smooth part

level

Selected level of wavelet decomposition

wavelet

Selected wavelet

wtrafo

Selected wavelet transformation

padzone

Selected padding zone expansion factor

padform

Selected matrix padding type

n.eff

Effective number of observations

AIC

Akaike information criterion

AICc

AIC score corrected for small sample sizes

LogLik

Log likelihood of the model

ac.glm

Autocorrelation of GLM residuals

ac.wrm

Autocorrelation of WRM residuals

b.ini

Initial parameter values

control

Control parameters for the fitting process

moran.params

Parameters for calculating Moran's I

pad

List of parameters for padding wavelet coefficients

plot

An object of class ggplot containing information on the autocorrelation of residuals from the fitted WRM and a GLM

Note

For those interested in multimodel inference approaches, WRM with level = 1 is identical to mmiWMRR with scale = 1.

Author(s)

Gudrun Carl, Sam Levin

References

Carl, G., Kuehn, I. (2010): A wavelet-based extension of generalized linear models to remove the effect of spatial autocorrelation. Geographical Analysis 42 (3), 323 - 337

Whitcher, B. (2005) Waveslim: basic wavelet routines for one-, two- and three-dimensional signal processing. R package version 1.5.

See Also

mmiWMRR, predict.WRM, summary.WRM, aic.calc

Examples

data(musdata)
coords <- musdata[,4:5]

## Not run: 
mwrm <- WRM(musculus ~ pollution + exposure,
            family = "poisson",
            data = musdata,
            coord = coords,
            level = 1)

pred <- predict(mwrm, newdata = musdata)

summary(mwrm)

plot(mwrm)

library(ggplot2)

my_wrm_plot <- mwrm$plot

# increase axis text size
print(my_wrm_plot + ggplot2::theme(axis.text = element_text(size = 15)))


## End(Not run)

Spatial autocorrelation diagnostics

Description

A function for calculating spatial autocorrelation using Moran's I.

Usage

acfft(coord, f, lim1 = 1, lim2 = 2, dmax = 10)

Arguments

Value

A vector of Moran's I values for each distance bin.

Author(s)

Gudrun Carl

Examples

data(musdata)
coords <- musdata[ ,4:5]
mglm <- glm(musculus ~ pollution + exposure, "poisson", musdata)

ac <- acfft(coords, resid(mglm, type = "pearson"), lim1 = 0, lim2 = 1)
ac

Adjusted actual values

Description

Adjusts actual presence/absence data based on the autocorrelation in the predictions of a model. The function will optionally plot results of model predictions, un-modified actual presence/absence, and adjusted values.

Usage

adjusted.actuals(data, coord, plot.maps = FALSE, color.maps = FALSE)

Arguments

Value

A vector of adjusted actual values.

Author(s)

Gudrun Carl

Examples

data(hook)
data <- hook[ ,1:2]
coord <- hook[ ,3:4]
aa <- adjusted.actuals(data, coord, plot.maps = TRUE)

Akaike Information Criterion with correction for sample size

Description

Calculates AIC and AICc

Usage

aic.calc(formula, family, data, mu, n.eff = NULL)

Arguments

Value

A list with the following components

loglik

Log likelihood of the model

df

Degrees of freedom

AIC

AIC score for the specified model

AICc

AIC score corrected for small sample sizes

Author(s)

Gudrun Carl, Sam Levin

Examples

data(musdata)
coords <- musdata[ ,4:5]
mglm <- glm(musculus ~ pollution + exposure, "poisson", musdata)

aic <- aic.calc(musculus ~ pollution + exposure, "poisson", musdata,
                mglm$fitted)
aic$AIC

Carlina data set

Description

A data frame containing simulated count data for the thistle, Carlina horrida.

