Dataset of Mid-Atlantic Highlands Fish

Description

This dataset was studied by Johnson and Hoeting (2011) for analyzing pollution tolerance in Mid-Atlantic Highlands Fish. Pollution intolerant fish were sampled, and several stream characteristics were measured to assess water quality at 119 sites in the Mid-Atlantic region of the United States. All covariates of the data had been standardized to have mean 0 and variance 1.

Usage

data(AtlanticFish)

Format

A data frame with 119 observations and 12 variables.

LON

Longitude of the location.

LAT

Latitude of the location.

ABUND

Fish abundance at given locations, the discrete response.

ORDER

Strahler stream order, a natural covariate measuring stream size.

DISTOT

Watershed classified as disturbed by human activity, a variable reflecting stream quality.

HAB

An index of fish habitat quality at the stream site, a variable reflecting stream quality.

WSA

Watershed area, a natural covariate.

ELEV

Elevation.

RD

Road density in the watershed, a variable reflecting stream quality.

DO

Concentration of dissolved oxygen in the stream at the sampling site, a stream quality variable.

XFC

Percent of areal fish cover at the sampling site, a stream quality variable.

PCT

Percent of sand in streambed substrate, a stream quality variable.

References

Johnson, D. and Hoeting, J. (2011) Bayesian Multimodel Inference for Geostatistical Regression Models, PLOS ONE, 6:e25677. https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0025677.

Examples

data(AtlanticFish)
str(AtlanticFish)

Compute the Frechet Hoeffding Upper Bound for Given Discrete Marginal Distributions

Description

This function implemented the method of computing the Frechet Hoeffding upper bound for discrete marginals described in Nelsen (1987), which can only be applied to discrete marginals. Four commonly used marginal distributions were implemented. The distribution "nb" (negative binomial) and "zip" (zero-inflated Poisson) are parameterized in terms of the mean and overdispersion, see Han and De Oliveira (2016).

Usage

FHUBdiscrete(marg1, marg2, mu1, mu2, od1 = 0, od2 = 0, binomial.size1 = 1,
 binomial.size2 = 1)

Arguments

Value

A scalar denoting the Frechet Hoeffding upper bound of the two specified marginal.

Author(s)

Zifei Han hanzifei1@gmail.com

References

Nelsen, R. (1987) Discrete bivariate distributions with given marginals and correlation. Communications in Statistics Simulation and Computation, 16:199-208.

Han, Z. and De Oliveira, V. (2016) On the correlation structure of Gaussian copula models for geostatistical count data. Australian and New Zealand Journal of Statistics, 58:47-69.

Han, Z. and De Oliveira, V. (2018) gcKrig: An R Package for the Analysis of Geostatistical Count Data Using Gaussian Copulas. Journal of Statistical Software, 87(13), 1–32. doi: 10.18637/jss.v087.i13.

Examples

## Not run: 
FHUBdiscrete(marg1 = 'nb', marg2 = 'zip',mu1 = 10, mu2 = 2, od1 = 2, od2 = 0.2)
FHUBdiscrete(marg1 = 'binomial', marg2 = 'zip', mu1 = 10, mu2 = 4, binomial.size1 = 25, od2 = 2)
FHUBdiscrete(marg1 = 'binomial', marg2 = 'poisson', mu1 = 0.3, mu2 = 20, binomial.size1 = 1)
NBmu = seq(0.01, 30, by = 0.02)
 fhub <- c()
 for(i in 1:length(NBmu)){
 fhub[i] = FHUBdiscrete(marg1 = 'nb', marg2 = 'nb',mu1 = 10, mu2 = NBmu[i], od1 = 0.2, od2 = 0.2)
}
plot(NBmu, fhub, type='l')
## End(Not run)

Locations and Botanical Classification of Trees in Lansing Woods

Description

The data is aggregated from the dataset lansing in library spatstat, which came from an investigation of a 924 ft x 924 ft (19.6 acres) plot in Lansing Woods, Clinton County, Michigan USA by D.J. Gerrard. The original point process data described the locations of 2,251 trees and their botanical classification (into maples, hickories, black oaks, red oaks, white oaks and miscellaneous trees). The original plot size has been rescaled to the unit square and the number of different types of trees has been counted within squares of length 1/16.

Usage

data(LansingTrees)

Format

A data frame with 256 observations and 8 variables.

Easting

Cartesian x-coordinate of the locations.

Northing

Cartesian y-coordinate of the locations.

maple

Number of maples in the area.

hickory

Number of hickories in the area.

blackoak

Number of black oaks in the area.

redoak

Number of red oaks in the area.

whiteoak

Number of white oaks in the area.

misc

Number of miscellaneous trees in the area.

References

Kazianka, H. (2013) Approximate copula-based estimation and prediction of discrete spatial data. Stoch Environ Res Risk Assess, 27:2015-2026

Examples

data(LansingTrees)
str(LansingTrees)

Location of Successful and Dry Wells

Description

A dataset recording locations of successful and unsuccessful drilling oil wells in the northwest shelf of Delaware basin in New Mexico, a region that is densely drilled but has some sparsely drilled areas. The original dataset was transformed to a central area of about 65 square kilometers, see Hohn (1999), Chapter 6.

Usage

data(OilWell)

Format

A data frame with 333 observations and 3 variables.

