Package 'sptotal'

Title: Predicting Totals and Weighted Sums from Spatial Data
Description: Performs predictions of totals and weighted sums, or finite population block kriging, on spatial data using the methods in Ver Hoef (2008) <doi:10.1007/s10651-007-0035-y>. The primary outputs are an estimate of the total, mean, or weighted sum in the region, an estimated prediction variance, and a plot of the predicted and observed values. This is useful primarily to users with ecological data that are counts or densities measured on some sites in a finite area of interest. Spatial prediction for the total count or average density in the entire region can then be done using the functions in this package.
Authors: Matt Higham [cre, aut], Jay Ver Hoef [aut], Bryce Frank [aut], Michael Dumelle [aut]
Maintainer: Matt Higham <[email protected]>
License: GPL (>= 2)
Version: 1.0.1
Built: 2024-11-07 05:28:29 UTC
Source: https://github.com/highamm/sptotal

Help Index

Extract the AIC from a slmfit object for comparing models.

Description

Extract the AIC from a slmfit object for comparing models.

Usage

## S3 method for class 'slmfit'
AIC(object, ...)

Arguments

object

a slmfit object
...

further arguments passed to or from other methods.

Value

The AIC value of the slmfit object. Here, AIC is computed as 2 times the negative log-likelihood plus 2 times the number of model parameters for Maximum Likelihood (ML) and 2 times the negative log-likelihood for REML. For REML, AIC should only be used to compare two models with the same covariates but different spatial covariance structures.

Examples

data(exampledataset) ## load a toy data set
slmobj <- slmfit(formula = counts ~ pred1 + pred2, data = exampledataset,
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
AIC(slmobj)

Data Set with Alaska Moose Counts.

Description

A data set that can be used with the sptotal package. In this example, the counts are of moose on 860 sites of equal area.

Usage

AKmoose_df

Format

A dataframe object. The data frame AKmoose_df contains 860 rows and 8 columns:

elev_mean

The mean elevation for each sitefor each site

strat

A stratification variable (either L or M)

surveyed

Assigned a 1 if the site was surveyed and a 0 otherwise

total

The total moose count on each site (NA if the site was not surveyed)

x

the x-coordinate centroid of the site (TM)

y

the y-coordinate centroid of the site (TM)

lon

the longitudinal centroid of the site

lat

the latitudinal centroid of the site

Source

Alaska Department of Fish and Game, Division of Wildlife Conservation has released this data set under the CC0 (creative commons) license. To the extent possible under law, Alaska Department of Fish and Game, Division of Wildlife Conservation waives all copyright and related or neighboring rights to An Alaskan GSPE (Geospatial Population Estimator) Survey of Moose, AKmoose_df.rda. This work is published from: United States.

Examples

data(AKmoose_df)
names(AKmoose_df)
summary(AKmoose_df)

Plot an Empirical Semi-Variogram of Residuals

Description

check.variogram() has been deprecated: use plot.slmfit() instead. Plots an empirical semi-variogram of the residuals from the spatial linear model with the fitted parametric model as a curve overtop of the binned points. By default, the empirical semi-variogram only shows distances that are less than or equal to the maximum distance in the data set divided by 2. Therefore, it's possible that the REML-fitted model will not "fit" the points perfectly.

Usage

check.variogram(object)

Arguments

object

is an object of class slmfit.

Value

a plot of the empirical semi-variogram with the fitted model overlayed.

Examples

data(exampledataset) ## load a toy data set
slmobj <- slmfit(formula = counts ~ pred1 + pred2, data = exampledataset,
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
## Not Run
## check.variogram(slmobj)

Extract Model Coefficients from a slmfit object

Description

Extract Model Coefficients from a slmfit object

Usage

## S3 method for class 'slmfit'
coef(object, ...)

Arguments

object

a slmfit object
...

further arguments passed to or from other methods.

Value

a vector of fitted model coefficients.

Examples

data(exampledataset) ## load a toy data set
slmobj <- slmfit(formula = counts ~ pred1 + pred2, data = exampledataset,
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
coef(slmobj)

Spatial Correlation Models

Description

Note that, currently, only three of these models are implemented in the sptotal package: corModelExponential(), corModelGaussian(), and corModelSpherical().

