Package 'convoSPAT' reference manual

Title:	Convolution-Based Nonstationary Spatial Modeling
Description:	Fits convolution-based nonstationary Gaussian process models to point-referenced spatial data. The nonstationary covariance function allows the user to specify the underlying correlation structure and which spatial dependence parameters should be allowed to vary over space: the anisotropy, nugget variance, and process variance. The parameters are estimated via maximum likelihood, using a local likelihood approach. Also provided are functions to fit stationary spatial models for comparison, calculate the Kriging predictor and standard errors, and create various plots to visualize nonstationarity.
Authors:	Mark D. Risser [aut, cre]
Maintainer:	Mark D. Risser <[email protected]>
License:	MIT + file LICENSE
Version:	1.2.5
Built:	2025-02-12 04:41:05 UTC
Source:	https://github.com/markdrisser/convospat

Fit the stationary spatial model

Description

Aniso_fit estimates the parameters of the stationary spatial model. Required inputs are the observed data and locations (a geoR object with $coords and $data). Optional inputs include the covariance model (exponential is the default).

Usage

Aniso_fit(geodata = NULL, sp.SPDF = NULL, coords = geodata$coords,
  data = geodata$data, cov.model = "exponential", mean.model = data ~ 1,
  fixed.nugg2.var = NULL, method = "reml", fix.tausq = FALSE, tausq = 0,
  fix.kappa = FALSE, kappa = 0.5, local.pars.LB = NULL,
  local.pars.UB = NULL, local.ini.pars = NULL)
Aniso_fit(geodata = NULL, sp.SPDF = NULL, coords = geodata$coords,
  data = geodata$data, cov.model = "exponential", mean.model = data ~ 1,
  fixed.nugg2.var = NULL, method = "reml", fix.tausq = FALSE, tausq = 0,
  fix.kappa = FALSE, kappa = 0.5, local.pars.LB = NULL,
  local.pars.UB = NULL, local.ini.pars = NULL)

Arguments

`geodata`	A list containing elements `coords` and `data` as described next. Typically an object of the class "`geodata`", although a geodata object only allows `data` to be a vector (no replicates). If not provided, the arguments `coords` and `data` must be provided instead.
`sp.SPDF`	A "`SpatialPointsDataFrame`" object, which contains the spatial coordinates and additional attribute variables corresponding to the spatoal coordinates
`coords`	An N x 2 matrix where each row has the two-dimensional coordinates of the N data locations. By default, it takes the `coords` component of the argument `geodata`, if provided.
`data`	A vector or matrix with N rows, containing the data values. Inputting a vector corresponds to a single replicate of data, while inputting a matrix corresponds to replicates. In the case of replicates, the model assumes the replicates are independent and identically distributed.
`cov.model`	A string specifying the model for the correlation function; following `geoR`, defaults to `"exponential"`. Options available in this package are: "`exponential`", `"cauchy"`, `"matern"`, `"circular"`, `"cubic"`, `"gaussian"`, `"spherical"`, and `"wave"`. For further details, see documentation for `cov.spatial`.
`mean.model`	An object of class `formula`, specifying the mean model to be used. Defaults to an intercept only.
`fixed.nugg2.var`	Optional; describes the variance/covariance for a fixed (second) nugget term (represents a known error term). Either a vector of length N containing a station-specific variances (implying independent error) or an NxN covariance matrix (implying dependent error). Defaults to zero.
`method`	Indicates the estimation method, either maximum likelihood (`"ml"`) or restricted maximum likelihood (`"reml"`).
`fix.tausq`	Logical; indicates whether the default nugget term (tau^2) should be fixed (`TRUE`) or estimated (`FALSE`). Defaults to `FALSE`.
`tausq`	Scalar; fixed value for the nugget variance (when `fix.tausq = TRUE`).
`fix.kappa`	Logical; indicates if the kappa parameter should be fixed (`TRUE`) or estimated (`FALSE`). Defaults to `FALSE` (only valid for `cov.model = "matern"` and `cov.model = "cauchy"`).
`kappa`	Scalar; value of the kappa parameter. Only used if `fix.kappa = TRUE`.
`local.pars.LB`, `local.pars.UB`	Optional vectors of lower and upper bounds, respectively, used by the `"L-BFGS-B"` method option in the `optim` function for the local parameter estimation. Each vector must be of length five, containing values for lam1, lam2, tausq, sigmasq, and nu. Default for `local.pars.LB` is `rep(1e-05,5)`; default for `local.pars.UB` is `c(max.distance/2, max.distance/2, 4resid.var, 4resid.var, 100)`, where `max.distance` is the maximum interpoint distance of the observed data and `resid.var` is the residual variance from using `lm` with `mean.model`.
`local.ini.pars`	Optional vector of initial values used by the `"L-BFGS-B"` method option in the `optim` function for the local parameter estimation. The vector must be of length five, containing values for lam1, lam2, tausq, sigmasq, and nu. Defaults to `c(max.distance/10, max.distance/10, 0.1resid.var, 0.9resid.var, 1)`, where `max.distance` is the maximum interpoint distance of the observed data and `resid.var` is the residual variance from using `lm` with `mean.model`.

Value

A list with the following components:

`MLEs.save`	Table of local maximum likelihood estimates for each mixture component location.
`data`	Observed data values.
`beta.GLS`	Vector of generalized least squares estimates of beta, the mean coefficients.
`beta.cov`	Covariance matrix of the generalized least squares estimate of beta.
`Mean.coefs`	"Regression table" for the mean coefficient estimates, listing the estimate, standard error, and t-value.
`Cov.mat`	Estimated covariance matrix (`N.obs` x `N.obs`) using all relevant parameter estimates.
`Cov.mat.chol`	Cholesky of `Cov.mat` (i.e., `chol(Cov.mat)`), the estimated covariance matrix (`N.obs` x `N.obs`).
`aniso.pars`	Vector of MLEs for the anisotropy parameters lam1, lam2, eta.
`aniso.mat`	2 x 2 anisotropy matrix, calculated from `aniso.pars`.
`tausq.est`	Scalar maximum likelihood estimate of tausq (nugget variance).
`sigmasq.est`	Scalar maximum likelihood estimate of sigmasq (process variance).
`kappa.MLE`	Scalar maximum likelihood estimate for kappa (when applicable).
`fixed.nugg2.var`	N x N matrix with the fixed variance/covariance for the second (measurement error) nugget term (defaults to zero).
`cov.model`	String; the correlation model used for estimation.
`coords`	N x 2 matrix of observation locations.
`global.loglik`	Scalar value of the maximized likelihood from the global optimization (if available).
`Xmat`	Design matrix, obtained from using `lm` with `mean.model`.
`fix.kappa`	Logical, indicating if kappa was fixed (`TRUE`) or estimated (`FALSE`).
`kappa`	Scalar; fixed value of kappa.