Easting

Cartesian x-coordinate of the locations.

Northing

Cartesian y-coordinate of the locations.

Success

A binary variable indicating the success of the drill at given locations. 1 for successful drilling oil wells and 0 for unsuccess.

References

Hohn, M. (1999) Geostatistics and petroleum geology, Second Edition. Springer Science & Business Media, APA

Examples

data(OilWell)
str(OilWell)

Counts of Weed Plants on a Field

Description

The weed species Viola Arvensis was counted within circular frames each of area 0.25 square meter except for 10 missing sites in the first row, from a 20 by 14 rectangular grid, so the total number of locations is 270. Also, the percentages of organic matter in a soil sample are collected. The data was studied by Christensen and Waagepetersen (2002) to investigate whether weed occurrence could be predicted from observations of soil texture and soil chemical properties.

Usage

data(Weed95)

Format

A data frame with 270 observations and 6 variables.

xloc

Cartesian x-coordinate of the locations (in meter).

yloc

Cartesian y-coordinate of the locations (in meter).

weedcount

Number of weed collected at the given site.

scaled Y coord

The scaled Y coordinate with range -1 to 1 as a covariate in regression.

organic

Another chemical component indicating the organic matter of the soil.

dummy

A dummy variable taking values 0 or 1. If 0 it is treated as observed location and 1 treated as predicted location in Christensen and Waagepetersen (2002).

References

Christensen,O. and Waagepetersen,R. (2002) Bayesian Prediction of Spatial Count Data Using Generalized Linear Mixed Models. Biometrics, 58:280-286

Examples

data(Weed95)
str(Weed95)

The Beta Marginal of Class marginal.gc

Description

The Beta marginal used for simulation and computing correlation in the trans-Gaussian random field in function simgc and corrTG of the package gcKrig. It cannot be used in function mlegc nor predgc to make model inferences.

Usage

beta.gc(shape1 = 1, shape2 = 1)

Arguments

Details

The Beta distribution with parameters shape1 = a and shape2 = b has density

\frac{\Gamma(a+b)}{\Gamma(a) \Gamma(b)} x^{a-1} (1-x)^{b-1}

for a > 0, b > 0 and 0 \le x \le 1 where the boundary values at x = 0 or x = 1 are defined as by continuity (as limits).

Value

An object of class marginal.gc representing the marginal component.

Author(s)

Zifei Han hanzifei1@gmail.com

See Also

marginal.gc , binomial.gc , gm.gc , gaussian.gc , negbin.gc , poisson.gc , weibull.gc , zip.gc

The Binomial Marginal of Class marginal.gc

Description

The binomial marginal parameterized in terms of its size and probability.

By default, this function is used for likelihood inference and spatial prediction in function mlegc and predgc of the package gcKrig. When all marginal parameters are given, the function is used for simulation and computing correlation in a trans-Gaussian random field in function simgc and corrTG.

Usage

binomial.gc(link = "logit", size = NULL, prob = NULL)

Arguments

Value

An object of class marginal.gc representing the marginal component.

Author(s)

Zifei Han hanzifei1@gmail.com

See Also

marginal.gc , beta.gc , gm.gc , gaussian.gc , negbin.gc , poisson.gc , weibull.gc , zip.gc

Spatial Correlation Functions for Simulation, Likelihood Inference and Spatial Prediction in Gaussian Copula Models with Geostatistical Count Data

Description

Class of isotropic correlation functions available in the gcKrig library.

Details

By default, range parameter is not provided, so this function is used for likelihood inference and spatial prediction with function mlegc and predgc. Users need to specify if the correlation model includes a nugget effect nugget = TRUE or not nugget = FALSE. For Matern and powered exponential correlation functions, the shape parameter kappa is also required from users.

When both range and nugget parameters are given, the function is used to specify the correlation structure in simulation with function simgc in package gcKrig.

Value

At the moment, the following three correlation functins are implemented:

Author(s)

Zifei Han hanzifei1@gmail.com

References

De Oliveira, V. (2013) Hierarchical Poisson models for spatial count data. Journal of Multivariate Analysis,122:393-408.

Han, Z. and De Oliveira, V. (2018) gcKrig: An R Package for the Analysis of Geostatistical Count Data Using Gaussian Copulas. Journal of Statistical Software, 87(13), 1–32. doi: 10.18637/jss.v087.i13.

See Also

matern.gc , powerexp.gc , spherical.gc

Compute the Correlation in Transformed Gaussian Random Fields

Description

This function implements two general methods for computing the correlation function in a transformed Gaussian random field.

Usage

corrTG(marg1, marg2, corrGauss = 0.5, method = "integral", nrep = 1000,
 kmax = 10, earlystop = FALSE, epscut = 1e-3)

Arguments

Value

If method = "mc" the output is a scalar between 0 and 1, denoting the correlation of the transformed Gaussian random field. If method = "integral" the output is a scalar of the correlation in the transformed Gaussian random field, and a list of the values in the series expansion based on the integral with Hermite polynomials.

Author(s)

Zifei Han hanzifei1@gmail.com

References

De Oliveira, V. (2013) Hierarchical Poisson models for spatial count data. Journal of Multivariate Analysis,122:393-408.