Usage

corModelExponential(distance.matrix, range)

corModelGaussian(distance.matrix, range)

corModelSpherical(distance.matrix, range)

Arguments

distance.matrix

The distance matrix for sampled sites
range

The range that determines how quickly covariance among sites tapers

Value

Correlation Matrix

Functions

  • corModelExponential(): Exponential Correlation Structure

  • corModelGaussian(): Gaussian Correlation Structure

  • corModelSpherical(): Spherical Correlation Structure

Data Set with Uncorrelated Poisson Counts.

Description

A toy data set that can be used with the sptotal package. In this example, the true counts are actually uncorrelated, the covariates are generated as uniform random variables, and the sites fall on a regular grid.

Usage

exampledataset

Format

A data frame with 40 rows and 7 variables:

counts

counts, with NA values for unsampled sites

pred1

a possible predictor

pred2

a second possible predictor

xcoords

coordinates on the x-axis

ycoords

coordinates on the y-axis

dummyvar

an extra variable

areavar

Variable for the area of each plot

...

Extract Fitted Values from an slmfit object.

Description

Extract Fitted Values from an slmfit object.

Usage

## S3 method for class 'slmfit'
fitted(object, ...)

Arguments

object

a slmfit object generated from the slmfit() function.
...

further arguments passed to or from other methods.

Value

a vector of fitted values (estimated means)

Examples

data(exampledataset) ## load a toy data set
slmobj <- slmfit(formula = counts ~ pred1 + pred2, data = exampledataset,
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
fitted(slmobj)

Simulate geostatistical data on set of given locations

Description

Spatially correlated data are simulated assuming a multivariate normal random error vector. For simplicity, only "Exponential" and "Spherical" simulation options are given here.

Usage

geostatSim(
  loc.data,
  xcol = "x",
  ycol = "y",
  parsil = 1,
  range = 1,
  nugget = 0,
  minorp = 1,
  rotate = 90,
  extrap = NULL,
  CorModel = "Exponential"
)

Arguments

loc.data

data.frame with x- and y-coordinates of locations for simulated data
xcol

name of the column in loc.data with x-coordinates, default is "x"
ycol

name of the column loc.data with y-coordinates, default is "y"
parsil

partial sill of autocorrelation model, default = 1
range

range of autocorrelation model, default = 1
nugget

range of autocorrelation model, default = 0
minorp

proportion of range in x direction to that of y direction for unrotated anisotropic model, default = 1
rotate

rotation of anisotropic axes, default = 90
extrap

extra covariance parameter
CorModel

autocorrelation model, default = "Exponential". Other possibilities are "Spherical".

Value

data.frame of three columns, the original location data appended with a 3rd column of simulated geostatistical data

Author(s)

Jay Ver Hoef

Examples

locations <- expand.grid(1:10, 1:10)
geostatSim(locations, xcol = "Var1", ycol = "Var2",
parsil = 4, range = 20, nugget = 1, CorModel = "Exponential")

Display basic summary information in a tabular form.

Description

get.predinfo() has been deprecated. Information given is now provided in the basic print of a predict.slmfit() object. Creates a list of tables that shows the prediction, standard error, and confidence interval for the prediction, as well as some summary information about the sample.

Usage

get.predinfo(x, conf_level = 0.9)

Arguments

x

the output of the predict.slmfit() function, of class predict.slmfit
conf_level

is the confidence level for a normal-based confidence interval (default = 0.90).

Value

a list of three tables, including

  • simptab, which contains the prediction and its standard error,

  • confbounds, which contains a confidence interval for the prediction, and

  • outptmat, a table of sampling information, including the number of sites sampled, the total number of sites, the total observed response, and the observed average density (equal to the average response if all site areas are equal).

Examples

data(exampledataset) ## load a toy data set
slmobj <- slmfit(formula = counts ~ pred1 + pred2, data = exampledataset,
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
predobj <- predict(slmobj)
## Not Run
## get.predinfo(predobj)

Create a default map from predictions

Description

Creates a default map for the predictions of unobserved sites. Note that all predictions are stored in a data frame in the output of predict.slmfit(). Therefore, if a user would like to create his or her own plot, he or she can easily do so using this data frame.