Usage

carlinadata

Format

A data frame with 961 rows and 5 columns

carlina.horrida

integer - Simulated count data

aridity

numeric - Simulated aridity index values. This variable has high spatial autocorrelation values.

land.use

numeric - Simulated land use intensity. This variable has no spatial autocorrelation.

x

integer - x-coordinates for each grid cell

y

integer - y-coordinates for each grid cell

Plot wavelet variance/covariance

Description

Plots the wavelet variance or covariance for the specified formula. The scale-dependent results are graphically displayed.

Usage

covar.plot(
  formula,
  data,
  coord,
  wavelet = "haar",
  wtrafo = "dwt",
  plot = "covar",
  customize_plot = NULL
)

Arguments

Details

Each variable or pair of variables in formula is passed to wavevar or wavecovar internally, and the result is plotted as a function of level.

Value

A list containing

1. result = a vector of results.

2. plot = a ggplot object

Author(s)

Gudrun Carl

See Also

wavevar, wavecovar

Examples

data(carlinadata)
coords <- carlinadata[,4:5]

covariance <- covar.plot(carlina.horrida ~ aridity + land.use - 1,
                         data = carlinadata,
                         coord = coords,
                         wavelet = "d4",
                         wtrafo = 'modwt',
                         plot = 'covar')

covariance$plot
covariance$result

variance <- covar.plot(carlina.horrida ~ aridity + land.use - 1,
                       data = carlinadata,
                       coord = coords,
                       wavelet = "d4",
                       wtrafo = 'modwt',
                       plot = 'var')

variance$plot
variance$result

Hook data set

Description

A data frame containing actual presence absence data and predicted probability of occurrence values.

Usage

hook

Format

A data frame with 100 rows and 4 columns

actuals

integer - Presence/absence records

predictions

numeric - predicted probabilities of occurrence

x

integer - x-coordinates for each grid cell

y

integer - y-coordinates for each grid cell

Multi-model inference for GEE models

Description

mmiGEE is a multimodel inference approach evaluating the relative importance of predictors used in GEE.

@details It performs automatically generated model selection and creates a model selection table according to the approach of multi-model inference (Burnham & Anderson, 2002). QIC is used to obtain model selection weights and to rank the models. Moreover, mmiGEE calculates relative variable importance of a given model. Finally, this function requires that all predictor variables be continuous.

Usage

mmiGEE(object, data, trace = FALSE)

Arguments

Details

Calculates the relative importance of each variable using multi-model inference methods in a Generalized Estimating Equations framework implemented in GEE.

Value

mmiGEE returns a list containing the following elements

result

A matrix containing slopes, degrees of freedom, quasilikelihood, QIC, delta, and weight values for the set of candidate models. The models are ranked by QIC.

rvi

A vector containing the relative importance of each variable in the regression.

Author(s)

Gudrun Carl, Sam Levin

References

Burnham, K.P. & Anderson, D.R. (2002) Model selection and multimodel inference. Springer, New York.

Carl G & Kuehn I, 2007. Analyzing Spatial Autocorrelation in Species Distributions using Gaussian and Logit Models, Ecol. Model. 207, 159 - 170

See Also

GEE, qic.calc, MuMIn

Examples

# data (for demonstration only)
library(MASS)
data(birthwt)

# impose an artificial (not fully appropriate) grid structure

x <- rep(1:14, 14)
y <- as.integer(gl(14, 14))
coords <- cbind(x[-(190:196)], y[-(190:196)])

## Not run: 

formula <- formula(low ~ race + smoke +  bwt)

mgee <- GEE(formula,
            family = "gaussian",
            data = birthwt,
            coord = coords,
            corstr = "fixed",
            scale.fix = TRUE)

mmi <- mmiGEE(mgee, birthwt)


## End(Not run)

Multi-model inference for wavelet multiresolution regression

Description

mmiWMRR is a multimodel inference approach evaluating the relative importance of predictors used in scaleWMRR.

Usage

mmiWMRR(object, data, scale, detail = TRUE, trace = FALSE)

Arguments

Details

It performs automatically generated model selection and creates a model selection table according to the approach of multi-model inference (Burnham & Anderson, 2002). The analysis is carried out for scale-specific regressions (i.e. where scaleWMRR can be used). AIC is used to obtain model selection weights and to rank the models. Furthermore, this function requires that all predictor variables be continuous.