Han, Z. and De Oliveira, V. (2016) On the correlation structure of Gaussian copula models for geostatistical count data. Australian and New Zealand Journal of Statistics, 58:47-69.

Han, Z. and De Oliveira, V. (2018) gcKrig: An R Package for the Analysis of Geostatistical Count Data Using Gaussian Copulas. Journal of Statistical Software, 87(13), 1–32. doi: 10.18637/jss.v087.i13.

Examples

## Not run: 
corrTG(marg1 = poisson.gc(lambda = 10), marg2 = binomial.gc(size = 1, prob = 0.1),
 corrGauss = 0.5, method = "integral", kmax = 10, earlystop = TRUE, epscut = 1e-5)
set.seed(12345)
corrTG(marg1 = poisson.gc(lambda = 10), marg2 = binomial.gc(size = 1, prob = 0.1),
 corrGauss = 0.5, nrep = 100000, method = "mc")
## End(Not run)

The Gaussian Marginal of Class marginal.gc

Description

The Gaussian marginal used for simulation and computing correlation in the trans-Gaussian random field in function simgc and corrTG of the package gcKrig. It cannot be used in function mlegc nor predgc to make model inferences.

Usage

gaussian.gc(mean = 0, sd = 1)

Arguments

Value

An object of class marginal.gc representing the marginal component.

Author(s)

Zifei Han hanzifei1@gmail.com

See Also

marginal.gc , beta.gc , binomial.gc , gm.gc , negbin.gc , poisson.gc , weibull.gc , zip.gc

The Gamma Marginal of Class marginal.gc

Description

The Gamma marginal used for simulation and computing correlation in the trans-Gaussian random field in functions simgc and corrTG of the package gcKrig. It cannot be used in functions mlegc nor predgc to make model inferences.

Usage

gm.gc(shape = 1, rate = 1)

Arguments

Details

The Gamma distribution with parameters shape = a and rate = r has density

\frac{r^{a}}{\Gamma(a)} x^{a-1} exp(-rx)

for x \ge 0, a > 0 and s > 0.

Value

An object of class marginal.gc representing the marginal component.

Author(s)

Zifei Han hanzifei1@gmail.com

See Also

marginal.gc , beta.gc , binomial.gc , gaussian.gc , negbin.gc , poisson.gc , weibull.gc , zip.gc

Marginals for Data Simulation, Correlation Assessment, Likelihood Inference and Spatial Prediction in Gaussian Copula Models for Geostatistical Data

Description

Class of marginals available in gcKrig library for geostatistical data simulation, correlation structure assessment (both continuous and discrete marginals) and model inferences (discrete marginals only). In former cases parameters of the marginals are given by users, otherwise parameters are estimated from the data (except when doing prediction with function predgc, users can choose to either input known estimates or estimate the parameters with input data).

Details

The package gcKrig does not include inference and prediction functionalities for continuous marginals. For inference with continuous marginals, see Masarotto and Varin (2012).

By default, when the marginals are discrete, they are used for estimation with function mlegc and prediction with function predgc. They can be used in function simgc and corrTG as well for the purpose of data simulation and correlation computation in a transformed Gaussian random field (Han and De Oliveira, 2016), if parameter values are specified.

For continuous marginals, they are used for simulation with function simgc and correlation computation with corrTG only, so parameters should always be specified.

Value

At the moment, the following marginals are implemented:

Author(s)

Zifei Han hanzifei1@gmail.com

References

Cribari-Neto, F. and Zeileis, A. (2010) Beta regression in R. Journal of Statistical Software, 34(2), 1–24. doi: 10.18637/jss.v034.i02.

Ferrari, S.L.P. and Cribari-Neto, F. (2004) Beta regression for modeling rates and proportions. Journal of Applied Statistics, 31:799-815.

Han, Z. and De Oliveira, V. (2016) On the correlation structure of Gaussian copula models for geostatistical count data. Australian and New Zealand Journal of Statistics, 58:47-69.

Masarotto, G. and Varin, C. (2012) Gaussian copula marginal regression. Electronic Journal of Statistics, 6:1517-1549.

Masarotto, G. and Varin C. (2017) Gaussian Copula Regression in R. Journal of Statistical Software, 77(8), 1–26. doi: 10.18637/jss.v077.i08.

Han, Z. and De Oliveira, V. (2018) gcKrig: An R Package for the Analysis of Geostatistical Count Data Using Gaussian Copulas. Journal of Statistical Software, 87(13), 1–32. doi: 10.18637/jss.v087.i13.

See Also

beta.gc , binomial.gc , gm.gc , gaussian.gc , negbin.gc , poisson.gc , weibull.gc , zip.gc

The Matern Correlation Function of Class corr.gc

Description

The Matern correlation function in spatial statistics.

By default, range parameter is not available, so this function is used for likelihood inference and spatial prediction in function mlegc and predgc. Users need to specify the shape parameter kappa and if the correlation model includes a nugget effect nugget = TRUE or not nugget = FALSE.

When both range and nugget parameters are given, the function is used for simulation with function simgc in package gcKrig.

