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AIRS data for May 2003

Description

Mid-tropospheric CO2 measurements from the Atmospheric InfraRed Sounder (AIRS).The data are measurements between 60 degrees S and 90 degrees N at roughly 1:30 pm localtime on 1 May through to 15 May 2003. (AIRS does not release data below 60 degrees S.)

Usage

AIRS_05_2003

Format

A data frame with 209631 rows and 7 variables:

year

year of retrieval

month

month of retrieval

day

day of retrieval

lon

longitude coordinate of retrieval

lat

latitude coordinate of retrieval

co2avgret

CO2 mole fraction retrieval in ppm

co2std

standard error of CO2 retrieval in ppm

References

Chahine, M. et al. (2006). AIRS: Improving weather forecasting andproviding new data on greenhouse gases. Bulletin of the American MeteorologicalSociety 87, 911–26.

Americium soil data

Description

Americium (Am) concentrations in a spatial domain immediately surrounding the location at which nuclear devices were detonated at Area 13 of the Nevada Test Site, between 1954 and 1963.

Usage

Am_data

Format

A data frame with 212 rows and 3 variables:

Easting

Easting in metres

Northing

Northing in metres

Am

Americium concentration in 1000 counts per minute

References

Paul R, Cressie N (2011). “Lognormal block kriging for contaminated soil.” European Journal of Soil Science, 62, 337–345.

Creates pixels around points

Description

Takes a SpatialPointsDataFrame and converts it into SpatialPolygonsDataFrame by constructing a tiny (within machine tolerance) BAU around each SpatialPoint.

Usage

BAUs_from_points(obj, offset = 1e-10)## S4 method for signature 'SpatialPoints'BAUs_from_points(obj, offset = 1e-10)## S4 method for signature 'ST'BAUs_from_points(obj, offset = 1e-10)

Arguments

Details

This function allows users to mimic standard geospatial analysis where BAUs are not used. SinceFRK is built on the concept of a BAU, this function constructs tiny BAUs around the observation and prediction locations that can be subsequently passed on to the functionsSRE andFRK. WithBAUs_from_points, the user supplies both the data and prediction locations accompanied with covariates.

See Also

auto_BAUs for automatically constructing generic BAUs.

Examples

library(sp)opts_FRK$set("parallel",0L)df <- data.frame(x = rnorm(10),                 y = rnorm(10))coordinates(df) <- ~x+yBAUs <- BAUs_from_points(df)

Generic basis-function constructor

Description

This function is meant to be used for manual construction of arbitrary basis functions. For‘local’ basis functions, please use the functionlocal_basis instead.

Usage

Basis(manifold, n, fn, pars, df, regular = FALSE)

Arguments

Details

This constructor checks that all parameters are valid before constructing the basis functions. The requirement that every function is encapsulated is tedious, but necessary forFRK to work with a large range of basis functions in the future. Please see the example below which exemplifiesthe process of constructing linear basis functions from scratch using this function.

See Also

auto_basis for constructing basis functions automatically,local_basis forconstructing ‘local’ basis functions, andshow_basis for visualising basis functions.

Examples

## Construct two linear basis functions on [0, 1]manifold <- real_line()n <- 2lin_basis_fn <- function(manifold, grad, intercept) {   function(s) grad*s + intercept}pars <- list(list(grad = 1, intercept = 0),             list(grad = -1, intercept = 1))fn <- list(lin_basis_fn(manifold, 1, 0),           lin_basis_fn(manifold, -1, 1))df <- data.frame(n = 1:2, grad = c(1, -1), m = c(1, -1))G <- Basis(manifold = manifold, n = n, fn = fn, pars = pars, df = df)## Not run: eval_basis(G, s = matrix(seq(0,1, by = 0.1), 11, 1))## End(Not run)

Basis functions

Description

An object of classBasis contains the basis functions used to construct the matrixS in FRK.

Details

Basis functions are a central component ofFRK, and the package is designed to work with user-defined specifications of these. For convenience, however, several functions are available to aid the user to construct a basis set for a given set of data points. Please seeauto_basis for more details. The functionlocal_basis helps the user construct a set of local basis functions (e.g., bisquare functions) from a collection of location and scale parameters.

Slots

manifold

an object of classmanifold that contains information on the manifold and the distance measure used on the manifold. Seemanifold-class for more details

n

the number of basis functions in this set

fn

a list of lengthn, with each item the function of a specific basis function

pars

a list of parameters where thei-th item in the list contains the parameters of thei-th basis function,fn[[i]]

df

a data frame containing other attributes specific to each basis function (for example the geometric centre of the local basis function)

regular

logical indicating if the basis functions (of each resolution) are in a regular grid

See Also

auto_basis for automatically constructing basis functions andshow_basis for visualising basis functions.

Construct SRE object, fit and predict

Description

The Spatial Random Effects (SRE) model is the central object inFRK. The functionFRK() provides a wrapper for the construction and estimation of the SRE object from data, using the functionsSRE() (the object constructor) andSRE.fit() (for fitting it to the data). Please seeSRE-class for more details on the SRE object's properties and methods.