Value

mmiWMRR returns a list containing the following elements

result

A matrix containing slopes, degrees of freedom, likelihood, AIC, delta, and weight values for the set of candidate models. The models are ranked by AIC.

level

An integer corresponding to scale

Author(s)

Gudrun Carl

References

Burnham, K.P. & Anderson, D.R. (2002) Model selection and multimodel inference. Springer, New York.

Carl G, Doktor D, Schweiger O, Kuehn I (2016) Assessing relative variable importance across different spatial scales: a two-dimensional wavelet analysis. Journal of Biogeography 43: 2502-2512.

See Also

aic.calc, rvi.plot, MuMIn, WRM

Examples

data(carlinadata)
coords <- carlinadata[ ,4:5]

## Not run: 


wrm <- WRM(carlina.horrida ~ aridity + land.use,
           family = "poisson",
           data = carlinadata,
           coord = coords,
           level = 1,
           wavelet = "d4")

mmi <- mmiWMRR(wrm,
               data = carlinadata,
               scale = 3,
               detail = TRUE,
               trace = FALSE)


## End(Not run)

Mus musculus data set

Description

A data frame containing simulated count data of a house mouse.

Usage

musdata

Format

A data frame with 400 rows and 5 columns

musculus

integer - Simulated count data for Mus musculus

pollution

numeric - Simulated variable that describes degree of pollution in corresponding grid cell

exposure

numeric - Simulated variable that describes degree of exposure for each grid cell

x

integer - x-coordinates for each grid cell

y

integer - y-coordinates for each grid cell

Quasi-Information Criterion for Generalized Estimating Equations

Description

A function for calculating quasi-likelihood and Quasi-Information Criterion values based on the method of Hardin & Hilbe (2003).

Usage

qic.calc(formula, family, data, mu, var.robust, var.indep.naive)

Arguments

Value

A list with the following components:

QIC

quasi-information criterion

loglik

quasi-likelihood

References

Hardin, J.W. & Hilbe, J.M. (2003) Generalized Estimating Equations. Chapman and Hall, New York.

Barnett et al. Methods in Ecology & Evolution 2010, 1, 15-24.

Relative Variable Importance

Description

Creates model selection tables, calculates and plots relative variable importance based on the scale level of a given model.

Usage

rvi.plot(
  formula,
  family,
  data,
  coord,
  maxlevel,
  detail = TRUE,
  wavelet = "haar",
  wtrafo = "dwt",
  n.eff = NULL,
  trace = FALSE,
  customize_plot = NULL
)

Arguments

Details

Calculates the relative importance of each variable using multi-model inference methods in a wavelet multi-resolution regression framework implemented in mmiWMRR. The scale level dependent results are then graphically displayed.

Value

A list containing

1. A matrix containing the relative importance of each variable in the regression at each value of the scale level.

2. A ggplot object containing a plot of the relative variable importance

Examples

data(carlinadata)
coords<- carlinadata[,4:5]

## Not run: 

wrm <- WRM(carlina.horrida ~ aridity + land.use,
           family = "poisson",
           data = carlinadata,
           coord = coords,
           level = 1,
           wavelet = "d4")

mmi <- mmiWMRR(wrm, data = carlinadata, scale = 3, detail = TRUE)


# Plot scale-dependent relative variable importance
rvi <- rvi.plot(carlina.horrida ~ aridity + land.use,
                family = "poisson",
                data = carlinadata,
                coord = coords,
                maxlevel = 4,
                detail = TRUE,
                wavelet = "d4")

rvi$plot
rvi$rvi


## End(Not run)

Scaling by wavelet multiresolution regression (WMRR)

Description

scaleWMRR performs a scale-specific regression based on a wavelet multiresolution analysis.