Usage

get.predplot(x)

Arguments

x

the output of the predict.slmfit() function, of class predict.slmfit

Value

a plot with x-coordinates on the x-axis and y-coordinates on the y-axis that is coloured by predictions, with points with an X denoting that a site was sampled and filled circles denoting unsampled sites.

Examples

data(exampledataset) ## load a toy data set
slmobj <- slmfit(formula = counts ~ pred1 + pred2, data = exampledataset,
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
predobj <- predict(slmobj)
## Not Run
## get.predplot(predobj)

Computes the Generalized R-squared.

Description

Computes the Generalized R-squared.

Usage

GR2(object)

Arguments

object

is an object of class slmfit.

Value

the value for generalized R-squared

Examples

data(exampledataset) ## load a toy data set
slmobj <- slmfit(formula = counts ~ pred1 + pred2, data = exampledataset,
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
GR2(slmobj)

Convert Lat and Long to Transverse Mercator (TM)

Description

Latitude and Longitude coordinates are converted to TM projection coordinates with a user-defined central meridian. The resulting units from applying the function are kilometers.

Usage

LLtoTM(cm, lat, lon, xcol = "x", ycol = "y", minx = NULL, miny = NULL)

Arguments

cm

is the user defined central median. A common choice is the mean of the longitude values in your data set
lat

is the vector of latitudes
lon

is the vector of longitudes
xcol

is the name of the output TM column of x coordinates
ycol

is the name of the output TM column of y coordinates
minx

is 'NULL' by default and sets the minimum x-coordinate value to 0. This is an optional minimum value for the x-coordinate vector.
miny

is 'NULL' by default and sets the minimum y-coordinate value to 0. This is an optional minimum value for the y-coordinate vector.

Details

This function only should only be used if the coordinates supplied by the user are latitude and longitude. The default TM projection here specifies that both the minimum x and y-coordinate values are 0 scaled to 1 km.

Value

A list with the TM coordinates as the first component of the list. The first component of the list contains x coordinates in the first column and y coordinates in the second column. The remaining elements of the list are the cm, minx, and miny values that were input.

Examples

## Add transverse Mercator x and y coordinates to a data frame with
## latitude/longitude coordinates.
exampledataset$xc_TM_ <- LLtoTM(cm = base::mean(exampledataset[ ,"xcoords"]),
 lat = exampledataset[ ,"ycoords"],
 lon = exampledataset[ ,"xcoords"])$xy[ ,1]
exampledataset$yc_TM_ <- LLtoTM(cm = base::mean(exampledataset[ ,"xcoords"]),
 lat = exampledataset[ ,"ycoords"],
 lon = exampledataset[ ,"xcoords"])$xy[ ,2]

Extract Log-Likelihood from a fitted class slmfit object

Description

Extract Log-Likelihood from a fitted class slmfit object

Usage

loglik.slmfit(object, ...)

Arguments

object

is a class slmfit object
...

additional arguments

Value

the log-likelihood of the model fit in the slmfit object

Examples

data(exampledataset) ## load a toy data set
slmobj <- slmfit(formula = counts ~ pred1 + pred2, data = exampledataset,
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
loglik.slmfit(slmobj)

Covariance Parameter Estimation Function.

Description

The primary purpose of m2LL.FPBK.nodet() is to estimate the spatial covariance parameters using REML. This is a helper function to slmfit().

Usage

m2LL.FPBK.nodet(theta, zcol, XDesign, distmat, CorModel, estmethod)

Arguments

theta

is the parameter vector of (nugget, partialsill, range)
zcol

is the response vector of densities
XDesign

is the design matrix containing the covariates used to predict animal or plant abundance (including a column of 1's for the intercept).
distmat

is the distance matrix of the sampled sites
CorModel

is the geostatistical spatial correlation model to be used. See the corModels documentation for possible models to use.
estmethod

is either "REML" for restricted maximum likelihood or "ML" for maximum likelihood.

Value

A numeric output of minus 2 times the restricted log likelihood to be minimized by 'optim' to obtain spatial parameter estimates.

Constructing the generalized inverse of a matrix

Description

Computes the generalized inverse of a matrix X. This function is used in the m2LL.FPBK.nodet functions in order to estimate the spatial covariance parameters

Usage

mginv(X, tol = sqrt(.Machine$double.eps))

Arguments

X

The matrix to be inverted
tol

The tolerance of the estimation

Value

The generalized inverse matrix

Create a default map from predictions

Description

Creates a default map for the predictions of unobserved sites. Note that all predictions are stored in a data frame in the output of predict.slmfit(). Therefore, if a user would like to create his or her own plot, they can easily do so using this data frame.