Examples

# Using iid standard Gaussian data
aniso.fit <- Aniso_fit( coords = cbind(runif(100), runif(100)),
data = rnorm(100) )


# Using iid standard Gaussian data
aniso.fit <- Aniso_fit( coords = cbind(runif(100), runif(100)),
data = rnorm(100) )

Evaluation criteria

Description

Calculate three evaluation criteria – continuous rank probability score (CRPS), prediction mean square deviation ratio (pMSDR), and mean squared prediction error (MSPE) – comparing hold-out data and predictions.

Usage

evaluate_CV(holdout.data, pred.mean, pred.SDs)
evaluate_CV(holdout.data, pred.mean, pred.SDs)

Arguments

`holdout.data`	Observed/true data that has been held out for model comparison.
`pred.mean`	Predicted mean values corresponding to the hold-out locations.
`pred.SDs`	Predicted standard errors corresponding to the hold-out locations.

Value

A list with the following components:

`CRPS`	The CRPS averaged over all hold-out locations.
`MSPE`	The mean squared prediction error.
`pMSDR`	The prediction mean square deviation ratio.

Examples

## Not run: 
evaluate_CV( holdout.data = simdata$sim.data[holdout.index],
pred.mean = pred.NS$pred.means, pred.SDs = pred.NS$pred.SDs )

## End(Not run)

## Not run: 
evaluate_CV( holdout.data = simdata$sim.data[holdout.index],
pred.mean = pred.NS$pred.means, pred.SDs = pred.NS$pred.SDs )

## End(Not run)

Calculate mixture component kernel matrices.

Description

f_mc_kernels calculates spatially-varying mixture component kernels using generalized linear models for each of the eigenvalues (lam1 and lam2) and the angle of rotation (eta).

Usage

f_mc_kernels(y.min = 0, y.max = 5, x.min = 0, x.max = 5, N.mc = 3^2,
  lam1.coef = c(-1.3, 0.5, -0.6), lam2.coef = c(-1.4, -0.1, 0.2),
  logit.eta.coef = c(0, -0.15, 0.15))
f_mc_kernels(y.min = 0, y.max = 5, x.min = 0, x.max = 5, N.mc = 3^2,
  lam1.coef = c(-1.3, 0.5, -0.6), lam2.coef = c(-1.4, -0.1, 0.2),
  logit.eta.coef = c(0, -0.15, 0.15))

Arguments

`y.min`	Lower bound for the y-coordinate axis.
`y.max`	Upper bound for the y-coordinate axis.
`x.min`	Lower bound for the y-coordinate axis.
`x.max`	Upper bound for the y-coordinate axis.
`N.mc`	Number of mixture component locations.
`lam1.coef`	Log-linear regression coefficients for lam1; the coefficients correspond to the intercept, longitude, and latitude.
`lam2.coef`	Log-linear regression coefficients for lam2; the coefficients correspond to the intercept, longitude, and latitude.
`logit.eta.coef`	Scaled logit regression coefficients for eta; the coefficients correspond to the intercept, longitude, and latitude.

Value

A list with the following components:

`mc.locations`	A `N.mc` x 2 matrix of the mixture component locations.
`mc.kernels`	A `N.mc` x 2 x 2 array of kernel matrices corresponding to each of the mixture component locations.

Examples

f_mc_kernels( y.min = 0, y.max = 5, x.min = 0,
x.max = 5, N.mc = 3^2, lam1.coef = c(-1.3, 0.5, -0.6),
lam2.coef = c(-1.4, -0.1, 0.2), logit.eta.coef = c(0, -0.15, 0.15) )


f_mc_kernels( y.min = 0, y.max = 5, x.min = 0,
x.max = 5, N.mc = 3^2, lam1.coef = c(-1.3, 0.5, -0.6),
lam2.coef = c(-1.4, -0.1, 0.2), logit.eta.coef = c(0, -0.15, 0.15) )

Calculate a kernel covariance matrix.

Description

kernel_cov calculates a 2 x 2 matrix based on the eigendecomposition components (two eigenvalues and angle of rotation).

Usage

kernel_cov(params)
kernel_cov(params)

Arguments

params

A vector of three parameters, corresponding to (lam1, lam2, eta). The eigenvalues (lam1 and lam2) must be positive.

Value

A 2 x 2 kernel covariance matrix.

Examples

kernel_cov(c(1, 2, pi/3))

kernel_cov(c(1, 2, pi/3))

Constructor functions for global parameter estimation.

Description

This function generates another function to be used within optim to obtain maximum likelihood estimates of global variance parameters tausq, sigmasq with a fixed correlation matrix (smoothness is fixed).

Usage

make_global_loglik1(data, Xmat, Corr, nugg2.var)
make_global_loglik1(data, Xmat, Corr, nugg2.var)

Arguments

`data`	A vector or matrix of data to use in the likelihood calculation.
`Xmat`	The design matrix for the mean model.
`Corr`	The correlation matrix.
`nugg2.var`	Fixed values for the covariance of the second nugget term.

Value

This function returns another function for use in optim.

Examples

## Not run: 
make_global_loglik1( data, Xmat, Corr, nugg2.var )

## End(Not run)

## Not run: 
make_global_loglik1( data, Xmat, Corr, nugg2.var )

## End(Not run)

Constructor functions for global parameter estimation.