Usage

scaleWMRR(
  formula,
  family,
  data,
  coord,
  scale = 1,
  detail = TRUE,
  wavelet = "haar",
  wtrafo = "dwt",
  b.ini = NULL,
  pad = list(),
  control = list(),
  moran.params = list(),
  trace = FALSE
)

Arguments

Details

This function fits generalized linear models while taking the two-dimensional grid structure of datasets into account. The following error distributions (in conjunction with appropriate link functions) are allowed: gaussian, binomial, or poisson. The model provides scale-specific results for data sampled on a contiguous geographical area. The dataset is assumed to be regular gridded and the grid cells are assumed to be square. A function from the package 'waveslim' is used for the wavelet transformations (Whitcher, 2005). Furthermore, this function requires that all predictor variables be continuous.

Value

scaleWMRR returns a list containing the following elements

call

Model call

b

Estimates of regression parameters

s.e.

Standard errors of the parameter estimates

z

Z values (or corresponding values for statistics)

p

p-values for each parameter estimate

df

Degrees of freedom

fitted

Fitted values

resid

Pearson residuals

converged

Logical value whether the procedure converged

trace

Logical. If TRUE:

• ac.glm Autocorrelation of glm.residuals

• ac Autocorrelation of wavelet.residuals

Author(s)

Gudrun Carl

References

Carl G, Doktor D, Schweiger O, Kuehn I (2016) Assessing relative variable importance across different spatial scales: a two-dimensional wavelet analysis. Journal of Biogeography 43: 2502-2512.

Whitcher, B. (2005) Waveslim: basic wavelet routines for one-, two- and three-dimensional signal processing. R package version 1.5.

See Also

waveslim,mra.2d

Examples

data(carlinadata)
coords <- carlinadata[ ,4:5]

## Not run: 

# scaleWMRR at scale = 0 is equivalent to GLM

ms0 <- scaleWMRR(carlina.horrida ~ aridity + land.use,
                 family = "poisson",
                 data = carlinadata,
                 coord = coords,
                 scale = 0,
                 trace = TRUE)

# scale-specific regressions for detail components
ms1 <- scaleWMRR(carlina.horrida ~ aridity + land.use,
                 family = "poisson",
                 data = carlinadata,
                 coord = coords,
                 scale = 1,
                 trace = TRUE)

ms2 <- scaleWMRR(carlina.horrida ~ aridity + land.use,
                 family = "poisson",
                 data = carlinadata,
                 coord = coords,
                 scale = 2,
                 trace = TRUE)

ms3<- scaleWMRR(carlina.horrida ~ aridity + land.use,
                 family = "poisson",
                 data = carlinadata,
                 coord = coords,
                 scale = 3,
                 trace = TRUE)


## End(Not run)

spind: Spatial Methods and Indices

Description

The spind package provides convenient implementation of Generalized estimating equations (GEEs) and Wavelet-revised models (WRMs) in the context of spatial models. It also provides tools for multi-model inference, stepwise model selection, and spatially corrected model diagnostics. This help section provides brief descriptions of each function and is organized by the type of model they apply to or the scenarios in which you might use them. Of course, these are recommendations - feel free to use them as you see fit. For a more detailed description of the package and its functions, please see the vignette Intro to spind (browseVignettes('spind')).

GEEs

The GEE function fits spatial models using a generalized estimating equation and a set of gridded data. The package also includes S3 methods for summary and predict so you can interact with these models in the same way you might interact with a glm or lm.

WRMs

The WRM function fits spatial models using a wavelet-revised model and a set of gridded data. The package also includes S3 methods for summary and predict so you can interact with these models in the same way you might interact with a glm or lm. There are also a number of helper functions that help you fine tune the fitting process that are specific to WRMs. Please see the documentation for WRM for more details on those.

WRM also has a few other features specific to it. For example, if you are interested in viewing the variance or covariance of your variables as a function of level, covar.plot is useful. upscale will plot your matrices as a function of level so you can examine the effect of cluster resolution on your results.