Usage

FRK(  f,  data,  basis = NULL,  BAUs = NULL,  est_error = TRUE,  average_in_BAU = TRUE,  sum_variables = NULL,  normalise_wts = TRUE,  fs_model = "ind",  vgm_model = NULL,  K_type = c("block-exponential", "precision", "unstructured"),  n_EM = 100,  tol = 0.01,  method = c("EM", "TMB"),  lambda = 0,  print_lik = FALSE,  response = c("gaussian", "poisson", "gamma", "inverse-gaussian", "negative-binomial",    "binomial"),  link = c("identity", "log", "sqrt", "logit", "probit", "cloglog", "inverse",    "inverse-squared"),  optimiser = nlminb,  fs_by_spatial_BAU = FALSE,  known_sigma2fs = NULL,  taper = NULL,  simple_kriging_fixed = FALSE,  ...)SRE(  f,  data,  basis,  BAUs,  est_error = TRUE,  average_in_BAU = TRUE,  sum_variables = NULL,  normalise_wts = TRUE,  fs_model = "ind",  vgm_model = NULL,  K_type = c("block-exponential", "precision", "unstructured"),  normalise_basis = TRUE,  response = c("gaussian", "poisson", "gamma", "inverse-gaussian", "negative-binomial",    "binomial"),  link = c("identity", "log", "sqrt", "logit", "probit", "cloglog", "inverse",    "inverse-squared"),  include_fs = TRUE,  fs_by_spatial_BAU = FALSE,  ...)SRE.fit(  object,  n_EM = 100L,  tol = 0.01,  method = c("EM", "TMB"),  lambda = 0,  print_lik = FALSE,  optimiser = nlminb,  known_sigma2fs = NULL,  taper = NULL,  simple_kriging_fixed = FALSE,  ...)## S4 method for signature 'SRE'predict(  object,  newdata = NULL,  obs_fs = FALSE,  pred_time = NULL,  covariances = FALSE,  nsim = 400,  type = "mean",  k = NULL,  percentiles = c(5, 95),  kriging = "simple")## S4 method for signature 'SRE'logLik(object)## S4 method for signature 'SRE'nobs(object, ...)## S4 method for signature 'SRE'coef(object, ...)## S4 method for signature 'SRE'coef_uncertainty(  object,  percentiles = c(5, 95),  nsim = 400,  random_effects = FALSE)simulate(object, newdata = NULL, nsim = 400, conditional_fs = FALSE, ...)## S4 method for signature 'SRE'fitted(object, ...)## S4 method for signature 'SRE'residuals(object, type = "pearson")## S4 method for signature 'SRE'AIC(object, k = 2)## S4 method for signature 'SRE'BIC(object)

Arguments

Details

The following details provide a summary of the model and basic workflowused inFRK. See Zammit-Mangion and Cressie(2021) and Sainsbury-Dale, Zammit-Mangion and Cressie (2023) for further details.

Model description

The hierarchical model implemented inFRK is a spatial generalisedlinear mixed model (GLMM), which may be summarised as

whereZ_j denotes a datum,EF corresponds to a probabilitydistribution in the exponential family with dispersion parameter\psi,μ_Z is the vector containing the conditional expectations of each datum,C_Z is a matrix which aggregates the BAU-level mean process over the observation supports,μ is the mean process evaluated over the BAUs,g is a link function,Y is a latent Gaussian process evaluated over the BAUs,the matrixT contains regression covariates at the BAU level associated with the fixed effectsα,the matrixG is a design matrix at the BAU level associated with random effectsγ,the matrixS contains basis-function evaluations over the BAUs associated with basis-function random effectsη, andξ is a vector containing fine-scale variation at the BAU level.

The prior distribution of the random effects,γ, is a mean-zero multivariate Gaussian with diagonal covariance matrix, with each group of random effects associated with its own variance parameter. These variance parameters are estimated during model fitting.

The prior distribution of the basis-function coefficients,η, is formulatedusing either a covariance matrixK or precision matrixQ, depending on the argumentK_type. The parameters of these matrices are estimated during model fitting.

The prior distribution of the fine-scale random effects,ξ, is a mean-zero multivariate Gaussian with diagonal covariance matrix,Σ_ξ.By default,Σ_ξ = σ²_ξV, whereV is aknown, positive-definite diagonal matrix whose elements are provided in thefieldfs in the BAUs. In the absence of problemspecific fine-scale information,fs can simply be set to 1, so thatV =I.In a spatio-temporal setting, another model forΣ_ξcan be used by settingfs_by_spatial_BAU = TRUE, in which case eachspatial BAU is associated with its own fine-scale variance parameter (see Sainsbury-Dale et al., 2023, Sec. 2.6).In either case, the fine-scale variance parameter(s) are either estimated during model fitting, or provided bythe user via the argumentknown_sigma2fs.

Gaussian data model with an identity link function

When the data is Gaussian, and an identity link function is used, the precedingmodel simplifies considerably: Specifically,

whereZ is the data vector,δ is systematic error at the BAU level, ande represents independent measurement error.

Distributions with size parameters

Two distributions considered in this framework, namely the binomialdistribution and the negative-binomial distribution, have an assumed-known‘size’ parameter and a ‘probability of success’ parameter.Given the vector of size parameters associated with the data,k_Z, the parameterisation used inFRK assumes thatZ_j represents either the number of ‘successes’ fromk_Zj trials (binomial data model) or that it represents the number of failures beforek_Zj successes (negative-binomial data model).

When model fitting, the BAU-level size parameters k are needed.The user must supply these size parameters either through the data or thoughthe BAUs. How this is done depends on whether the data are areal orpoint-referenced, and whether they overlap common BAUs or not.The simplest case is when each observation is associated with a single BAUonly and each BAU is associated with at most one observation support; then,it is straightforward to assign elements fromk_Z to elements of k and vice-versa, and so the user may provide either k ork_Z.If each observation is associated withexactly one BAU, but some BAUs are associated with multiple observations,the user must providek_Z, which is used to infer k; inparticular,k_i = Σ_j∈ai k_Zj ,i = 1, \dots, N, wherea_idenotes the indices of the observations associated with BAUA_i.If one or more observations encompass multiple BAUs, kmust be provided with the BAUs, as we cannot meaningfullydistributek_Zjover multiple BAUs associated with datumZ_j.In this case, we inferk_Z usingk_Zj = Σ_i∈cj k_i ,j = 1, \dots, m, wherec_jdenotes the indices of the BAUs associated with observationZ_j.

Set-up

SRE() constructs a spatial random effects model from the user-defined formula, data object (a listof spatially-referenced data), basis functions and a set of Basic Areal Units (BAUs).It first takes each object in the listdata and maps it to the BAUs – thisentails binning point-referenced data into the BAUs (and averaging within theBAU ifaverage_in_BAU = TRUE), and finding which BAUs are associatedwith observations. Following this, the incidence matrix,C_Z, isconstructed.All required matrices (S,T,C_Z, etc.)are constructed withinSRE() and returned as part of theSRE object.SRE() also intitialises the parameters and random effects usingsensible defaults. Please seeSRE-class for more details.The functionsobserved_BAUs() andunobserved_BAUs() return theindices of the observed and unobserved BAUs, respectively.