Description

This function generates another function to be used within optim to obtain maximum likelihood estimates of global variance parameters tausq, sigmasq, and nu.

Usage

make_global_loglik1_kappa(data, Xmat, cov.model, Scalemat, Distmat, nugg2.var)
make_global_loglik1_kappa(data, Xmat, cov.model, Scalemat, Distmat, nugg2.var)

Arguments

`data`	A vector or matrix of data to use in the likelihood calculation.
`Xmat`	The design matrix for the mean model.
`cov.model`	String; the covariance model.
`Scalemat`	Matrix; contains the scaling quantities from the covariance function.
`Distmat`	Matrix; contains the scaled distances.
`nugg2.var`	Fixed values for the covariance of the second nugget term.

Value

This function returns another function for use in optim.

Examples

## Not run: 
make_global_loglik1_kappa( data, Xmat, cov.model, Scalemat, Distmat, nugg2.var )

## End(Not run)

## Not run: 
make_global_loglik1_kappa( data, Xmat, cov.model, Scalemat, Distmat, nugg2.var )

## End(Not run)

Constructor functions for global parameter estimation.

Description

This function generates another function to be used within optim to obtain maximum likelihood estimates of global variance parameter sigmasq with a fixed correlation matrix (smoothness is fixed). The nugget variance is taken to be spatially-varing.

Usage

make_global_loglik2(data, Xmat, Corr, obs.nuggets, nugg2.var)
make_global_loglik2(data, Xmat, Corr, obs.nuggets, nugg2.var)

Arguments

`data`	A vector or matrix of data to use in the likelihood calculation.
`Xmat`	The design matrix for the mean model.
`Corr`	The correlation matrix.
`obs.nuggets`	A vector containing the spatially-varying nuggets corresponding to each data location.
`nugg2.var`	Fixed values for the covariance of the second nugget term.

Value

This function returns another function for use in optim.

Examples

## Not run: 
make_global_loglik2( data, Xmat, Corr, obs.nuggets, nugg2.var )

## End(Not run)

## Not run: 
make_global_loglik2( data, Xmat, Corr, obs.nuggets, nugg2.var )

## End(Not run)

Constructor functions for global parameter estimation.

Description

This function generates another function to be used within optim to obtain maximum likelihood estimates of global variance parameters sigmasq and nu. The nugget variance is taken to be spatially-varying.

Usage

make_global_loglik2_kappa(data, Xmat, cov.model, Scalemat, Distmat, obs.nuggets,
  nugg2.var)
make_global_loglik2_kappa(data, Xmat, cov.model, Scalemat, Distmat, obs.nuggets,
  nugg2.var)

Arguments

`data`	A vector or matrix of data to use in the likelihood calculation.
`Xmat`	The design matrix for the mean model.
`cov.model`	String; the covariance model.
`Scalemat`	Matrix; contains the scaling quantities from the covariance function.
`Distmat`	Matrix; contains the scaled distances.
`obs.nuggets`	A vector containing the spatially-varying nuggets corresponding to each data location.
`nugg2.var`	Fixed values for the covariance of the second nugget term.

Value

This function returns another function for use in optim.

Examples

## Not run: 
make_global_loglik2_kappa( data, Xmat, cov.model, Scalemat, Distmat, obs.nuggets, nugg2.var )

## End(Not run)

## Not run: 
make_global_loglik2_kappa( data, Xmat, cov.model, Scalemat, Distmat, obs.nuggets, nugg2.var )

## End(Not run)

Constructor functions for global parameter estimation.

Description

This function generates another function to be used within optim to obtain maximum likelihood estimates of global variance parameter tausq with a fixed correlation matrix (smoothness is fixed). The process variance is taken to be spatially-varing.

Usage

make_global_loglik3(data, Xmat, Corr, obs.variance, nugg2.var)
make_global_loglik3(data, Xmat, Corr, obs.variance, nugg2.var)

Arguments

`data`	A vector or matrix of data to use in the likelihood calculation.
`Xmat`	The design matrix for the mean model.
`Corr`	The correlation matrix matrix.
`obs.variance`	A vector containing the spatially-varying variance corresponding to each data location.
`nugg2.var`	Fixed values for the covariance of the second nugget term.

Value

This function returns another function for use in optim.

Examples

## Not run: 
make_global_loglik3( data, Xmat, Corr, obs.variance, nugg2.var )

## End(Not run)

## Not run: 
make_global_loglik3( data, Xmat, Corr, obs.variance, nugg2.var )

## End(Not run)

Constructor functions for global parameter estimation.

Description

This function generates another function to be used within optim to obtain maximum likelihood estimates of global variance parameters tausq and nu. The process variance is taken to be spatially-varying.

Usage

make_global_loglik3_kappa(data, Xmat, cov.model, Scalemat, Distmat,
  obs.variance, nugg2.var)
make_global_loglik3_kappa(data, Xmat, cov.model, Scalemat, Distmat,
  obs.variance, nugg2.var)

Arguments

`data`	A vector or matrix of data to use in the likelihood calculation.
`Xmat`	The design matrix for the mean model.
`cov.model`	String; the covariance model.
`Scalemat`	Matrix; contains the scaling quantities from the covariance function.
`Distmat`	Matrix; contains the scaled distances.
`obs.variance`	A vector containing the spatially-varying variance corresponding to each data location.
`nugg2.var`	Fixed values for the covariance of the second nugget term.

Value

This function returns another function for use in optim.

Examples

## Not run: 
make_global_loglik3_kappa( data, Xmat, cov.model, Scalemat, Distmat, obs.variance, nugg2.var )

## End(Not run)

## Not run: 
make_global_loglik3_kappa( data, Xmat, cov.model, Scalemat, Distmat, obs.variance, nugg2.var )

## End(Not run)

Constructor functions for global parameter estimation.

Description

This function generates another function to be used within optim to obtain maximum likelihood estimates of global variance parameters nu. The process variance and nugget variance are taken to be spatially-varying.