Usage

matern.gc(range = NULL, kappa = 0.5, nugget = TRUE)

Arguments

Details

The Matern correlation function with a nugget \tau^2 is of the form:

\rho(h) = \frac{1-\tau^2}{2^{\kappa-1}\Gamma(\kappa)}\Big(\frac{h}{\phi}\Big)^\kappa K_{\kappa}\Big(\frac{h}{\phi}\Big)

when h > 0 and \rho(h) = 1 when h = 0. Here \phi is range parameter, \kappa is the shape parameter and \tau^2 is the nugget parameter. K_\kappa(\cdot) denotes the modified Bessel function of the third kind of order \kappa.

Value

An object of class corr.gc representing the correlation component.

Author(s)

Zifei Han hanzifei1@gmail.com

References

Diggle, P. and Ribeiro, P.J. (2007) Model-based Geostatistics. Springer.

See Also

powerexp.gc , spherical.gc

Maximum Likelihood Estimation in Gaussian Copula Models for Geostatistical Count Data

Description

Computes the maximum likelihood estimates. Two methods are implemented. If method = 'GHK' then the maximum simulated likelihood estimates are computed, if method = 'GQT' then the maximum surrogate likelihood estimates are computed.

Usage

mlegc(y, x = NULL, locs, marginal, corr, effort = 1, longlat = FALSE,
 distscale = 1, method = "GHK", corrpar0 = NULL, ghkoptions = list(nrep
 = c(100, 1000), reorder = FALSE, seed = 12345))

Arguments

Details

This program implemented one simulated likelihood method via sequential importance sampling (see Masarotto and Varin 2012), which is same as the method implemented in package gcmr (Masarotto and Varin 2016) except an antithetic variable is used. It also implemented one surrogate likelihood method via distributional transform (see Kazianka and Pilz 2010), which is generally faster.

The argument effort is the sampling effort (known). It can be used to consider the heterogeneity of the measurement time or area at different locations. The default is 1 for all locations. See Han and De Oliveira (2016) for more details.

Value

A list of class "mlegc" with the following elements:

Author(s)

Zifei Han hanzifei1@gmail.com

References

Han, Z. and De Oliveira, V. (2016) On the correlation structure of Gaussian copula models for geostatistical count data. Australian and New Zealand Journal of Statistics, 58:47-69.

Kazianka, H. and Pilz, J. (2010) Copula-based geostatistical modeling of continuous and discrete data including covariates. Stoch Environ Res Risk Assess 24:661-673.

Masarotto, G. and Varin, C. (2012) Gaussian copula marginal regression. Electronic Journal of Statistics 6:1517-1549. https://projecteuclid.org/euclid.ejs/1346421603.

Masarotto, G. and Varin C. (2017). Gaussian Copula Regression in R. Journal of Statistical Software, 77(8), 1–26. doi: 10.18637/jss.v077.i08.

Han, Z. and De Oliveira, V. (2018) gcKrig: An R Package for the Analysis of Geostatistical Count Data Using Gaussian Copulas. Journal of Statistical Software, 87(13), 1–32. doi: 10.18637/jss.v087.i13.

See Also

gcmr

Examples

## Not run: 
## Fit a Simulated Dataset with 100 locations
grid <- seq(0.05, 0.95, by = 0.1)
xloc <- expand.grid(x = grid, y = grid)[,1]
yloc <- expand.grid(x = grid, y = grid)[,2]
set.seed(123)
simData1 <- simgc(locs = cbind(xloc,yloc), sim.n = 1,
 marginal = negbin.gc(mu = exp(1+xloc), od = 1),
 corr = matern.gc(range = 0.4, kappa = 0.5, nugget = 0))
simFit1 <- mlegc(y = simData1$data, x = xloc, locs = cbind(xloc,yloc),
 marginal = negbin.gc(link = 'log'),
 corr = matern.gc(kappa = 0.5, nugget = FALSE), method = 'GHK')
simFit2 <- mlegc(y = simData1$data, x = xloc, locs = cbind(xloc,yloc),
 marginal = negbin.gc(link = 'log'),
 corr = matern.gc(kappa = 0.5, nugget = FALSE), method = 'GQT')
#summary(simFit1);summary(simFit2)
#plot(simFit1);plot(simFit2)
## Time consuming examples
## Fit a real dataset with 70 sampling locations.
data(Weed95)
weedobs <- Weed95[Weed95$dummy==1, ]
weedpred <- Weed95[Weed95$dummy==0, ]
Weedfit1 <- mlegc(y = weedobs$weedcount, x = weedobs[,4:5], locs = weedobs[,1:2],
 marginal = poisson.gc(link='log'),
 corr = matern.gc(kappa = 0.5, nugget = TRUE),
 method = 'GHK')
summary(Weedfit1)
plot(Weedfit1)
## Fit a real dataset with 256 locations
data(LansingTrees)
Treefit1 <- mlegc(y = LansingTrees[,3], x = LansingTrees[,4], locs = LansingTrees[,1:2],
 marginal = negbin.gc(link = 'log'),
 corr = matern.gc(kappa = 0.5, nugget = FALSE), method = 'GHK')
summary(Treefit1)
plot(Treefit1)
# Try to use GQT method
Treefit2<- mlegc(y = LansingTrees[,3], x = LansingTrees[,4],
 locs = LansingTrees[,1:2], marginal = poisson.gc(link='log'),
 corr = matern.gc(kappa = 0.5, nugget = TRUE), method = 'GQT')
summary(Treefit2)
plot(Treefit2)
## Fit a real dataset with randomized locations
data(AtlanticFish)
Fitfish <- mlegc(y = AtlanticFish[,3], x = AtlanticFish[,4:6], locs = AtlanticFish[,1:2],
 longlat = TRUE, marginal = negbin.gc(link='log'),
 corr = matern.gc(kappa = 0.5, nugget = TRUE), method = 'GHK')
summary(Fitfish)
## Fit a real dataset with binomial counts; see Masarotto and Varin (2016).
library(gcmr)
data(malaria)
malariax <- data.frame(netuse = malaria$netuse,
 green = malaria$green/100,
 phc = malaria$phc)
Fitmalaria <- mlegc(y = malaria$cases, x = malariax, locs = malaria[,1:2],
 marginal = binomial.gc(link='logit'), corrpar0 = 1.5,
 corr = matern.gc(kappa = 0.5, nugget = FALSE),
 distscale = 0.001, effort = malaria$size, method = 'GHK')
summary(Fitmalaria)
## Fit a real spatial binary dataset with 333 locations using probit link
data(OilWell)
Oilest1 <- mlegc(y = OilWell[,3], x = NULL, locs = OilWell[,1:2],
 marginal = binomial.gc(link = 'probit'),
 corr = matern.gc(nugget = TRUE), method = 'GHK')
summary(Oilest1)
plot(Oilest1, col = 2)
## End(Not run)