Usage

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

Arguments

x

the output of the predict.slmfit() function, of class predict.slmfit
...

further arguments passed to or from other methods.

Value

a plot with x-coordinates on the x-axis and y-coordinates on the y-axis that is coloured by predictions, with points with an X denoting that a site was sampled and filled circles denoting unsampled sites.

Examples

data(exampledataset) ## load a toy data set
slmobj <- slmfit(formula = counts ~ pred1 + pred2, data = exampledataset,
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
predobj <- predict(slmobj)
plot(predobj)

Plot an Empirical Semi-Variogram of Residuals

Description

Plots an empirical semi-variogram of the residuals from the spatial linear model with the fitted parametric model as a curve overtop of the binned points. By default, the empirical semi-variogram only shows distances that are less than or equal to the maximum distance in the data set divided by 2. Therefore, it's possible that the REML-fitted model will not "fit" the points perfectly.

Usage

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

Arguments

x

is an object of class slmfit.
...

further arguments passed to or from other methods.

Value

a plot of the empirical semi-variogram with the fitted model overlayed.

Examples

data(exampledataset) ## load a toy data set
slmobj <- slmfit(formula = counts ~ pred1 + pred2, data = exampledataset,
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
plot(slmobj)

data(exampledataset) ## load a toy data set
exampledataset$strata <- c(rep("A", 19), rep("B", 21))
strataobj <- slmfit(formula = counts ~ pred1 + pred2,
  data = exampledataset, stratacol = "strata",
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
plot(strataobj[[1]])

simulate completely spatially random point patterns.

Description

simulates a completely spatially random point patterns. This function is only used in simulating data sets.

Usage

pointSimCSR(
  npoints = 100,
  lower_x_lim = 0,
  upper_x_lim = 1,
  lower_y_lim = 0,
  upper_y_lim = 1
)

Arguments

npoints

number of points to add that are completely spatially random (CSR), default = 100
lower_x_lim

left limit of boundary, default = 0
upper_x_lim

right limit of boundary, default = 1
lower_y_lim

lower limit of boundary, default = 0
upper_y_lim

upper limit of boundary, default = 1

Value

data.frame of two columns, x-coordinate in the first, and y-coordinate in the second.

Author(s)

Jay Ver Hoef

Creates a systematic grid of points.

Description

Creates a systematic grid of points. This function is only used in simulating data sets.

Usage

pointSimSyst(
  nrow = 10,
  ncol = 10,
  lower_x_lim = 0,
  upper_x_lim = 1,
  lower_y_lim = 0,
  upper_y_lim = 1
)

Arguments

nrow

the number of rows in the systematic grid, default is 10
ncol

the number of cols in the systematic grid, default is 10
lower_x_lim

the lower limit for x-coordinate, default is 0
upper_x_lim

the upper limit for x-coordinate, default is 1
lower_y_lim

the lower limit for y-coordinate, default is 0
upper_y_lim

the upper limit for y-coordinate, default is 1

Value

A data.frame with x- and y-coordinates of simulated locations

Author(s)

Jay Ver Hoef

Perform Finite Population Block Kriging

Description

Uses an object of class slmfit from the slmfit() function to predict the response on the unsampled sites. The column of the data set that has the response should have numeric values for the observed response on the sampled sites and 'NA' for any site that was not sampled. Note that there is no newdata argument to predict.slmfit(): any point in space for which a prediction is needed should be included in the original data set in slmfit() with the response variable as NA.

Usage

## S3 method for class 'slmfit'
predict(object, wtscol = NULL, conf_level = 0.9, ...)

Arguments

object

is an object generated from slmfit()
wtscol

is the name of the column that contains the weights for prediction. The default setting predicts the population total
conf_level

is the confidence level for a prediction interval, 0.90 by default
...

further arguments passed to or from other methods.