Usage

make_global_loglik4_kappa(data, Xmat, cov.model, Scalemat, Distmat,
  obs.variance, obs.nuggets, nugg2.var)
make_global_loglik4_kappa(data, Xmat, cov.model, Scalemat, Distmat,
  obs.variance, obs.nuggets, nugg2.var)

Arguments

`data`	A vector or matrix of data to use in the likelihood calculation.
`Xmat`	The design matrix for the mean model.
`cov.model`	String; the covariance model.
`Scalemat`	Matrix; contains the scaling quantities from the covariance function.
`Distmat`	Matrix; contains the scaled distances.
`obs.variance`	A vector containing the spatially-varying variance corresponding to each data location.
`obs.nuggets`	A vector containing the spatially-varying nuggets corresponding to each data location.
`nugg2.var`	Fixed values for the covariance of the second nugget term.

Value

This function returns another function for use in optim.

Examples

## Not run: 
make_global_loglik4_kappa( data, Xmat, cov.model, Scalemat, Distmat,
obs.variance, obs.nuggets, nugg2.var )

## End(Not run)

## Not run: 
make_global_loglik4_kappa( data, Xmat, cov.model, Scalemat, Distmat,
obs.variance, obs.nuggets, nugg2.var )

## End(Not run)

Constructor functions for local parameter estimation.

Description

This function generates another function to be used within optim to obtain maximum likelihood estimates of covariance (and possibly mean) parameters. The function includes options for (1) maximum likelihood ("ml") vs. restricted maximum likelihood ("reml"), (2) smoothness (kappa): models without smoothness vs. estimating the smoothness vs. using fixed smoothness, (3) locally isotropic vs. locally anisotropic, and (4) fixed nugget variance (tausq): fixed vs. estimated.

Usage

make_local_lik(locations, cov.model, data, Xmat, nugg2.var = matrix(0,
  nrow(locations), nrow(locations)), tausq = 0, kappa = 0.5,
  fixed = rep(FALSE, 6), method = "reml", local.aniso = TRUE,
  fix.tausq = FALSE, fix.kappa = FALSE)
make_local_lik(locations, cov.model, data, Xmat, nugg2.var = matrix(0,
  nrow(locations), nrow(locations)), tausq = 0, kappa = 0.5,
  fixed = rep(FALSE, 6), method = "reml", local.aniso = TRUE,
  fix.tausq = FALSE, fix.kappa = FALSE)

Arguments

`locations`	A matrix of locations.
`cov.model`	String; the covariance model.
`data`	A vector or matrix of data to use in the likelihood calculation.
`Xmat`	The design matrix for the mean model.
`nugg2.var`	Fixed values for the variance/covariance of the second nugget term; defaults to a matrix of zeros.
`tausq`	Scalar; fixed value for the nugget variance (when `fix.tausq = TRUE`).
`kappa`	Scalar; fixed value for the smoothness (when `fix.kappa = TRUE`).
`fixed`	Logical vector of `FALSE` values; length corresponds to the number of parameters to be estimated.
`method`	Indicates the estimation method, either maximum likelihood (`"ml"`) or restricted maximum likelihood (`"reml"`).
`local.aniso`	Logical; indicates if the local covariance should be anisotropic (`TRUE`) or isotropic (`FALSE`). Defaults to `TRUE`.
`fix.tausq`	Logical; indicates whether the default nugget term (tau^2) should be fixed (`TRUE`) or estimated (`FALSE`). Defaults to `FALSE`.
`fix.kappa`	Logical; indicates if the kappa parameter should be fixed (`TRUE`) or estimated (`FALSE`). Defaults to `FALSE` (only valid for `cov.model = "matern"` and `cov.model = "cauchy"`).

Value

This function returns another function for use in optim.

Examples

## Not run: 
make_local_lik( locations, cov.model, data, Xmat )

## End(Not run)

## Not run: 
make_local_lik( locations, cov.model, data, Xmat )

## End(Not run)

Calculate local sample sizes.

Description

mc_N calculates the number of observations (sample size) that fall within a certain fit radius for each mixture component location.

Usage

mc_N(coords, mc.locations, fit.radius)
mc_N(coords, mc.locations, fit.radius)

Arguments

`coords`	A matrix of observation locations.
`mc.locations`	A matrix of the mixture component locations to use in the model fitting.
`fit.radius`	Scalar; defines the fitting radius for local likelihood estimation.

Value

A vector mc.N.fit, which summarizes the number of observation locations in coords that fall within the fit radius for each mixture component location.

Examples

## Not run: 
mc_N( coords = simdata$sim.locations, mc.locations = simdata$mc.locations,
fit.radius = 1 )

## End(Not run)

## Not run: 
mc_N( coords = simdata$sim.locations, mc.locations = simdata$mc.locations,
fit.radius = 1 )

## End(Not run)

Fit the nonstationary spatial model

Description

NSconvo_fit estimates the parameters of the nonstationary convolution-based spatial model. Required inputs are the observed data and locations (a geoR object with $coords and $data). Optional inputs include mixture component locations (if not provided, the number of mixture component locations are required), the fit radius, the covariance model (exponential is the default), and whether or not the nugget and process variance will be spatially-varying.

Usage

NSconvo_fit(geodata = NULL, sp.SPDF = NULL, coords = geodata$coords,
  data = geodata$data, cov.model = "exponential", mean.model = data ~ 1,
  mc.locations = NULL, N.mc = NULL, lambda.w = NULL,
  fixed.nugg2.var = NULL, mean.model.df = NULL, mc.kernels = NULL,
  fit.radius = NULL, ns.nugget = FALSE, ns.variance = FALSE,
  ns.mean = FALSE, local.aniso = TRUE, fix.tausq = FALSE, tausq = 0,
  fix.kappa = FALSE, kappa = 0.5, method = "reml",
  print.progress = TRUE, local.pars.LB = NULL, local.pars.UB = NULL,
  global.pars.LB = NULL, global.pars.UB = NULL, local.ini.pars = NULL,
  global.ini.pars = NULL)
NSconvo_fit(geodata = NULL, sp.SPDF = NULL, coords = geodata$coords,
  data = geodata$data, cov.model = "exponential", mean.model = data ~ 1,
  mc.locations = NULL, N.mc = NULL, lambda.w = NULL,
  fixed.nugg2.var = NULL, mean.model.df = NULL, mc.kernels = NULL,
  fit.radius = NULL, ns.nugget = FALSE, ns.variance = FALSE,
  ns.mean = FALSE, local.aniso = TRUE, fix.tausq = FALSE, tausq = 0,
  fix.kappa = FALSE, kappa = 0.5, method = "reml",
  print.progress = TRUE, local.pars.LB = NULL, local.pars.UB = NULL,
  global.pars.LB = NULL, global.pars.UB = NULL, local.ini.pars = NULL,
  global.ini.pars = NULL)