To include random effects inFRK please follow the notation as used inlme4. For example, to add a random effect according to a variablefct, simply add '(1 | fct)' to the formula used when callingFRK() orSRE(). Note thatFRK only supports simple, uncorrelated random effects and that a formula term such as '(1 + x | fct)' will throw an error (since inlme4 parlance this implies that the random effect corresponding to the intercept and the slope are correlated). If one wishes to model a an intercept and linear trend for each level infct, then one can force the intercept and slope terms to be uncorrelated by using the notation "(x || fct)", which is shorthand for "(1 | fct) + (x - 1 | x2)".

Model fitting

SRE.fit() takes an object of classSRE and estimates all unknownparameters, namely the covariance matrixK, the fine scale variance(σ²_ξ orσ²_δ, depending on whether Case 1or Case 2 is chosen; see the vignette "FRK_intro") and the regression parametersα.There are two methods of model fitting currently implemented, both of whichimplement maximum likelihood estimation (MLE).

MLE via the expectation maximisation(EM) algorithm.

This method is implemented onlyfor Gaussian data and an identity link function.The log-likelihood (given in Section 2.2 of the vignette) is evaluated at eachiteration at the current parameter estimate. Optimation continues untilconvergence is reached (when the log-likelihood stops changing by more thantol), or when the number of EM iterations reachesn_EM.The actual computations for the E-step and M-step are relatively straightforward.The E-step contains an inverse of anr \times r matrix, whereris the number of basis functions which should not exceed 2000. The M-stepfirst updates the matrixK, which only depends on the sufficientstatistics of the basis-function coefficientsη. Then, the regressionparametersα are updated and a simple optimisation routine(a line search) is used to update the fine-scale varianceσ²_δ orσ²_ξ. If the fine-scale errors andmeasurement random errors are homoscedastic, then a closed-form solution isavailable for the update ofσ²_ξ orσ²_δ.Irrespectively, since the updates ofα, andσ²_δorσ²_ξ, are dependent, these two updates are iterated untilthe change inσ²_. is no more than 0.1%.

MLE viaTMB.

This method is implemented forall available data models and link functions offered byFRK. Furthermore,this method facilitates the inclusion of many more basis function than possiblewith the EM algorithm (in excess of 10,000).TMB appliesthe Laplace approximation to integrate out the latent random effects from thecomplete-data likelihood. The resulting approximation of the marginallog-likelihood, and its derivatives with respect to the parameters, are thencalled from withinR using the optimising functionoptimiser(defaultnlminb()).

Wrapper for set-up and model fitting

The functionFRK() acts as a wrapper for the functionsSRE() andSRE.fit(). An added advantage of usingFRK() directly is that itautomatically generates BAUs and basis functions based on the data. HenceFRK() can be called using only a list of data objects and anRformula, although theR formula can only contain space or time ascovariates when BAUs are not explicitly supplied with the covariate data.

Prediction

Once the parameters are estimated, theSRE object is passed onto thefunctionpredict() in order to carry out optimal predictions over thesame BAUs used to construct the SRE model withSRE(). The first partof the prediction process is to construct the matrixS over theprediction polygons. This is made computationally efficient by treating theprediction over polygons as that of the prediction over a combination of BAUs.This will yield valid results only if the BAUs are relatively small. Once thematrixS is found, a standard Gaussian inversion (through conditioning)using the estimated parameters is used for prediction.

predict() returns the BAUs (or an object specified innewdata),which are of classSpatialPixelsDataFrame,SpatialPolygonsDataFrame,orSTFDF, with predictions anduncertainty quantification added.Ifmethod = "TMB", the returned object is a list, containing thepreviously described predictions, and a list of Monte Carlo samples.The predictions and uncertainties can be easily plotted usingplotorspplot from the packagesp.

References

Zammit-Mangion, A. and Cressie, N. (2021). FRK: An R package for spatial and spatio-temporal prediction with large datasets. Journal of Statistical Software, 98(4), 1-48. doi:10.18637/jss.v098.i04.

Sainsbury-Dale, M. and Zammit-Mangion, A. and Cressie, N. (2024) Modelling Big, Heterogeneous, Non-Gaussian Spatial and Spatio-Temporal Data using FRK. Journal of Statistical Software, 108(10), 1–39. doi:10.18637/jss.v108.i10.

See Also

SRE-class for details on the SRE object internals,auto_basis for automatically constructing basis functions, andauto_BAUs for automatically constructing BAUs.

Examples

library("FRK")library("sp")## Generate process and datam <- 250                                                   # Sample sizezdf <- data.frame(x = runif(m), y= runif(m))               # Generate random locszdf$Y <- 3 + sin(7 * zdf$x) + cos(9 * zdf$y)               # Latent processzdf$z <- rnorm(m, mean = zdf$Y)                            # Simulate datacoordinates(zdf) = ~x+y                                    # Turn into sp object## Construct BAUs and basis functionsBAUs <- auto_BAUs(manifold = plane(), data = zdf,                  nonconvex_hull = FALSE, cellsize = c(0.03, 0.03), type="grid")BAUs$fs <- 1 # scalar fine-scale covariance matrixbasis <- auto_basis(manifold =  plane(), data = zdf, nres = 2)## Construct the SRE modelS <- SRE(f = z ~ 1, list(zdf), basis = basis, BAUs = BAUs)## Fit with 2 EM iterations so to take as little time as possibleS <- SRE.fit(S, n_EM = 2, tol = 0.01, print_lik = TRUE)## Check fit info, final log-likelihood, and estimated regression coefficientsinfo_fit(S)logLik(S)coef(S)## Predict over BAUspred <- predict(S)## Plot## Not run: plotlist <- plot(S, pred)ggpubr::ggarrange(plotlist = plotlist, nrow = 1, align = "hv", legend = "top")## End(Not run)

MODIS cloud data

Description

An image of a cloud taken by the Moderate ResolutionImaging Spectroradiometer (MODIS) instrument aboard the Aqua satellite (MODISCharacterization Support Team, 2015).