Multi-model inference and stepwise model selection

spind includes a couple of functions to help you find the best fit for your data. The first two are multimodel inference tools specific to GEEs and WRMs and are called mmiGEE and mmiWMRR. These generate outputs very similar to those from the MuMIn package. If you would like to see how variable importance changes as a function of the scale of the WMRR, you can call rvi.plot. This will generate a model selection table for each degree of level (from 1 to maxlevel) and then plot the weight of each variable as a function of level.

spind also includes a function for stepwise model selection that is loosely based on step and stepAIC. step.spind differs from these in that it is specific to classes WRM and GEE. It performs model selection using AIC or AICc for WRMs and QIC for GEEs.

Spatial indices of goodness of fit

Finally, spind has a number of functions that provide spatially corrected goodness of fit diagnostics for any type of model (i.e. they are not specific to classes WRM or GEE). These first appeared in spind v1.0 and have not been updated in this release. The first two are divided into whether or not they are threshold dependent or not. Threshold dependent metrics can be calculated using th.dep and threshold independent metrics can be calculated using th.indep.

acfft calculates spatial autocorrelation of residuals from a model using Moran's I. You can set the number of distance bins you'd like to examine using dmax argument and the size of those bins using lim1 and lim2.

Conclusion

The vignette titled Intro to spind provides more information on these functions and some example workflows that will demonstrate them in greater depth than this document. Of course, if you have suggestions on how to improve this document or any of the other ones in here, please don't hesitate to contact us.

Stepwise model selection for GEEs and WRMs

Description

Stepwise model selection by AIC or AICc for WRMS and QIC for GEEs

Usage

step.spind(object, data, steps = NULL, trace = TRUE, AICc = FALSE)

Arguments

Details

This function performs stepwise variable elimination for model comparison. Each iteration will try to find the best combination of predictors for a given number of variables based on AIC, AICc, or QIC, and then use that as the base model for the next iteration until there are no more variables to eliminate. Alternatively, it will terminate when reducing the number of variables while respecting the model hierarchy no longer produces lower information criterion values.

Value

A list with components model and table. model is always formula for the best model found by the procedure. table is always a data frame, but the content varies for each type of model. For WRM's, the columns returned are

• Deleted.Vars Variables retained from the previous iteration which were tested in the current iteration.

• LogLik Log-likelihood of the model.

• AIC AIC score for the model.

• AICc AICc score for the model.

For GEEs:

• Deleted.Vars Variables retained from the previous iteration which were tested in the current iteration.

• QIC Quasi-information criterion of the model.

• Quasi.Lik Quasi-likelihood of the model.

Note

Currently, the function only supports backwards model selection (i.e. one must start with a full model and subtract variables). Forward and both directions options may be added later.

Author(s)

Sam Levin

References

Hardin, J.W. & Hilbe, J.M. (2003) Generalized Estimating Equations. Chapman and Hall, New York.

See Also

qic.calc, aic.calc, add1, step, stepAIC

Examples

# For demonstration only. We are artificially imposing a grid structure
# on data that is not actually spatial data

library(MASS)
data(birthwt)

x <- rep(1:14, 14)
y <- as.integer(gl(14, 14))
coords <- cbind(x[-(190:196)], y[-(190:196)])

## Not run: 
formula <- formula(low ~ age + lwt + race + smoke + ftv + bwt)

mgee <- GEE(formula,
            family = "gaussian",
            data = birthwt,
            coord = coords,
            corstr = "fixed",
            scale.fix = TRUE)

ss <- step.spind(mgee, birthwt)

best.mgee <- GEE(ss$model,
                 family = "gaussian",
                 data = birthwt,
                 coord = coords,
                 corstr = "fixed",
                 scale.fix = TRUE)

summary(best.mgee, printAutoCorPars = FALSE)

## End(Not run)

Spatial threshold-dependent accuracy measures

Description

Calculates spatially corrected, threshold-dependent metrics for an observational data set and model predictions (Kappa and confusion matrix)

Usage

th.dep(data, coord, thresh = 0.5, spatial = TRUE)