Arguments

`geodata`	A list containing elements `coords` and `data` as described next. Typically an object of the class "`geodata`", although a geodata object only allows `data` to be a vector (no replicates). If not provided, the arguments `coords` and `data` must be provided instead.
`sp.SPDF`	A "`SpatialPointsDataFrame`" object, which contains the spatial coordinates and additional attribute variables corresponding to the spatoal coordinates
`coords`	An N x 2 matrix where each row has the two-dimensional coordinates of the N data locations. By default, it takes the `coords` component of the argument `geodata`, if provided.
`data`	A vector or matrix with N rows, containing the data values. Inputting a vector corresponds to a single replicate of data, while inputting a matrix corresponds to replicates. In the case of replicates, the model assumes the replicates are independent and identically distributed.
`cov.model`	A string specifying the model for the correlation function; following `geoR`, defaults to `"exponential"`. Options available in this package are: "`exponential`", `"cauchy"`, `"matern"`, `"circular"`, `"cubic"`, `"gaussian"`, `"spherical"`, and `"wave"`. For further details, see documentation for `cov.spatial`.
`mean.model`	An object of class `formula`, specifying the mean model to be used. Defaults to an intercept only.
`mc.locations`	Optional; matrix of mixture component locations.
`N.mc`	Optional; if `mc.locations` is not specified, the function will create a rectangular grid of size `N.mc` over the spatial domain.
`lambda.w`	Scalar; tuning parameter for the weight function. Defaults to be the square of one-half of the minimum distance between mixture component locations.
`fixed.nugg2.var`	Optional; describes the variance/covariance for a fixed (second) nugget term (represents a known error term). Either a vector of length N containing a station-specific variances (implying independent error) or an NxN covariance matrix (implying dependent error). Defaults to zero.
`mean.model.df`	Optional data frame; refers to the variables used in `mean.model`. Important when using categorical variables in `mean.model`, as a subset of the full design matrix will likely be rank deficient. Specifying `mean.model.df` allows `NSconvo_fit` to calculate a design matrix specific to the points used to fit each local model.
`mc.kernels`	Optional specification of mixture component kernel matrices (based on expert opinion, etc.).
`fit.radius`	Scalar; specifies the fit radius or neighborhood size for the local likelihood estimation.
`ns.nugget`	Logical; indicates if the nugget variance (tausq) should be spatially-varying (`TRUE`) or constant (`FALSE`).
`ns.variance`	Logical; indicates if the process variance (sigmasq) should be spatially-varying (`TRUE`) or constant (`FALSE`).
`ns.mean`	Logical; indicates if the mean coefficeints (beta) should be spatially-varying (`TRUE`) or constant (`FALSE`).
`local.aniso`	Logical; indicates if the local covariance should be anisotropic (`TRUE`) or isotropic (`FALSE`). Defaults to `TRUE`. In the case of a locally isotropic model, the bounds and initial values for lam will default to the first element of `local.pars.LB`, `local.pars.UB`, and `local.ini.pars` (while still required, the second and third elements of these vectors will be ignored.)
`fix.tausq`	Logical; indicates whether the default nugget term (tau^2) should be fixed (`TRUE`) or estimated (`FALSE`). Defaults to `FALSE`.
`tausq`	Scalar; fixed value for the nugget variance (when `fix.tausq = TRUE`).
`fix.kappa`	Logical; indicates if the kappa parameter should be fixed (`TRUE`) or estimated (`FALSE`). Defaults to `FALSE` (only valid for `cov.model = "matern"` and `cov.model = "cauchy"`).
`kappa`	Scalar; value of the kappa parameter. Only used if `fix.kappa = TRUE`.
`method`	Indicates the estimation method, either maximum likelihood (`"ml"`) or restricted maximum likelihood (`"reml"`).
`print.progress`	Logical; if `TRUE`, text indicating the progress of local model fitting in real time.
`local.pars.LB`, `local.pars.UB`	Optional vectors of lower and upper bounds, respectively, used by the `"L-BFGS-B"` method option in the `optim` function for the local parameter estimation. Each vector must be of length five, containing values for lam1, lam2, tausq, sigmasq, and nu. Default for `local.pars.LB` is `rep(1e-05,5)`; default for `local.pars.UB` is `c(max.distance/2, max.distance/2, 4resid.var, 4resid.var, 100)`, where `max.distance` is the maximum interpoint distance of the observed data and `resid.var` is the residual variance from using `lm` with `mean.model`.
`global.pars.LB`, `global.pars.UB`	Optional vectors of lower and upper bounds, respectively, used by the `"L-BFGS-B"` method option in the `optim` function for the global parameter estimation. Each vector must be of length three, containing values for tausq, sigmasq, and nu. Default for `global.pars.LB` is `rep(1e-05,3)`; default for `global.pars.UB` is `c(4resid.var, 4resid.var, 100)`, where `resid.var` is the residual variance from using `lm` with `mean.model`.
`local.ini.pars`	Optional vector of initial values used by the `"L-BFGS-B"` method option in the `optim` function for the local parameter estimation. The vector must be of length five, containing values for lam1, lam2, tausq, sigmasq, and nu. Defaults to `c(max.distance/10, max.distance/10, 0.1resid.var, 0.9resid.var, 1)`, where `max.distance` is the maximum interpoint distance of the observed data and `resid.var` is the residual variance from using `lm` with `mean.model`.
`global.ini.pars`	Optional vector of initial values used by the `"L-BFGS-B"` method option in the `optim` function for the global parameter estimation. The vector must be of length three, containing values for tausq, sigmasq, and nu. Defaults to `c(0.1resid.var, 0.9resid.var, 1)`, where `resid.var` is the residual variance from using `lm` with `mean.model`.