Usage

MODIS_cloud_df

Format

A data frame with 33,750 rows and 3 variables:

x

x-coordinate

y

y-coordinate

z

binary dependent variable: 1 if cloud is present, 0 if no cloud. Thisvariable has been thresholded from the original continuous measurement ofradiance supplied by the MODIS instrument

z_unthresholded

The original continuous measurement ofradiance supplied by the MODIS instrument

References

MODIS Characterization Support Team (2015). MODIS 500m Calibrated Radiance Product.NASA MODIS Adaptive Processing System, Goddard Space Flight Center, USA.

NOAA maximum temperature data for 1990–1993

Description

Maximum temperature data obtained from the National Oceanic and AtmosphericAdministration (NOAA) for a part of the USA between 1990 and 1993 (inclusive).See https://iridl.ldeo.columbia.edu/ SOURCES/.NOAA/.NCDC/.DAILY/.FSOD/.

Usage

NOAA_df_1990

Format

A data frame with 196,253 rows and 8 variables:

year

year of retrieval

month

month of retrieval

day

day of retrieval

z

dependent variable

proc

variable name (Tmax)

id

station id

lon

longitude coordinate of measurement station

lat

latitude coordinate of measurement station

References

National Climatic Data Center, March 1993: Local Climatological Data.Environmental Information summary (C-2), NOAA-NCDC, Asheville, NC.

Spatial Random Effects class

Description

This is the central class definition of theFRK package, containing the model and all other information required for estimation and prediction.

Details

The spatial random effects (SRE) model is the model employed in Fixed Rank Kriging, and theSRE object contains all information required for estimation and prediction from spatial data. Object slots contain both other objects (for example, an object of classBasis) and matrices derived from these objects (for example, the matrixS) in order to facilitate computations.

Slots

f

formula used to define the SRE object. All covariates employed need to be specified in the objectBAUs

data

the original data from which the model's parameters are estimated

basis

object of classBasis used to construct the matrixS

BAUs

object of classSpatialPolygonsDataFrame,SpatialPixelsDataFrame ofSTFDF that contains the Basic Areal Units (BAUs) that are used to both (i) project the data onto a common discretisation if they are point-referenced and (ii) provide a BAU-to-data relationship if the data has a spatial footprint

S

matrix constructed by evaluating the basis functions at all the data locations (of classMatrix)

S0

matrix constructed by evaluating the basis functions at all BAUs (of classMatrix)

D_basis

list of distance-matrices of classMatrix, one for each basis-function resolution

Ve

measurement-error variance-covariance matrix (typically diagonal and of classMatrix)

Vfs

fine-scale variance-covariance matrix at the data locations (typically diagonal and of classMatrix) up to a constant of proportionality estimated using the EM algorithm

Vfs_BAUs

fine-scale variance-covariance matrix at the BAU centroids (typically diagonal and of classMatrix) up to a constant of proportionality estimated using the EM algorithm

Qfs_BAUs

fine-scale precision matrix at the BAU centroids (typically diagonal and of classMatrix) up to a constant of proportionality estimated using the EM algorithm

Z

vector of observations (of classMatrix)

Cmat

incidence matrix mapping the observations to the BAUs

X

design matrix of covariates at all the data locations

G

list of objects of class Matrix containing the design matrices for random effects at all the data locations

G0

list of objects of class Matrix containing the design matrices for random effects at all BAUs

K_type

type of prior covariance matrix of random effects. Can be "block-exponential" (correlation between effects decays as a function of distance between the basis-function centroids), "unstructured" (all elements inK are unknown and need to be estimated), or "neighbour" (a sparse precision matrix is used, whereby only neighbouring basis functions have non-zero precision matrix elements).

mu_eta

updated expectation of the basis-function random effects (estimated)

mu_gamma

updated expectation of the random effects (estimated)

S_eta

updated covariance matrix of random effects (estimated)

Q_eta

updated precision matrix of random effects (estimated)

Khat

prior covariance matrix of random effects (estimated)

Khat_inv

prior precision matrix of random effects (estimated)

alphahat

fixed-effect regression coefficients (estimated)

sigma2fshat

fine-scale variation scaling (estimated)

sigma2gamma

random-effect variance parameters (estimated)

fs_model

type of fine-scale variation (independent or CAR-based). Currently only "ind" is permitted

info_fit

information on fitting (convergence etc.)

response

A character string indicating the assumed distribution of the response variable

link

A character string indicating the desired link function. Can be "log", "identity", "logit", "probit", "cloglog", "reciprocal", or "reciprocal-squared". Note that only sensible link-function and response-distribution combinations are permitted.

mu_xi

updated expectation of the fine-scale random effects at all BAUs (estimated)

Q_posterior

updated joint precision matrix of the basis function random effects and observed fine-scale random effects (estimated)

log_likelihood

the log likelihood of the fitted model

method

the fitting procedure used to fit the SRE model

phi

the estimated dispersion parameter (assumed constant throughout the spatial domain)

k_Z

vector of known size parameters at the observation support level (only applicable to binomial and negative-binomial response distributions)

k_BAU

vector of known size parameters at the observed BAUs (only applicable to binomial and negative-binomial response distributions)

include_fs

flag indicating whether the fine-scale variation should be included in the model

include_gamma

flag indicating whether there are gamma random effects in the model

normalise_wts

ifTRUE, the rows of the incidence matricesC_Z andC_P are normalised to sum to 1, so that the mapping represents a weighted average; if false, no normalisation of the weights occurs (i.e., the mapping corresponds to a weighted sum)

fs_by_spatial_BAU

ifTRUE, then each BAU is associated with its own fine-scale variance parameter

obsidx

indices of observed BAUs

simple_kriging_fixed

logical indicating whether one wishes to commit to simple kriging at the fitting stage: IfTRUE, model fitting is faster, but the option to conduct universal kriging at the prediction stage is removed

References

Zammit-Mangion, A. and Cressie, N. (2017). FRK: An R package for spatial and spatio-temporal prediction with large datasets. Journal of Statistical Software, 98(4), 1-48. doi:10.18637/jss.v098.i04.

See Also

SRE for details on how to construct and fit SRE models.

Deprecated: Please usepredict

Description

Deprecated: Please usepredict

Usage

SRE.predict(...)