Value

a list with

  • the estimated population total

  • the estimated prediction variance

  • a data frame containing

    1. x-coordinates

    2. y-coordinates

    3. density predictions

    4. count predictions

    5. site-by-site density prediction variances

    6. site-by-site count prediction variances

    7. indicator variable for whether or not the each site was sampled

    8. estimated mean for each site

    9. area of each site

  • vector with estimated covariance parameters

  • the formula used to fit the model in slmfit()

  • the confidence level

  • the confidence interval bounds

Examples

data(exampledataset) ## load a toy data set
slmobj <- slmfit(formula = counts ~ pred1 + pred2, data = exampledataset,
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
predict(slmobj)

Perform Finite Population Block Kriging

Description

Uses an object of class stratafit from the stratafit() function to predict the response on the unsampled sites for separate strata. The column of the data set that has the response should have numeric values for the observed response on the sampled sites and 'NA' for any site that was not sampled. Note that there is no newdata argument to predict.stratafit(): any point in space for which a prediction is needed should be included in the original data set in stratafit() with the response variable as NA.

Usage

## S3 method for class 'stratafit'
predict(object, wtscol = NULL, conf_level = 0.9, ...)

Arguments

object

is an object generated from stratafit()
wtscol

is the name of the column that contains the weights for prediction. The default setting predicts the population total
conf_level

by default, 0.90, this is the desired confidence level for a prediction interval
...

further arguments passed to or from other methods.

Value

a list with

  • the estimated population total

  • the estimated prediction variance

  • a data frame containing

    1. x-coordinates

    2. y-coordinates

    3. density predictions

    4. count predictions

    5. site-by-site density prediction variances

    6. site-by-site count prediction variances

    7. indicator variable for whether or not the each site was sampled

    8. estimated mean for each site

    9. area of each site

  • vector with estimated covariance parameters

  • the formula used to fit the model in slmfit()

Examples

data(exampledataset) ## load a toy data set
exampledataset$strata <- c(rep("A", 19), rep("B", 21))
strataobj <- stratafit(formula = counts ~ pred1 + pred2,
 data = exampledataset, stratacol = "strata",
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
predict(strataobj)

Prints a short summary for the predict.slmfit() function.

Description

This function uses the object that is output from predict.slmfit() of class predict.slmfit.

Usage

## S3 method for class 'predict.slmfit'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

x

is a prediction object generated from predict.slmfit()
digits

is the number of digits to be displayed in the model output
...

further arguments passed to or from other methods.

Examples

data(exampledataset) ## load a toy data set
slmobj <- slmfit(formula = counts ~ pred1 + pred2, data = exampledataset,
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
print(predict(slmobj), digits = 4)

Prints a short summary for the predict.stratafit() function.

Description

This function uses the object that is output from predict.stratafit() of class predict.stratafit.

Usage

## S3 method for class 'predict.stratafit'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

x

is a prediction object generated from predict.stratafit()
digits

is the number of digits to be displayed in the model output
...

further arguments passed to or from other methods.

Value

a list with

  • a table of predictions, standard errors, and confidence intervals for each stratum and for the total.

Examples

data(exampledataset) ## load a toy data set
exampledataset$strata <- c(rep("A", 19), rep("B", 21))
strataobj <- stratafit(formula = counts ~ pred1 + pred2,
 data = exampledataset, stratacol = "strata",
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
predict(strataobj)

Prints the fitted coefficient table of a fitted spatial linear model.

Description

This function uses the object that is output from slmfit() of class slmfit.

Usage

## S3 method for class 'slmfit'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

x

is an object generated from slmfit()
digits

is the number of digits to be displayed in the model output
...

further arguments passed to or from other methods.

Value

a list with

  • model formula

  • summary statistics for the residuals.

  • a table of fixed effects estimates and associated standard errors.

  • estimated spatial covariance parameter estimates.

  • generalized r-squared value.

Examples

data(exampledataset) ## load a toy data set
slmobj <- slmfit(formula = counts ~ pred1 + pred2, data = exampledataset,
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
print(slmobj)

Prints the summary of a fitted spatial linear model.

Description

This function uses the object that is output from summary.slmfit().

Usage

## S3 method for class 'summary.slmfit'
print(
  x,
  digits = max(3L, getOption("digits") - 3L),
  signif.stars = getOption("show.signif.stars"),
  ...
)

Arguments

x

is an summary object generated from summary.slmfit()
digits

is the number of digits to be displayed in the model output
signif.stars

is an option to show which predictors are significant.
...

further arguments passed to or from other methods.