Computing Multivariate Normal Rectangle Probability

Description

Computes the multivariate normal rectangle probability for arbitrary limits and covariance matrices using (reordered) sequential importance sampling.

Usage

mvnintGHK(mean, sigma, lower, upper, nrep = 5000, log = TRUE,
 reorder = TRUE)

Arguments

Details

This program implemented the Geweke-Hajivassiliou-Keane simulator of computing the multivariate normal rectangle probability. For more details see Keane (1994). Also a variable reordering algorithm in Gibson, etal (1994) was implemented.

Note that both -Inf and Inf may be specified in lower and upper.

Value

A list of the following two components:

Author(s)

Zifei Han hanzifei1@gmail.com

References

Gibson GJ., Glasbey CA. and Elston DA. (1994) Monte Carlo evaluation of multivariate normal integrals and sensitivity to variate ordering. Advances in Numerical Methods and Applications, World Scientific Publishing, River Edge.

Keane, M. (1994) A computationally practical simulation estimator for panel data. Econometrica, 62:95-116.

See Also

pmvnorm

Examples

mvnintGHK(mean = rep(0, 51), sigma = diag(0.2, 51) + matrix(0.8, 51, 51),
 lower = rep(-2,51), upper = rep(2,51), nrep = 10000)

The Negative Binomial Marginal of Class marginal.gc

Description

The negative binomial marginal parameterized in terms of its mean and overdispersion.

By default, this function is used for likelihood inference and spatial prediction in functions mlegc and predgc of the package gcKrig. When all marginal parameters are given, the function is used for simulation and computing correlation in a trans-Gaussian random field in functions simgc and corrTG.

Usage

negbin.gc(link = "log", mu = NULL, od = NULL)

Arguments

Details

The negative binomial distribution with parameters mu = a and od = 1/b has density

\frac{\Gamma(y+b)}{\Gamma(b)y!} \Big(\frac{b}{b+a}\Big)^b \Big(1 - \frac{b}{b+a}\Big)^y

which is called NB2 by Cameron and Trivedi (2013). Under this parameterization, var(Y)= mu + od*mu^2, where mu is the mean parameter and od is the overdispersion parameter. For more details see Han and De Oliveira (2016).

Value

An object of class marginal.gc representing the marginal component.

Author(s)

Zifei Han hanzifei1@gmail.com

References

Cameron,A.C. and Trivedi,P.K. (2013) Regression Analysis of Count Data. Cambridge University Press, 2nd Edition.

Han, Z. and De Oliveira, V. (2016) On the correlation structure of Gaussian copula models for geostatistical count data. Australian and New Zealand Journal of Statistics, 58:47-69.

See Also

marginal.gc , beta.gc , binomial.gc , gm.gc , gaussian.gc , poisson.gc , weibull.gc , zip.gc

Plot Geostatistical Data and Fitted Mean

Description

Four plots can be generated: the 2-D level plot or 3-D scatterplot with the number of counts or fitted values.

Usage

## S3 method for class 'mlegc'
plot(x, plotdata = "Observed", plottype = "2D", xlab = "xloc", ylab = "yloc",
 xlim = NULL, ylim = NULL, pch = 20, textcex = 0.8, plotcex = 1,
 angle = 60, col = 4, col.regions = gray(90:0/100),...)
 

Arguments

Author(s)

Zifei Han hanzifei1@gmail.com

See Also

plot.simgc , plot.predgc

Plot Geostatistical Data at Sampling and Prediction Locations

Description

Five plots can be generated. A level plot with the number of counts at both observed and prediction locations; a level plot with predicted means (intensity); a level plot with the predicted counts; a level plot with estimated variances of the prediction; a 3-D scatter plot with both observed and predicted counts.