Arguments

plane in space-time

Description

Initialisation of a 2D plane with a temporal dimension.

Usage

STplane(measure = Euclid_dist(dim = 3L))

Arguments

Details

A 2D plane with a time component added is initialised using ameasure object. By default, the measure object (measure) is the Euclidean distance in 3 dimensions,Euclid_dist.

Examples

P <- STplane()print(type(P))print(sp::dimensions(P))

Space-time sphere

Description

Initialisation of a 2-sphere (S2) with a temporal dimension

Usage

STsphere(radius = 6371)

Arguments

Details

As with the spatial-only sphere, the sphere surface is initialised using aradius parameter. The default value of the radiusR isR=6371, which is the Earth's radius in km, while the measure used to compute distances on the sphere is the great-circle distance on a sphere of radiusR. By default Euclidean geometry is used to factor in the time component, so that dist((s1,t1),(s2,t2)) = sqrt(gc_dist(s1,s2)^2 + (t1 - t2)^2). Frequently this distance can be used since separate correlation length scales for space and time are estimated in the EM algorithm (that effectively scale space and time separately).

Examples

S <- STsphere()print(sp::dimensions(S))

SpatialPolygonsDataFrame to df

Description

ConvertSpatialPolygonsDataFrame orSpatialPixelsDataFrame object to data frame.

Usage

SpatialPolygonsDataFrame_to_df(sp_polys, vars = names(sp_polys))

Arguments

Details

This function is mainly used for plottingSpatialPolygonsDataFrame objects withggplot rather thanspplot. The coordinates of each polygon are extracted and concatenated into one long data frame. The attributes of each polygon are then attached to this data frame as variables that vary by polygonid (the rownames of the object).

Examples

library(sp)library(ggplot2)opts_FRK$set("parallel",0L)df <- data.frame(id = c(rep(1,4),rep(2,4)),                 x = c(0,1,0,0,2,3,2,2),                 y=c(0,0,1,0,0,1,1,0))pols <- df_to_SpatialPolygons(df,"id",c("x","y"),CRS())polsdf <- SpatialPolygonsDataFrame(pols,data.frame(p = c(1,2),row.names=row.names(pols)))df2 <- SpatialPolygonsDataFrame_to_df(polsdf)## Not run: ggplot(df2,aes(x=x,y=y,group=id)) + geom_polygon()

Tensor product of basis functions

Description

Constructs a new set of basis functions by finding the tensor product of two sets of basis functions.

Usage

TensorP(Basis1, Basis2)## S4 method for signature 'Basis,Basis'TensorP(Basis1, Basis2)

Arguments

See Also

auto_basis for automatically constructing basis functions andshow_basis for visualising basis functions.

Examples

library(spacetime)library(sp)library(dplyr)sim_data <- data.frame(lon = runif(20,-180,180),                       lat = runif(20,-90,90),                       t = 1:20,                       z = rnorm(20),                       std = 0.1)time <- as.POSIXct("2003-05-01",tz="") + 3600*24*(sim_data$t-1)space <- sim_data[,c("lon","lat")]coordinates(space) = ~lon+lat # change into an sp objectslot(space, "proj4string") = CRS("+proj=longlat +ellps=sphere")STobj <- STIDF(space,time,data=sim_data)G_spatial <- auto_basis(manifold = sphere(),                        data=as(STobj,"Spatial"),                        nres = 1,                        type = "bisquare",                        subsamp = 20000)G_temporal <- local_basis(manifold=real_line(),loc = matrix(c(1,3)),scale = rep(1,2))G <- TensorP(G_spatial,G_temporal)# show_basis(G_spatial)# show_basis(G_temporal)

Automatic BAU generation

Description

This function calls the generic functionauto_BAU (not exported) after a series of checks and is the easiest way to generate a set of Basic Areal Units (BAUs) on the manifold being used; see details.

Usage

auto_BAUs(  manifold,  type = NULL,  cellsize = NULL,  isea3h_res = NULL,  data = NULL,  nonconvex_hull = TRUE,  convex = -0.05,  tunit = NULL,  xlims = NULL,  ylims = NULL,  spatial_BAUs = NULL,  ...)

Arguments

Details

auto_BAUs constructs a set of Basic Areal Units (BAUs) used both for data pre-processing and for prediction. As such, the BAUs need to be of sufficienly fine resolution so that inferences are not affected due to binning.

Two types of BAUs are supported byFRK: “hex” (hexagonal) and “grid” (rectangular). In order to have a “grid” set of BAUs, the user should specify a cellsize of length one, or of length equal to the dimensions of the manifold, that is, of length 1 forreal_line and of length 2 for the surface of asphere andplane. When a “hex” set of BAUs is desired, the first element ofcellsize is used to determine the side length by dividing this value by approximately 2. The argumenttype is ignored withreal_line and “hex” is not available for this manifold.

If the objectdata is provided, then automatic domain selection may be carried out by employing thefmesher functionfm_nonconvex_hull_inla, which finds a (non-convex) hull surrounding the data points (or centroids of the data polygons). This domain is extended and smoothed using the parameterconvex. The parameterconvex should be negative, and a larger absolute value forconvex results in a larger domain with smoother boundaries.

See Also

auto_basis for automatically constructing basis functions.

Examples

## First a 1D examplelibrary(sp)set.seed(1)data <- data.frame(x = runif(10)*10, y = 0, z= runif(10)*10)coordinates(data) <- ~x+yGrid1D_df <- auto_BAUs(manifold = real_line(),                       cellsize = 1,                       data=data)## Not run: spplot(Grid1D_df)## Now a 2D exampledata(meuse)coordinates(meuse) = ~x+y # change into an sp object## Grid BAUsGridPols_df <- auto_BAUs(manifold = plane(),                         cellsize = 200,                         type = "grid",                         data = meuse,                         nonconvex_hull = 0)## Not run: plot(GridPols_df)## Hex BAUsHexPols_df <- auto_BAUs(manifold = plane(),                        cellsize = 200,                        type = "hex",                        data = meuse,                        nonconvex_hull = 0)## Not run: plot(HexPols_df)

Automatic basis-function placement

Description

Automatically generate a set of local basis functions in the domain, and automatically prune in regions of sparse data.