Value

a list with

  • model formula

  • summary statistics for the residuals.

  • a table of fixed effects estimates and associated standard errors.

  • estimated spatial covariance parameter estimates.

  • generalized r-squared value.

Examples

data(exampledataset) ## load a toy data set
slmobj <- slmfit(formula = counts ~ pred1 + pred2, data = exampledataset,
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
print(summary(slmobj))

Extract Model Residuals from an slmfit object.

Description

Extract Model Residuals from an slmfit object.

Usage

## S3 method for class 'slmfit'
residuals(object, type = "raw", cross.validation = FALSE, ...)

Arguments

object

a slmfit object generated from the slmfit() function.
type

residual type: "raw" (the default) or "normalized"
cross.validation

a logical (TRUE or FALSE) that indicates whether the residuals computed should be found using leave one out cross-validation. Set to FALSE by default.
...

further arguments passed to or from other methods.

Value

a vector of residuals, consisting of each observed response/density minus the estimated mean, or, in the case of cross-validation, the observed response/density minus the leave-one-out-cross-validation prediction.

Examples

data(exampledataset) ## load a toy data set
slmobj <- slmfit(formula = counts ~ pred1 + pred2, data = exampledataset,
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
residuals(slmobj)
residuals(slmobj, cross.validation = TRUE)

Simulated Spatially Autocorrelated Data.

Description

A simulated data set that can be used with the sptotal package.

Usage

simdata

Format

A data frame object including:

x

The x-coordinate for each site

y

The y-coordinate for each site

X1

Simulated independent variable to be used as a predictor

X2

Simulated independent variable to be used as a predictor

X3

Simulated independent variable to be used as a predictor

X4

Simulated independent variable to be used as a predictor

X5

Simulated independent variable to be used as a predictor

X6

Simulated spatially correlated random variable to be used as a predictor

X7

Simulated spatially correlated random variable to be used as a predictor

F1

Simulated factor variable to be used as a predictor

F2

Simulated factor variable to be used as a predictor

Z

The simulated response variable.

wts1

Prediction weights if estimating an overall mean

wts2

Prediction weights for estimating a total over a subset of 25 contiguous plots

Examples

data(simdata)
names(simdata)
summary(simdata)

Fits a Spatial Linear Model

Description

Estimates regression coefficients and spatial autocorrelation parameters, given spatial coordinates and a model formula.

Usage

slmfit(
  formula,
  data,
  xcoordcol,
  ycoordcol,
  areacol = NULL,
  stratacol = NULL,
  CorModel = "Exponential",
  estmethod = "REML",
  covestimates = c(NA, NA, NA)
)

Arguments

formula

is an R linear model formula specifying the response variable as well as covariates for predicting the response on the unsampled sites.
data

is a data frame or tibble with the response column, the covariates to be used for the block kriging, and the spatial coordinates for all of the sites. Alternatively, data can be an sp Spatial Points Data Frame or sf object with POINT geometry.
xcoordcol

is the name of the column in the data frame with x coordinates or longitudinal coordinates
ycoordcol

is the name of the column in the data frame with y coordinates or latitudinal coordinates
areacol

is the name of the column with the areas of the sites. By default, we assume that all sites have equal area, in which case a vector of 1's is used as the areas.
stratacol

is the name of the the column with the stratification variable, if strata are to be fit separately, with different covariance parameter estimates.
CorModel

is the covariance structure. By default, CorModel is Exponential but other options include the Spherical and Gaussian.
estmethod

is either the default "REML" for restricted maximum likelihood to estimate the covariance parameters and regression coefficients or "ML" to estimate the covariance parameters and regression coefficients. This argument can also be set to "None", in which case covestimates must be provided.
covestimates

is an optional vector of covariance parameter estimates (nugget, partial sill, range). If these are given and estmethod = "None", the the provided vector are treated as the estimators to create the covariance structure.

Value

a list of class slmfit with

  • the spatial covariance estimates

  • the regression coefficient estimates

  • the covariance matrix of the fixed effects

  • minus two times the log-likelihood of the model

  • the names of the predictors

  • the sample size

  • the name of the covariance model used

  • a vector of residuals

  • the design matrix

  • a vector of the sampled densities

  • a list containing

    1. formula, the model formula

    2. data, the data set input as the data argument

    3. xcoordcol, the name of the x-coordinate column

    4. ycoordcol, the name of the y-coordinate column

    5. estmethod, either REML or ML

    6. CorModel, the correlation model used

    7. estimated covariance matrix of all sites

    8. Inverted covariance matrix on the sampled sites

    9. the vector of areas.