Usage

## S3 method for class 'predgc'
plot(x, plottype = "2D", xlab = "xloc", ylab = "yloc", xlim = NULL,
 ylim = NULL, pch = 20, textcex = 0.6, plotcex = 1, angle = 60,
 col = c(2, 4), col.regions = gray(90:0/100),...)
 

Arguments

Author(s)

Zifei Han hanzifei1@gmail.com

See Also

plot.simgc , plot.mlegc , mlegc , predgc

Plot Geostatistical Data Simulated From Gaussian Copula

Description

Three plots will be generated. A level plot with the number of counts at given locations; a level plot with point referenced locations and varying colors and a 3-D scatter plot.

Usage

## S3 method for class 'simgc'
plot(x, index = 1, plottype = "Text", xlab = "xloc", ylab = "yloc",
 xlim = NULL, ylim = NULL, pch = 20, textcex = 0.8, plotcex = 1,
 angle = 60, col = 4, col.regions = gray(90:0/100),...)
 

Arguments

Author(s)

Zifei Han hanzifei1@gmail.com

See Also

plot.mlegc , plot.predgc

Plot Geostatistical Count Data

Description

This funtion generates two plots describing a geostatistical count data. The first plot is a bubble plot with size proportional to the response. The second plot is a lattice plot with text describing the number of counts.

Usage

plotgc(data = NULL, locs = NULL, bdry = NULL, col = 2, pch = 1,
 textcex = 1, col.regions = gray(90:0/100), size=c(0.3, 2.7), ...)

Arguments

Author(s)

Zifei Han hanzifei1@gmail.com

See Also

plot.simgc plot.mlegc , plot.predgc

The Poisson Marginal of Class marginal.gc

Description

The Poisson marginal parameterized in terms of its mean.

By default, this function is used for likelihood inference and spatial prediction in function mlegc and predgc of the package gcKrig. When all marginal parameters are given, the function is used for simulation and computing correlation in a trans-Gaussian random field in function simgc and corrTG.

Usage

poisson.gc(link = "log", lambda = NULL)

Arguments

Value

An object of class marginal.gc representing the marginal component.

Author(s)

Zifei Han hanzifei1@gmail.com

See Also

marginal.gc , beta.gc , binomial.gc , gm.gc , gaussian.gc , negbin.gc , weibull.gc , zip.gc

The Powered Exponential Correlation Function of Class corr.gc

Description

The powered exponential correlation function in spatial statistics.

By default, range parameter is not available, so this function is used for likelihood inference and spatial prediction in function mlegc and predgc. Users need to specify the shape parameter kappa and if the correlation model includes a nugget effect nugget = TRUE or not nugget = FALSE.

When both range and nugget parameters are given, the function is used for simulation with function simgc in package gcKrig.

Usage

powerexp.gc(range = NULL, kappa = 1, nugget = TRUE)

Arguments

Details

The powered exponential correlation function with a nugget \tau^2 is of the form:

\rho(h) = (1-\tau^2) exp((-h/\phi)^\kappa)

when h > 0 and \rho(h) = 1 when h = 0. Here h is distance, \phi is range parameter, \kappa is the shape parameter and \tau^2 is the nugget effect.

When using the powered exponential correlation function, note that 0<\kappa \le 2.

Value

An object of class corr.gc representing the correlation component.

Author(s)

Zifei Han hanzifei1@gmail.com

See Also

matern.gc , spherical.gc

Prediction at Unobserved Locations in Gaussian Copula Models for Geostatistical Count Data

Description

Computes the plug-in prediction at unobserved sites. Two methods are implemented. If method = 'GHK' then the maximum simulated likelihood estimates are computed and the sequential importance sampling method is used in the integral evaluation. If method = 'GQT' then the maximum surrogate likelihood estimates are computed and the generalized quantile transform method is used in integral approximation.

Usage

predgc(obs.y, obs.x = NULL, obs.locs, pred.x = NULL, pred.locs,
 longlat = FALSE, distscale = 1, marginal, corr, obs.effort = 1,
 pred.effort = 1, method = "GHK", estpar = NULL, corrpar0 = NULL,
 pred.interval = NULL, parallel = FALSE,
 ghkoptions = list(nrep = c(100,1000), reorder = FALSE, seed = 12345),
 paralleloptions = list(n.cores = 2, cluster.type = "SOCK"))

Arguments

Details

This program implemented two methods in predicting the response at unobserved sites. See mlegc .

The argument obs.effort and pred.effort are the sampling effort (known). It can be used to consider heterogeneity of the measurement time or area at different locations. The default is 1 for all locations. See Han and De Oliveira (2016) for more details.

The program computes two types of prediction intervals at a given confidence level. The shortest prediction interval is obtained from evaluating the highest to lowest prediction densities; the equal tail prediction interval has equal tail probabilities.

Value

A list of class "predgc" with the following elements:

Author(s)

Zifei Han hanzifei1@gmail.com

References

Han, Z. and De Oliveira, V. (2016) On the correlation structure of Gaussian copula models for geostatistical count data. Australian and New Zealand Journal of Statistics, 58:47-69.

Kazianka, H. and Pilz, J. (2010) Copula-based geostatistical modeling of continuous and discrete data including covariates. Stoch Environ Res Risk Assess 24:661-673.

Kazianka, H. (2013) Approximate copula-based estimation and prediction of discrete spatial data. Stoch Environ Res Risk Assess 27:2015-2026.