Value

A "NSconvo" object, with the following components:

`mc.locations`	Mixture component locations used for the simulated data.
`mc.kernels`	Mixture component kernel matrices used for the simulated data.
`MLEs.save`	Table of local maximum likelihood estimates for each mixture component location.
`kernel.ellipses`	`N.obs` x 2 x 2 array, containing the kernel matrices corresponding to each of the simulated values.
`data`	Observed data values.
`beta.GLS`	Generalized least squares estimates of beta, the mean coefficients. For `ns.mean = FALSE`, this is a vector (containing the global mean coefficients); for `ns.mean = TRUE`, this is a matrix (one column for each mixture component location).
`beta.cov`	Covariance matrix of the generalized least squares estimate of beta. For `ns.mean = FALSE`, this is a matrix (containing the covariance of theglobal mean coefficients); for `ns.mean = TRUE`, this is an array (one matrix for each mixture component location).
`Mean.coefs`	"Regression table" for the mean coefficient estimates, listing the estimate, standard error, and t-value (for `ns.mean = FALSE` only).
`tausq.est`	Estimate of tausq (nugget variance), either scalar (when `ns.nugget = "FALSE"`) or a vector of length N (when `ns.nugget = "TRUE"`), which contains the estimated nugget variance for each observation location.
`sigmasq.est`	Estimate of sigmasq (process variance), either scalar (when `ns.variance = "FALSE"`) or a vector of length N (when `ns.variance = "TRUE"`), which contains the estimated process variance for each observation location.
`beta.est`	Estimate of beta (mean coefficients), either a vector (when `ns.mean = "FALSE"`) or a matrix with N rows (when `ns.mean = "TRUE"`), each row of which contains the estimated (smoothed) mean coefficients for each observation location.
`kappa.MLE`	Scalar maximum likelihood estimate for kappa (when applicable).
`Cov.mat`	Estimated covariance matrix (`N.obs` x `N.obs`) using all relevant parameter estimates.
`Cov.mat.chol`	Cholesky of `Cov.mat` (i.e., `chol(Cov.mat)`), the estimated covariance matrix (`N.obs` x `N.obs`).
`cov.model`	String; the correlation model used for estimation.
`ns.nugget`	Logical, indicating if the nugget variance was estimated as spatially-varing (`TRUE`) or constant (`FALSE`).
`ns.variance`	Logical, indicating if the process variance was estimated as spatially-varying (`TRUE`) or constant (`FALSE`).
`fixed.nugg2.var`	N x N matrix with the fixed variance/covariance for the second (measurement error) nugget term (defaults to zero).
`coords`	N x 2 matrix of observation locations.
`global.loglik`	Scalar value of the maximized likelihood from the global optimization (if available).
`Xmat`	Design matrix, obtained from using `lm` with `mean.model`.
`lambda.w`	Tuning parameter for the weight function.
`fix.kappa`	Logical, indicating if kappa was fixed (`TRUE`) or estimated (`FALSE`).
`kappa`	Scalar; fixed value of kappa.

Examples

# Using white noise data
fit.model <- NSconvo_fit( coords = cbind( runif(100), runif(100)),
data = rnorm(100), fit.radius = 0.4, N.mc = 4 )

# Using white noise data
fit.model <- NSconvo_fit( coords = cbind( runif(100), runif(100)),
data = rnorm(100), fit.radius = 0.4, N.mc = 4 )

Simulate data from the nonstationary model.

Description

NSconvo_sim simulates data from the nonstationary model, given mixture component kernel matrices. The function requires either a mixture component kernel object, from the function f.mc.kernels(), or a direct specification of the mixture component locations and mixture component kernels.

Usage

NSconvo_sim(grid = TRUE, y.min = 0, y.max = 5, x.min = 0, x.max = 5,
  N.obs = 20^2, sim.locations = NULL, mc.kernels.obj = NULL,
  mc.kernels = NULL, mc.locations = NULL, lambda.w = NULL, tausq = 0.1,
  sigmasq = 1, beta.coefs = 4, kappa = NULL, covariates = rep(1, N.obs),
  cov.model = "exponential")
NSconvo_sim(grid = TRUE, y.min = 0, y.max = 5, x.min = 0, x.max = 5,
  N.obs = 20^2, sim.locations = NULL, mc.kernels.obj = NULL,
  mc.kernels = NULL, mc.locations = NULL, lambda.w = NULL, tausq = 0.1,
  sigmasq = 1, beta.coefs = 4, kappa = NULL, covariates = rep(1, N.obs),
  cov.model = "exponential")

Arguments

`grid`	Logical; indicates of the simulated data should fall on a grid (`TRUE`) or not (`FALSE`).
`y.min`	Lower bound for the y-coordinate axis.
`y.max`	Upper bound for the y-coordinate axis.
`x.min`	Lower bound for the y-coordinate axis.
`x.max`	Upper bound for the y-coordinate axis.
`N.obs`	Number of simulated data values.
`sim.locations`	Optional `N.obs` x 2 matrix; allows the user to specify the locations of the simulated data.
`mc.kernels.obj`	Object from the `f_mc_kernels` function.
`mc.kernels`	Optional specification of mixture component kernel matrices.
`mc.locations`	Optional specification of mixture component locations.
`lambda.w`	Scalar; tuning parameter for the weight function.
`tausq`	Scalar; true nugget variance.
`sigmasq`	Scalar; true process variance.
`beta.coefs`	Vector of true regression coefficients. Length must match the number of columns in `covariates`.
`kappa`	Scalar; true smoothness.
`covariates`	Matrix with `N.obs` rows, corresponding to covariate information for each of the simualted values.
`cov.model`	A string specifying the correlation function. Options available in this package are: "`exponential`", `"cauchy"`, `"matern"`, `"circular"`, `"cubic"`, `"gaussian"`, `"spherical"`, and `"wave"`. See `cov.spatial` for further documentation.