Arguments

Value

A list with the following components:

kappa

Kappa statistic

cm

Confusion matrix

sensitivity

Sensitivity

specificity

Specificity

actuals

Actual occurrence data or adjusted actual occurrence data

splitlevel.pred

Level splitting of predicted values

splitlevel.act

Level splitting of actuals or adjusted actuals

splitposition.pred

Position splitting of predicted values

splitposition.act

Position splitting of actuals or adjusted actuals

Author(s)

Gudrun Carl

References

Carl G, Kuehn I (2017) Spind: a package for computing spatially corrected accuracy measures. Ecography 40: 675-682. DOI: 10.1111/ecog.02593

See Also

th.indep

Examples

data(hook)
data <- hook[ ,1:2]
coord <- hook[ ,3:4]
si1 <- th.dep(data, coord, spatial = TRUE)
si1$kappa
si1$cm

Spatial threshold-independent accuracy measures

Description

Calculates spatially corrected, threshold-independent metrics for an observational data set and model predictions (AUC, ROC, max-TSS)

Usage

th.indep(data, coord, spatial = TRUE, plot.ROC = FALSE, customize_plot = NULL)

Arguments

Value

A list with the following components:

AUC

Area under curve

opt.thresh

optimal threshold for maximum TSS value

TSS

Maximum TSS value

sensitivity

Sensitivity

Specificity

Specificity

AUC.plot

A ggplot object

Author(s)

Gudrun Carl

References

Carl G, Kuehn I (2017) Spind: a package for computing spatially corrected accuracy measures. Ecography 40: 675-682. DOI: 10.1111/ecog.02593

See Also

th.dep

Examples

data(hook)
data <- hook[ ,1:2]
coord <- hook[ ,3:4]
si2 <- th.indep(data, coord, spatial = TRUE)
si2$AUC
si2$TSS
si2$opt.thresh
si2$plot

Upscaling of smooth components

Description

The analysis is based a wavelet multiresolution analysis using only smooth wavelet components. It is a 2D analysis taking the grid structure and provides scale-specific results for data sampled on a contiguous geographical area. The dataset is assumed to be regular gridded and the grid cells are assumed to be square. The scale-dependent results are graphically displayed.

Usage

upscale(
  f,
  coord,
  wavelet = "haar",
  wtrafo = "dwt",
  pad = mean(f),
  color.maps = FALSE
)

Arguments

Value

A set of plots showing the matrix image at each value for level.

Author(s)

Gudrun Carl

Examples

data(carlinadata)
coords <- carlinadata[ ,4:5]

# Upscaling of smooth components
upscale(carlinadata$land.use, coord = coords)

Wavelet covariance analysis

Description

Calculates the wavelet covariance based on a wavelet multiresolution analysis.

Usage

wavecovar(f1, f2, coord, wavelet = "haar", wtrafo = "dwt")

Arguments

Value

Wavelet covariance for f1 and f2.

Author(s)

Gudrun Carl

See Also

waveslim, WRM, covar.plot, scaleWMRR

Examples

data(carlinadata)

coords <- carlinadata[ ,4:5]
pc <- covar.plot(carlina.horrida ~ aridity + land.use,
                 data = carlinadata,
                 coord = coords,
                 wavelet = 'd4',
                 wtrafo = 'modwt',
                 plot = 'covar')

pc$plot

Wavelet variance analysis

Description

Calculates the wavelet variance based on a wavelet multiresolution analysis.

Usage

wavevar(f, coord, wavelet = "haar", wtrafo = "dwt")

Arguments

Value

Wavelet variance for f.

Author(s)

Gudrun Carl

See Also

waveslim, WRM, covar.plot, scaleWMRR

Examples

data(carlinadata)

coords <- carlinadata[ ,4:5]
pv <- covar.plot(carlina.horrida ~ aridity + land.use,
                 data = carlinadata,
                 coord = coords,
                 wavelet = 'd4',
                 wtrafo = 'modwt',
                 plot = 'var')

pv$plot