Masarotto, G. and Varin, C. (2012) Gaussian copula marginal regression. Electronic Journal of Statistics 6:1517-1549. https://projecteuclid.org/euclid.ejs/1346421603.

Masarotto, G. and Varin C. (2017). Gaussian Copula Regression in R. Journal of Statistical Software, 77(8), 1–26. doi: 10.18637/jss.v077.i08.

Han, Z. and De Oliveira, V. (2018) gcKrig: An R Package for the Analysis of Geostatistical Count Data Using Gaussian Copulas. Journal of Statistical Software, 87(13), 1–32. doi: 10.18637/jss.v087.i13.

See Also

gcmr ; mlegc

Examples

## Not run: 
## For fast check predict at four locations only
data(Weed95)
weedobs <- Weed95[Weed95$dummy==1, ]
weedpred <- Weed95[Weed95$dummy==0, ]
predweed1 <- predgc(obs.y = weedobs$weedcount, obs.x = weedobs[,4:5], obs.locs = weedobs[,1:2],
 pred.x = weedpred[1:4,4:5], pred.locs = weedpred[1:4,1:2],
 marginal = negbin.gc(link = 'log'), pred.interval = 0.9,
 corr = matern.gc(kappa = 0.5, nugget = TRUE), method = 'GHK')
#summary(predweed1)
#plot(predweed1)
## Time consuming examples
## Weed prediction at 200 locations using parallel programming
predweed2 <- predgc(obs.y = weedobs$weedcount, obs.x = weedobs[,4:5], obs.locs = weedobs[,1:2],
 pred.x = weedpred[,4:5], pred.locs = weedpred[,1:2],
 marginal = negbin.gc(link = 'log'),
 corr = matern.gc(kappa = 0.5, nugget = TRUE), method = 'GHK',
 pred.interval = 0.95, parallel = TRUE,
 paralleloptions = list(n.cores = 4))
#summary(predweed2)
#plot(predweed2)
## A more time consuming example for generating a prediction map at a fine grid
data(OilWell)
gridstep <- seq(0.5, 30.5, length = 40)
locOilpred <- data.frame(Easting = expand.grid(gridstep, gridstep)[,1],
 Northing = expand.grid(gridstep, gridstep)[,2])
PredOil <- predgc(obs.y = OilWell[,3], obs.locs = OilWell[,1:2], pred.locs = locOilpred,
 marginal = binomial.gc(link = 'logit'),
 corr = matern.gc(nugget = FALSE), obs.effort = 1,
 pred.effort = 1, method = 'GHK',
 parallel = TRUE, paralleloptions = list(n.cores = 4))
PredMat <- summary(PredOil)
## To generate better prediction maps
library(colorspace)
filled.contour(seq(0.5,30.5,length=40), seq(0.5,30.5,length=40),
 matrix(PredMat$predMean,40,), zlim = c(0, 1), col=rev(heat_hcl(12)),
 nlevels=12, xlab = "Eastings", ylab = "Northings",
 plot.axes = {axis(1); axis(2); points(OilWell[,1:2], col = 1,
 cex = 0.25 + 0.25*OilWell[,3])})
filled.contour(seq(0.5,30.5,length=40), seq(0.5,30.5,length=40),
 matrix(PredMat$predVar,40,),
 zlim = c(0, 0.3), col = rev(heat_hcl(12)), nlevels = 10,
 xlab = "Eastings", ylab = "Northings",
 plot.axes = {axis(1); axis(2); points(OilWell[,1:2], col = 1,
 cex = 0.25 + 0.25*OilWell[,3])})
## End(Not run)

Profile Likelihood Based Confidence Interval of Parameters for Gaussian Copula Models in Geostatistical Count Data

Description

This function computes the (approximate) profile likelihood based confidence interval. The algorithm starts by choosing two starting points at different sides of the MLE and using an iterative process to find the approximate lower and upper bound.

Usage

## S3 method for class 'mlegc'
profile(fitted, par.index, alpha = 0.05, start.point = NULL,
 method = 'GQT', nrep = 1000, seed = 12345, ...)
 

Arguments

Value

Lower and upper bounds of the approximate confidence interval.

Author(s)

Zifei Han hanzifei1@gmail.com

References

Masarotto, G. and Varin, C. (2012) Gaussian copula marginal regression. Electronic Journal of Statistics 6:1517-1549. https://projecteuclid.org/euclid.ejs/1346421603.

Masarotto, G. and Varin C. (2017). Gaussian Copula Regression in R. Journal of Statistical Software, 77(8), 1–26. doi: 10.18637/jss.v077.i08.

Han, Z. and De Oliveira, V. (2018) gcKrig: An R Package for the Analysis of Geostatistical Count Data Using Gaussian Copulas. Journal of Statistical Software, 87(13), 1–32. doi: 10.18637/jss.v087.i13.