Value

A list with the following components:

`sim.locations`	Matrix of locations for the simulated values.
`mc.locations`	Mixture component locations used for the simulated data.
`mc.kernels`	Mixture component kernel matrices used for the simulated data.
`kernel.ellipses`	`N.obs` x 2 x 2 array, containing the kernel matrices corresponding to each of the simulated values.
`Cov.mat`	True covariance matrix (`N.obs` x `N.obs`) corresponding to the simulated data.
`sim.data`	Simulated data values.
`lambda.w`	Tuning parameter for the weight function.

Examples

## Not run: 
NSconvo_sim( grid = TRUE, y.min = 0, y.max = 5, x.min = 0,
x.max = 5, N.obs = 20^2, sim.locations = NULL, mc.kernels.obj = NULL,
mc.kernels = NULL, mc.locations = NULL, lambda.w = NULL,
tausq = 0.1, sigmasq = 1, beta.coefs = 4, kappa = NULL,
covariates = rep(1,N.obs), cov.model = "exponential" )

## End(Not run)

## Not run: 
NSconvo_sim( grid = TRUE, y.min = 0, y.max = 5, x.min = 0,
x.max = 5, N.obs = 20^2, sim.locations = NULL, mc.kernels.obj = NULL,
mc.kernels = NULL, mc.locations = NULL, lambda.w = NULL,
tausq = 0.1, sigmasq = 1, beta.coefs = 4, kappa = NULL,
covariates = rep(1,N.obs), cov.model = "exponential" )

## End(Not run)

Plot of the estimated correlations from the stationary model.

Description

This function plots the estimated correlation between a reference point and all other prediction locations.

Usage

## S3 method for class 'Aniso'
plot(x, ref.loc = NULL, all.pred.locs = NULL, grid = TRUE,
  ...)
## S3 method for class 'Aniso'
plot(x, ref.loc = NULL, all.pred.locs = NULL, grid = TRUE,
  ...)

Arguments

`x`	An "Aniso" object, from Aniso_fit().
`ref.loc`	Vector of length 2; the reference location.
`all.pred.locs`	A matrix of all prediction locations.
`grid`	Logical; indicates if the `all.pred.locs` are on a rectangular grid (`TRUE`) or not (`FALSE`).
`...`	Arguments passed to `plot` functions.

Value

A plot of either the estimated ellipses or estimated correlation is printed.

Examples

## Not run: 
plot.Aniso( Aniso.object )

## End(Not run)

## Not run: 
plot.Aniso( Aniso.object )

## End(Not run)

Plot from the nonstationary model.

Description

This function plots either the estimated anisotropy ellipses for each of the mixture component locations or the estimated correlation between a reference point and all other prediction locations.

Usage

## S3 method for class 'NSconvo'
plot(x, plot.ellipses = TRUE, fit.radius = NULL,
  aniso.mat = NULL, true.mc = NULL, ref.loc = NULL,
  all.pred.locs = NULL, grid = TRUE, true.col = 1, aniso.col = 4,
  ns.col = 2, plot.mc.locs = TRUE, ...)
## S3 method for class 'NSconvo'
plot(x, plot.ellipses = TRUE, fit.radius = NULL,
  aniso.mat = NULL, true.mc = NULL, ref.loc = NULL,
  all.pred.locs = NULL, grid = TRUE, true.col = 1, aniso.col = 4,
  ns.col = 2, plot.mc.locs = TRUE, ...)

Arguments

`x`	A "NSconvo" object, from NSconvo_fit().
`plot.ellipses`	Logical; indicates whether the estimated ellipses should be plotted (`TRUE`) or estiamted correlations (`FALSE`).
`fit.radius`	Scalar; defines the fit radius used for the local likelihood estimation.
`aniso.mat`	2 x 2 matrix; contains the estimated anisotropy ellipse from the stationary model (for comparison).
`true.mc`	The true mixture component ellipses, if known.
`ref.loc`	Vector of length 2; the reference location.
`all.pred.locs`	A matrix of all prediction locations.
`grid`	Logical; indicates if the `all.pred.locs` are on a rectangular grid (`TRUE`) or not (`FALSE`).
`true.col`	Color value for the true mixture component ellipses (if plotted).
`aniso.col`	Color value for the anisotropy ellipse (if plotted).
`ns.col`	Color value for the mixture component ellipses.
`plot.mc.locs`	Logical; indicates whether the mixture component locations should be plotted (`TRUE`) or not (`FALSE`).
`...`	Other options passed to `plot`.

Value

A plot of either the estimated ellipses or estimated correlation is printed.

Examples

## Not run: 
plot.NSconvo( NSconvo.object )

## End(Not run)

## Not run: 
plot.NSconvo( NSconvo.object )

## End(Not run)

Obtain predictions at unobserved locations for the stationary spatial model.

Description

predict.Aniso calculates the kriging predictor and corresponding standard errors at unmonitored sites.

Usage

## S3 method for class 'Aniso'
predict(object, pred.coords, pred.covariates = NULL,
  pred.fixed.nugg2.var = NULL, ...)
## S3 method for class 'Aniso'
predict(object, pred.coords, pred.covariates = NULL,
  pred.fixed.nugg2.var = NULL, ...)

Arguments

`object`	An "Aniso" object, from `Aniso_fit`.
`pred.coords`	Matrix of locations where predictions are required.
`pred.covariates`	Matrix of covariates for the prediction locations, NOT including an intercept. The number of columns for this matrix must match the design matrix from `mean.model` in `NSconvo_fit`. Defaults to an intercept only.
`pred.fixed.nugg2.var`	An optional vector or matrix describing the the variance/covariance a fixed second nugget term (corresponds to `fixed.nugg2.var` in `Aniso_fit`; often useful if conducting prediction for held-out data). Defaults to zero.
`...`	additional arguments affecting the predictions produced.

Value

A list with the following components:

`pred.means`	Vector of the kriging predictor, for each location in `pred.coords`.
`pred.SDs`	Vector of the kriging standard errors, for each location in `pred.coords`.