Usage

auto_basis(  manifold = plane(),  data,  regular = 1,  nres = 3,  prune = 0,  max_basis = NULL,  subsamp = 10000,  type = c("bisquare", "Gaussian", "exp", "Matern32"),  isea3h_lo = 2,  bndary = NULL,  scale_aperture = ifelse(is(manifold, "sphere"), 1, 1.25),  verbose = 0L,  buffer = 0,  tunit = NULL,  ...)

Arguments

Details

This function automatically places basis functions within the domain of interest. If the domain is a plane or the real line, then the objectdata is used to establish the domain boundary.

Let\phi(u) denote the value of a basis function evaluated atu = s - c, wheres is a spatial coordinate andc is the basis-function centroid. The argumenttype can be either “Gaussian”, in which case

“bisquare”, in which case

“exp”, in which case

or “Matern32”, in which case

where the parameters\sigma, R, \tau and\kappa arescale arguments.

If the manifold is the real line, the basis functions are placed regularly inside the domain, and the number of basis functions at the coarsest resolution is dictated by the integer parameterregular which has to be greater than zero. On the real line, each subsequent resolution has twice as many basis functions. The scale of the basis function is set based on the minimum distance between the centre locations following placement. The scale is equal to the minimum distance if the type of basis function is Gaussian, exponential, or Matern32, and is equal to 1.5 times this value if the function is bisquare.

If the manifold is a plane, andregular > 0, then basis functions are placed regularly within the bounding box ofdata, with the smallest number of basis functions in each row or column equal to the value ofregular in the coarsest resolution (note, this is just the smallest number of basis functions). Subsequent resolutions have twice the number of basis functions in each row or column. Ifregular = 0, then the functionfmesher::fm_nonconvex_hull_inla() is used to construct a (non-convex) hull around the data. The buffer and smoothness of the hull is determined by the parameterconvex. Once the domain boundary is found,fmesher::fm_mesh_2d_inla() is used to construct a triangular mesh such that the node vertices coincide with data locations, subject to some minimum and maximum triangular-side-length constraints. The result is a mesh that is dense in regions of high data density and not dense in regions of sparse data. Even basis functions are irregularly placed, the scale is taken to be a function of the minimum distance between basis function centres, as detailed above. This may be changed in a future revision of the package.

If the manifold is the surface of a sphere, then basis functions are placed on the centroids of the discrete global grid (DGG), with the first basis resolution corresponding to the third resolution of the DGG (ISEA3H resolution 2, which yields 92 basis functions globally). It is not recommended to go abovenres == 3 (ISEA3H resolutions 2–4) for the whole sphere;nres=3 yields a total of 1176 basis functions. Up to ISEA3H resolution 6 is available withFRK; for finer resolutions; please installdggrids fromhttps://github.com/andrewzm/dggrids usingdevtools.

Basis functions that are not influenced by data points may hinder convergence of the EM algorithm whenK_type = "unstructured", since the associated hidden states are, by and large, unidentifiable. We hence provide a means to automatically remove such basis functions through the parameterprune. The final set only contains basis functions for which the column sums in the associated matrixS (which, recall, is the value/average of the basis functions at/over the data points/polygons) is greater thanprune. Ifprune == 0, no basis functions are removed from the original design.

See Also

remove_basis for removing basis functions andshow_basis for visualising basis functions

Examples

## Not run: library(sp)library(ggplot2)## Create a synthetic datasetset.seed(1)d <- data.frame(lon = runif(n=1000,min = -179, max = 179),                lat = runif(n=1000,min = -90, max = 90),                z = rnorm(5000))coordinates(d) <- ~lon + latslot(d, "proj4string") = CRS("+proj=longlat +ellps=sphere")## Now create basis functions over sphereG <- auto_basis(manifold = sphere(),data=d,                nres = 2,prune=15,                type = "bisquare",                subsamp = 20000)## Plotshow_basis(G,draw_world())## End(Not run)

Uncertainty quantification of the fixed effects

Description

Compute confidence intervals for the fixed effects (upper and lower bound specifed by percentiles; default 90% confidence central interval)

Usage

coef_uncertainty(  object,  percentiles = c(5, 95),  nsim = 400,  random_effects = FALSE)

Arguments

Combine basis functions

Description

Takes a list of objects of classBasis and returns a single object of classBasis.

Usage

combine_basis(Basis_list)## S4 method for signature 'list'combine_basis(Basis_list)

Arguments

See Also

auto_basis for automatically constructing basis functions andshow_basis for visualising basis functions

Examples

## Construct two resolutions of basis functions using local_basis() Basis1 <- local_basis(manifold = real_line(),                      loc = matrix(seq(0, 1, length.out = 3), ncol = 1),                      scale = rep(0.4, 3))Basis2 <- local_basis(manifold = real_line(),                      loc = matrix(seq(0, 1, length.out = 6), ncol = 1),                      scale = rep(0.2, 6))## Combine basis-function resolutions into a single Basis objectcombine_basis(list(Basis1, Basis2))

Basis-function data frame object

Description

Tools for retrieving and manipulating the data frame within Basis objects. Use the assignmentdata.frame()<- with care; no checks are made to ensure the data frame conforms with the object.

Usage

data.frame(x) <- value## S4 method for signature 'Basis'x$name## S4 replacement method for signature 'Basis'x$name <- value## S4 replacement method for signature 'Basis'data.frame(x) <- value## S4 replacement method for signature 'TensorP_Basis'data.frame(x) <- value## S3 method for class 'Basis'as.data.frame(x, ...)## S3 method for class 'TensorP_Basis'as.data.frame(x, ...)

Arguments

Examples

G <- local_basis()df <- data.frame(G)print(df$res)df$res <- 2data.frame(G) <- df

Convert data frame to SpatialPolygons

Description

Convert data frame to SpatialPolygons object.