Examples

data(exampledataset) ## load a toy data set
slmobj <- slmfit(formula = counts ~ pred1 + pred2, data = exampledataset,
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
summary(slmobj)

data(exampledataset) ## load a toy data set
exampledataset$strata <- c(rep("A", 19), rep("B", 21))
strataobj <- slmfit(formula = counts ~ pred1 + pred2,
  data = exampledataset, stratacol = "strata",
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
summary(strataobj)

sptotal: A package used for performing Finite Population Block Kriging (FPBK) on polygonal count data.

Description

The package provides an option to perform FPBK on counts assuming perfect detection of counts on the sites that were in the survey sample. The functions in the package use methods in (Ver Hoef, 2008, <doi:10.1007/s10651-007-0035-y>)

Details

sptotal Main Functions:

slmfit fits a spatial linear model to the response on the observed/sampled sites.

predict.slmfit uses the spatial linear model fit from slmfit and finite population block kriging to predict the response at unobserved locations. A prediction for the total response as well as a prediction variance are given by default.

Most of the remaining functions in the package are either helper functions or extra optional functions to extract various specific things from an slmfit object, such as residuals, AIC, log-likelihood, etc.

See the Vignette for more details: browseVignettes("sptotal") Reference for Mathematical Details:

Ver Hoef, Jay M. "Spatial methods for plot-based sampling of wildlife populations." A Environmental and Ecological Statistics 15, no. 1 (2008): 3-13.

Fits a Separate Spatial Linear Model for Each Stratum

Description

Estimates regression coefficients and spatial autocorrelation parameters, given spatial coordinates, a model formula, and a stratification variable. Arguments are the same here as they are for slmfit(), with an extra argument for stratacol, the name of the stratification column. Note that stratum can either by incorporated as a covariate in slmfit(), in which case the errors have the same spatial covariance, or, models with differing spatial covariances for the errors can be fit to each level of stratum, as is done here in stratafit().

Usage

stratafit(
  formula,
  data,
  xcoordcol,
  ycoordcol,
  stratacol = NULL,
  areacol = NULL,
  CorModel = "Exponential",
  estmethod = "REML"
)

Arguments

formula

is an R linear model formula specifying the response variable as well as covariates for predicting the response on the unsampled sites.
data

is the data set with the response column, the covariates to be used for the block kriging, and the spatial coordinates for all of the sites.
xcoordcol

is the name of the column in the data frame with x coordinates or longitudinal coordinates
ycoordcol

is the name of the column in the data frame with y coordinates or latitudinal coordinates
stratacol

is the name of the stratification column
areacol

is the name of the column with the areas of the sites. By default, we assume that all sites have equal area, in which case a vector of 1's is used as the areas.
CorModel

is the covariance structure. By default, CorModel is Exponential but other options include the Spherical and Gaussian.
estmethod

is either the default "REML" for restricted maximum likelihood to estimate the covariance parameters and regression coefficients or "ML" to estimate the covariance parameters and regression coefficients.

Value

a list of class slmfit with

  • the spatial covariance estimates

  • the regression coefficient estimates

  • the covariance matrix of the fixed effects

  • minus two times the log-likelihood of the model

  • the names of the predictors

  • the sample size

  • the name of the covariance model used

  • a vector of residuals

  • the design matrix

  • a vector of the sampled densities

  • a list containing

    1. formula, the model formula

    2. data, the data set input as the data argument

    3. xcoordcol, the name of the x-coordinate column

    4. ycoordcol, the name of the y-coordinate column

    5. estmethod, either REML or ML

    6. CorModel, the correlation model used

    7. estimated covariance matrix of all sites

    8. Inverted covariance matrix on the sampled sites

    9. the vector of areas.

Examples

data(exampledataset) ## load a toy data set
exampledataset$strata <- c(rep("A", 19), rep("B", 21))
strataobj <- stratafit(formula = counts ~ pred1 + pred2,
 data = exampledataset, stratacol = "strata",
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
summary(strataobj)

Summarizes a fitted spatial linear model.