Examples

## Not run: 
pred.S <- predict( Aniso.obj,
pred.coords = cbind(runif(300),runif(300)) )

## End(Not run)

## Not run: 
pred.S <- predict( Aniso.obj,
pred.coords = cbind(runif(300),runif(300)) )

## End(Not run)

Obtain predictions at unobserved locations for the nonstationary spatial model.

Description

predict.NSconvo calculates the kriging predictor and corresponding standard errors at unmonitored sites.

Usage

## S3 method for class 'NSconvo'
predict(object, pred.coords, pred.covariates = NULL,
  pred.fixed.nugg2.var = NULL, ...)
## S3 method for class 'NSconvo'
predict(object, pred.coords, pred.covariates = NULL,
  pred.fixed.nugg2.var = NULL, ...)

Arguments

`object`	A "NSconvo" object, from `NSconvo_fit`.
`pred.coords`	Matrix of locations where predictions are required.
`pred.covariates`	Matrix of covariates for the prediction locations, NOT including an intercept. The number of columns for this matrix must match the design matrix from `mean.model` in `NSconvo_fit`. Defaults to an intercept only.
`pred.fixed.nugg2.var`	An optional vector or matrix describing the the variance/covariance a fixed second nugget term (corresponds to `fixed.nugg2.var` in `NSconvo_fit`; often useful if conducting prediction for held-out data). Defaults to zero.
`...`	additional arguments affecting the predictions produced.

Value

A list with the following components:

`pred.means`	Vector of the kriging predictor, for each location in `pred.coords`.
`pred.SDs`	Vector of the kriging standard errors, for each location in `pred.coords`.

Examples

## Not run: 
pred.NS <- predict( NSconvo.obj,
pred.coords = matrix(c(1,1), ncol=2),
pred.covariates = matrix(c(1,1), ncol=2) )

## End(Not run)

## Not run: 
pred.NS <- predict( NSconvo.obj,
pred.coords = matrix(c(1,1), ncol=2),
pred.covariates = matrix(c(1,1), ncol=2) )

## End(Not run)

Simulated nonstationary dataset

Description

A data set containing the necessary components to fit the nonstationary spatial model, simulated from the true model.

Usage

simdata
simdata

Format

A list with the following objects:

sim.locations: A matrix of longitude/latitude coordinates of the simulated locations.
mc.locations: A matrix of longitude/latitude coordinates of the mixture component locations.
mc.kernel: A three-dimensional array, containing the true 2 x 2 kernel covariance matrices for each mixture component location.
kernel.ellipses: A three-dimensional array, containing the true 2 x 2 kernel covariance matrices for each simulated location.
sim.data: A matrix of the simulated data; each of the ten columns correspond to an independent and identically distribured replicate.
lambda.w: Scalar; the value of the tuning parameter used in the weight function.
holdout.index: Vector; indicates which of the simulated locations should be used in the hold-out sample.

Summarize the stationary model fit.

Description

summary.Aniso prints relevant output from the model fitting procedure.

Usage

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

Arguments

`object`	An "Aniso" object, from `Aniso_fit`.
`...`	additional arguments affecting the summary produced.

Value

Text containing the model fitting results.

Examples

## Not run: 
summary.Aniso( Aniso.object )

## End(Not run)

## Not run: 
summary.Aniso( Aniso.object )

## End(Not run)

Summarize the nonstationary model fit.

Description

summary.NSconvo prints relevant output from the model fitting procedure.

Usage

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

Arguments

`object`	A "NSconvo" object, from `NSconvo_fit`.
`...`	additional arguments affecting the summary produced.

Value

Text containing the model fitting results.

Examples

## Not run: 
summary.NSconvo( NSconvo.object )

## End(Not run)

## Not run: 
summary.NSconvo( NSconvo.object )

## End(Not run)

Mixture component grids for the western United States

Description

A list of two mixture component grids for fitting the nonstationary model to the western United States precipitation data.

Usage

US.mc.grids
US.mc.grids

Format

A list with two elements:

Element 1: Coarse mixture component grid.
Element 2: Fine mixture component grid.

Prediction locations for the western United States

Description

A matrix with two columns containing a fine grid of locations for which to make a filled-in prediction map for the western United States.

Usage

US.prediction.locs
US.prediction.locs

Format

A matrix with two columns:

Column 1: Longitude of the prediction grid.
Column 2: Latitude of the prediction grid.

Annual precipitation measurements from the western United States, 1997

Description

A data set containing the annual precipitation for 1270 locations in the western United States.

Usage

USprecip97
USprecip97

Format

A data frame with the following variables:

longitude: Longitude of the monitoring site.
latitude: Latitude of the monitoring site.
annual.ppt: Annual precipitation for the monitoring site, in millimeters.
log.annual.ppt: Annual precipitation for the monitoring site, in log millimeters.

Source

http://www.image.ucar.edu/GSP/Data/US.monthly.met/

Package 'convoSPAT'

Help Index

Fit the stationary spatial model

Description

Usage

Arguments

Value

Examples

Evaluation criteria

Description

Usage

Arguments

Value

Examples

Calculate mixture component kernel matrices.

Description

Usage

Arguments

Value

Examples

Calculate a kernel covariance matrix.

Description

Usage

Arguments

Value

Examples

Constructor functions for global parameter estimation.

Description

Usage

Arguments

Value

Examples

Constructor functions for global parameter estimation.

Description

Usage

Arguments

Value

Examples

Constructor functions for global parameter estimation.

Description

Usage

Arguments

Value

Examples

Constructor functions for global parameter estimation.

Description

Usage

Arguments

Value

Examples

Constructor functions for global parameter estimation.

Description

Usage

Arguments

Value

Examples

Constructor functions for global parameter estimation.

Description

Usage

Arguments

Value

Examples

Constructor functions for global parameter estimation.

Description

Usage

Arguments

Value

Examples

Constructor functions for local parameter estimation.

Description

Usage

Arguments

Value

Examples

Calculate local sample sizes.

Description

Usage

Arguments

Value

Examples