Usage

df_to_SpatialPolygons(df, keys, coords, proj)

Arguments

Details

Each row in the data framedf contains both coordinates and labels (or keys) that identify to which polygon the coordinates belong. This function groups the data frame according tokeys and forms aSpatialPolygons object from the coordinates in each group. It is important that all rings are closed, that is, that the last row of each group is identical to the first row. Sincekeys can be of length greater than one, we identify each polygon with a new key by forming an MD5 hash made out of the respectivekeys variables that in themselves are unique (and therefore the hashed key is also unique). For lon-lat coordinates useproj = CRS("+proj=longlat +ellps=sphere").

Examples

library(sp)df <- data.frame(id = c(rep(1,4),rep(2,4)),                 x = c(0,1,0,0,2,3,2,2),                 y=c(0,0,1,0,0,1,1,0))pols <- df_to_SpatialPolygons(df,"id",c("x","y"),CRS())## Not run: plot(pols)

Distance Matrix Computation from Two Matrices

Description

This function extendsdist to accept two arguments.

Usage

distR(x1, x2 = NULL)

Arguments

Details

Computes the distances between the coordinates inx1 and the coordinates inx2. The matricesx1 andx2 do not need to have the same number of rows, but need to have the same number of columns (e.g., manifold dimensions).

Value

Matrix of size N1 x N2

Examples

A <- matrix(rnorm(50),5,10)D <- distR(A,A[-3,])

Compute distance

Description

Compute distance using object of classmeasure ormanifold.

Usage

distance(d, x1, x2 = NULL)## S4 method for signature 'measure'distance(d, x1, x2 = NULL)## S4 method for signature 'manifold'distance(d, x1, x2 = NULL)

Arguments

See Also

real_line,plane,sphere,STplane andSTsphere for constructing manifolds, anddistances for the type of distances available.

Examples

distance(sphere(),matrix(0,1,2),matrix(10,1,2))distance(plane(),matrix(0,1,2),matrix(10,1,2))

Pre-configured distances

Description

Useful objects of classdistance included in package.

Usage

measure(dist, dim)Euclid_dist(dim = 2L)gc_dist(R = NULL)gc_dist_time(R = NULL)

Arguments

Details

Initialises an object of classmeasure which contains a functiondist used for computing the distance between two points. Currently the Euclidean distance and the great-circle distance are included withFRK.

Examples

M1 <- measure(distR,2)D <- distance(M1,matrix(rnorm(10),5,2))

Draw a map of the world with country boundaries.

Description

Layers aggplot2 map of the world over the currentggplot2 object.

Usage

draw_world(g = ggplot() + theme_bw() + xlab("") + ylab(""), inc_border = TRUE)

Arguments

Details

This function usesggplot2::map_data() in order to create a world map. Since, by default, this creates lines crossing the world at the (-180,180) longitude boundary, the function.homogenise_maps() is used to split the polygons at this boundary into two. Ifinc_border is TRUE, then a border is drawn around the lon-lat space; this option is most useful for projections that do not yield rectangular plots (e.g., the sinusoidal global projection).

See Also

the help file for the datasetworldmap

Examples

## Not run: library(ggplot2)draw_world(g = ggplot())## End(Not run)

Evaluate basis functions

Description

Evaluate basis functions at points or average functions over polygons.

Usage

eval_basis(basis, s)## S4 method for signature 'Basis,matrix'eval_basis(basis, s)## S4 method for signature 'Basis,SpatialPointsDataFrame'eval_basis(basis, s)## S4 method for signature 'Basis,SpatialPolygonsDataFrame'eval_basis(basis, s)## S4 method for signature 'Basis,STIDF'eval_basis(basis, s)## S4 method for signature 'TensorP_Basis,matrix'eval_basis(basis, s)## S4 method for signature 'TensorP_Basis,STIDF'eval_basis(basis, s)## S4 method for signature 'TensorP_Basis,STFDF'eval_basis(basis, s)

Arguments

Details

This function evaluates the basis functions at isolated points, or averagesthe basis functions over polygons, for computing the matrixS. The latteroperation is carried out using Monte Carlo integration with 1000 samples per polygon. Whenusing space-time basis functions, the object must contain a fieldt containing a numericrepresentation of the time, for example, containing the number of seconds, hours, or days since the firstdata point.

See Also

auto_basis for automatically constructing basis functions.

Examples

library(sp)### Create a synthetic datasetset.seed(1)d <- data.frame(lon = runif(n=500,min = -179, max = 179),                lat = runif(n=500,min = -90, max = 90),                z = rnorm(500))coordinates(d) <- ~lon + latslot(d, "proj4string") = CRS("+proj=longlat")### Now create basis functions on sphereG <- auto_basis(manifold = sphere(),data=d,                nres = 2,prune=15,                type = "bisquare",                subsamp = 20000)### Now evaluate basis functions at originS <- eval_basis(G,matrix(c(0,0),1,2))

Retrieve fit information for SRE model

Description

Takes an object of classSRE and returns a list containing all the relevant information on parameter estimation

Usage

info_fit(object)## S4 method for signature 'SRE'info_fit(object)

Arguments

See Also

SeeFRK for more information on the SRE model and available fitting methods.

Examples

# See example in the help file for FRK

manifold

Description

Manifold initialisation. This function should not be called directly asmanifold is a virtual class.

Usage

## S4 method for signature 'manifold'initialize(.Object)

Arguments

ISEA Aperture 3 Hexagon (ISEA3H) Discrete Global Grid

Description

The data used here were obtained fromhttps://webpages.sou.edu/~sahrk/dgg/isea.old/gen/isea3h.html and represent ISEAdiscrete global grids (DGGRIDs) generated using theDGGRID software.The original .gen files were converted to a data frame using the functiondggrid_gen_to_df,available with thedggrids package. Only resolutions 0–6 are supplied withFRKand note that resolution 0 of ISEA3H is equal to resolution 1 inFRK. For higherresolutionsdggrids can be installed fromhttps://github.com/andrewzm/dggrids/usingdevtools.

Usage

isea3h

Format

A data frame with 284,208 rows and 5 variables:

id

grid identification number within the given resolution

lon

longitude coordinate

lat

latitude coordinate

res

DGGRID resolution (0 – 6)

centroid

A 0-1 variable, indicating whether the point describes the centroid of the polygon,or whether it is a boundary point of the polygon

References

Sahr, K. (2008). Location coding on icosahedral aperture 3 hexagon discrete global grids. Computers, Environment and Urban Systems, 32, 174–187.