See Also

mlegc

Examples

## Not run: 
data(LansingTrees)
Treefit4 <- mlegc(y = LansingTrees[,3], x = LansingTrees[,4],
 locs = LansingTrees[,1:2], marginal = zip.gc(link = 'log'),
 corr = matern.gc(kappa = 0.5, nugget = TRUE), method = 'GHK')
summary(Treefit4)
profile(Treefit4, 1, 0.05, method = 'GHK', nrep = 1000, seed = 12345)
profile(Treefit4, 2, 0.05, method = 'GHK', nrep = 1000, seed = 12345)
profile(Treefit4, 3, 0.05, method = 'GHK', nrep = 1000, seed = 12345)
profile(Treefit4, 4, 0.05, method = 'GHK', nrep = 1000, seed = 12345)
profile(Treefit4, 5, 0.05, method = 'GHK', nrep = 1000, seed = 12345)
## End(Not run)

Simulate Geostatistical Data from Gaussian Copula Model at Given Locations

Description

Simulate geostatistical data from Gaussian copula model at given locations. This function can simulate multiple datasets simultaneously.

Usage

simgc(locs, sim.n = 1, marginal, corr, longlat = FALSE)

Arguments

Value

A list of two elements:

Author(s)

Zifei Han hanzifei1@gmail.com

Examples

grid <- seq(0.05, 0.95, by = 0.1)
xloc <- expand.grid(x = grid, y = grid)[,1]
yloc <- expand.grid(x = grid, y = grid)[,2]
set.seed(12345)
sim1 <- simgc(locs = cbind(xloc,yloc), sim.n = 10, marginal = negbin.gc(mu = 5, od = 1),
 corr = matern.gc(range = 0.3, kappa = 0.5, nugget = 0.1))
#plot(sim1, index = 1)

The Spherical Correlation Function of Class corr.gc

Description

The spherical correlation function in spatial statistics.

By default, range parameter is not available, so this function is used for likelihood inference and spatial prediction in function mlegc and predgc. Users need to specify if the correlation model includes a nugget effect nugget = TRUE or not nugget = FALSE.

When both range and nugget parameters are given, the function is used for simulation with function simgc in package gcKrig.

Usage

spherical.gc(range = NULL, nugget = TRUE)

Arguments

Details

The spherical correlation function with a nugget \tau^2 is of the form:

\rho(h) = (1-\tau^2) (1 - 1.5(h/\phi) + 0.5(-h/\phi)^3)

when h > 0 and \rho(h) = 1 when h = 0, h is distance.

Value

An object of class corr.gc representing the correlation component.

Author(s)

Zifei Han hanzifei1@gmail.com

See Also

matern.gc , spherical.gc

Methods for Extracting Information from Fitted Object of Class mlegc

Description

Return a summary table of results from model fitting.

Usage

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

Arguments

Value

A table summary of the estimates, standard error, z-value and several information criteria.

Author(s)

Zifei Han hanzifei1@gmail.com

See Also

mlegc

Methods for Extracting Information from Fitted Object of Class predgc

Description

Output a summary data frame.

Usage

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

Arguments

Value

A table including the following information:

Author(s)

Zifei Han hanzifei1@gmail.com

See Also

mlegc , predgc

Covariance Matrix of the Maximum Likelihood Estimates

Description

Calculate covariance and correlation matrix.

Usage

## S3 method for class 'mlegc'
vcov(object, digits = max(3, getOption("digits") - 3), ...)
 

Arguments

Value

The estimated variance-covariance matrix and estimated correlation matrix.

Author(s)

Zifei Han hanzifei1@gmail.com

See Also

mlegc

The Weibull Marginal of Class marginal.gc

Description

The Weibull marginal used for simulation and computing correlation in the trans-Gaussian random field in function simgc and corrTG of the package gcKrig. It cannot be used in function mlegc nor predgc to make model inferences.

Usage

weibull.gc(shape = 1, scale = 1)

Arguments

Details

The Weibull distribution with shape parameter a and scale parameter b has density given by

(a/b) (x/b)^{a-1} exp(-(x/b)^a)

Value

An object of class marginal.gc representing the marginal component.

Author(s)

Zifei Han hanzifei1@gmail.com

See Also

marginal.gc , beta.gc , binomial.gc , gm.gc , gaussian.gc , negbin.gc , poisson.gc , zip.gc

The Zero-inflated Poisson Marginal of Class marginal.gc

Description

The zero-inflated Poisson marginal parameterized in terms of its mean and overdispersion.

By default, this function is used for likelihood inference and spatial prediction in function mlegc and predgc of the package gcKrig. When all marginal parameters are given, the function is used for simulation and computing correlation in a trans-Gaussian random field in function simgc and corrTG.

Usage

zip.gc(link = "log", mu = NULL, od = NULL)

Arguments

Details

The zero-inflated Poisson distribution with parameters mu = a and od = b has density

b/(1+b) + exp(-(a+ab))/(1+b)

when y = 0, and

exp(-(a+ab))*(a+ab)^y/((1+b)y!)

when y = 1, 2, \ldots

Under this parameterization, var(Y)= mu + od*mu^2, where mu is the mean parameter and od is the overdispersion parameter. For more details see Han and De Oliveira (2016).

Value

An object of class marginal.gc representing the marginal component.

Author(s)

Zifei Han hanzifei1@gmail.com

References

Han, Z. and De Oliveira, V. (2016) On the correlation structure of Gaussian copula models for geostatistical count data. Australian and New Zealand Journal of Statistics, 58:47-69.

See Also

marginal.gc , beta.gc , binomial.gc , gm.gc , gaussian.gc , negbin.gc , poisson.gc , weibull.gc