Description

In conjunction with print.summary.slmfit(), the output looks similar to output from R's standard lm() function.

Usage

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

Arguments

object

is an object generated from slmfit() of class slmfit.
...

further arguments passed to or from other methods.

Value

a list with

  • model formula

  • a table of fixed effects estimates and associated standard errors

  • estimated spatial covariance parameter estimates

  • residuals

  • generalized r-squared.

Examples

data(exampledataset) ## load a toy data set
slmobj <- slmfit(formula = counts ~ pred1 + pred2, data = exampledataset,
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
summary(slmobj)

Summarizes a fitted spatial linear model with a stratification variable..

Description

If a model is fitted with stratafit(), then this summary function produces summary output for each level of the stratification variable in the same style as the summary.slmfit() function.

Usage

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

Arguments

object

is an object generated from slmfit() of class slmfit.
...

further arguments passed to or from other methods.

Value

a list with

  • model formula

  • a table of fixed effects estimates and associated standard errors

  • estimated spatial covariance parameter estimates

  • residuals

  • generalized r-squared.

Examples

data(exampledataset) ## load a toy data set
exampledataset$strata <- c(rep("A", 25), rep("B", 15))
strataobj <- stratafit(formula = counts ~ pred1 + pred2,
 data = exampledataset, stratacol = "strata",
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
summary(strataobj)

Semi-variogram computation

Description

Compute the empirical semivariogram for a data set with specified x and y spatial coordinates and residuals.

Usage

sv(data, xcoordcol, ycoordcol, residcol, bins = 15, cutoff = NULL, ...)

Arguments

data

A data frame or tibble that contains variables for the x coordinates, y coordinates, and residuals.
xcoordcol

is the name of the column in the data frame with x coordinates or longitudinal coordinates
ycoordcol

is the name of the column in the data frame with y coordinates or latitudinal coordinates
residcol

is the name of the column in the data frame with residuals.
bins

Number of equally spaced semivariogram bins. The default is 15.
cutoff

The maximum spatial distance to be considered. The default is half of the maximum observed distance in the data frame.
...

Additional arguments to be used by stats::dist() for spatial distance calculations.

Value

A data frame with the average distance in each bin (dist), the semivariance (gamma), and the number of unique pairs in each bin (np)

Examples

data(exampledataset) ## load a toy data set
slmobj <- slmfit(formula = counts ~ pred1 + pred2, data = exampledataset,
xcoordcol = 'xcoords', ycoordcol = 'ycoords', areacol = 'areavar')
sampleddataset <- na.omit(exampledataset)
svexample <- data.frame(
  xcoords = sampleddataset$xcoords,
  ycoords = sampleddataset$ycoords,
  resids = residuals(slmobj)
)
svdata <- sv(svexample, "xcoords", "ycoords", "resids")

Dissolved Organic Carbon in U.S. Lakes

Description

These data contain dissolved organic carbon (DOC) in National Lakes Data from the U.S. Environmental Protection Agency

Usage

USlakes

Format

A data frame with 1206 rows and 9 variables:

XCOORD

x-coordinate from US Contiguous Albers Equal Area Conic projection

YCOORD

y-coordinate from US Contiguous Albers Equal Area Conic projection

DOC_RESULT

Analyte value, in mg/L, for Dissolved Organic Carbon

ELEVATION

Elevation at lake coordinates (LAT_DD_N83, LON_DD_N83) from NHD Digital Elevation Map layer

FCIBIG_LIT

Fish cover: index of fish cover due to large structures in the littoral zone

RVFCGNDBARE_RIP

riparian zone and vegetation: fraction of ground lacking cover in the riparian zone

RVFCGNDWOODY_RIP

riparian zone and vegetation: fraction of ground cover by woody vegetation in the riparian zone

RVFPUNDWOODY_RIP

riparian zone and vegetation: fraction of understory with nonwoody cover present in the riparian zone

UID

A unique lake identifier in the EPA lake survey databases

Source

National Aquatic Resource Surveys webpage. We combined site data, DOC data, and habitat metrics to create a data set of 1206 lakes in the conterminous United States.

Examples

data(USlakes)
names(USlakes)
summary(USlakes)