Construct a set of local basis functions

Description

Construct a set of local basis functions based on pre-specified location and scale parameters.

Usage

local_basis(  manifold = sphere(),  loc = matrix(c(1, 0), nrow = 1),  scale = 1,  type = c("bisquare", "Gaussian", "exp", "Matern32"),  res = 1,  regular = FALSE)radial_basis(  manifold = sphere(),  loc = matrix(c(1, 0), nrow = 1),  scale = 1,  type = c("bisquare", "Gaussian", "exp", "Matern32"))

Arguments

Details

This functions lays out local basis functions in a domain of interest based on pre-specified location and scale parameters. Iftype is “bisquare”, then

\phi(u) = \left(1- \left(\frac{\| u \|}{R}\right)^2\right)^2 I(\|u\| < R),

andscale is given byR, the range of support of the bisquare function. Iftype is “Gaussian”, then

\phi(u) = \exp\left(-\frac{\|u \|^2}{2\sigma^2}\right),

andscale is given by\sigma, the standard deviation. Iftype is “exp”, then

\phi(u) = \exp\left(-\frac{\|u\|}{ \tau}\right),

andscale is given by\tau, the e-folding length. Iftype is “Matern32”, then

\phi(u) = \left(1 + \frac{\sqrt{3}\|u\|}{\kappa}\right)\exp\left(-\frac{\sqrt{3}\| u \|}{\kappa}\right),

andscale is given by\kappa, the function's scale.

See Also

auto_basis for constructing basis functions automatically, andshow_basis for visualising basis functions.

Examples

library(ggplot2)G <-  local_basis(manifold = real_line(),                   loc=matrix(1:10,10,1),                   scale=rep(2,10),                   type="bisquare")## Not run: show_basis(G)

(Deprecated) Retrieve log-likelihood

Description

This function is deprecated; please uselogLik

Usage

loglik(object)## S4 method for signature 'SRE'loglik(object)

Arguments

Retrieve manifold

Description

Retrieve manifold fromFRK object.

Usage

manifold(.Object)## S4 method for signature 'Basis'manifold(.Object)## S4 method for signature 'TensorP_Basis'manifold(.Object)

Arguments

See Also

real_line,plane,sphere,STplane andSTsphere for constructing manifolds.

Examples

G <-  local_basis(manifold = plane(),                   loc=matrix(0,1,2),                   scale=0.2,                   type="bisquare")manifold(G)

manifold

Description

The classmanifold is virtual; other manifold classes inherit from this class.

Details

Amanifold object is characterised by a character variabletype, which contains a description of the manifold, and a variablemeasure of typemeasure. A typical measure is the Euclidean distance.

FRK supports five manifolds; the real line (in one dimension), instantiated by usingreal_line(); the 2D plane, instantiated by usingplane(); the 2D-sphere surface S2, instantiated by usingsphere(); the R2 space-time manifold, instantiated by usingSTplane(), and the S2 space-time manifold, instantiated by usingSTsphere(). User-specific manifolds can also be specified, however helper functions that are manifold specific, such asauto_BAUs andauto_basis, only work with the pre-configured manifolds. Importantly, one can change the distance function used on the manifold to synthesise anisotropy or heterogeneity. See the vignette for one such example.

See Also

real_line,plane,sphere,STplane andSTsphere for constructing manifolds.

measure

Description

Measure class used for defining measures used to compute distances between points in objects constructed with theFRK package.

Details

An object of classmeasure contains a distance function and a variabledim with the dimensions of the Riemannian manifold over which the distance is computed.

See Also

distance for computing a distance anddistances for a list of implemented distance functions.

Number of basis functions

Description

Retrieve the number of basis functions fromBasis orSRE object.

Usage

nbasis(.Object)## S4 method for signature 'Basis_obj'nbasis(.Object)## S4 method for signature 'SRE'nbasis(.Object)

Arguments

See Also

auto_basis for automatically constructing basis functions.

Examples

library(sp)data(meuse)coordinates(meuse) = ~x+y # change into an sp objectG <- auto_basis(manifold = plane(),                data=meuse,                nres = 2,                regular=1,                type = "Gaussian")print(nbasis(G))

Return the number of resolutions

Description

Return the number of resolutions from a basis function object.

Usage

nres(b)## S4 method for signature 'Basis'nres(b)## S4 method for signature 'TensorP_Basis'nres(b)## S4 method for signature 'SRE'nres(b)

Arguments

See Also

auto_basis for automatically constructing basis functions andshow_basis for visualising basis functions.

Examples

library(sp)set.seed(1)d <- data.frame(lon = runif(n=500,min = -179, max = 179),                lat = runif(n=500,min = -90, max = 90),                z = rnorm(500))coordinates(d) <- ~lon + latslot(d, "proj4string") = CRS("+proj=longlat")### Now create basis functions on sphereG <- auto_basis(manifold = sphere(),data=d,                nres = 2,prune=15,                type = "bisquare",                subsamp = 20000)nres(G)

Observed (or unobserved) BAUs

Description

Computes the indices (a numeric vector) of the observed (or unobserved) BAUs

Usage

observed_BAUs(object)unobserved_BAUs(object)## S4 method for signature 'SRE'observed_BAUs(object)## S4 method for signature 'SRE'unobserved_BAUs(object)

Arguments

See Also

SeeFRK for more information on the SRE model and available fitting methods.

Examples

# See example in the help file for FRK

FRK options

Description

The main options list for the FRK package.

Usage

opts_FRK

Format

List of 2

$

set:function(opt,value)

$

get:function(opt)

Details

opts_FRK is a list containing two functions,set andget, which can be used to set options and retrieve options, respectively. CurrentlyFRK uses three options:

"progress":

a flag indicating whether progress bars should be displayed or not

"verbose":

a flag indicating whether certain progress messages should be shown or not. Currently this is the only option applicable tomethod = "TMB"

"parallel":

an integer indicating the number of cores to use. A number 0 or 1 indicates no parallelism

Examples

opts_FRK$set("progress",1L)opts_FRK$get("parallel")

plane

Description

Initialisation of a 2D plane.

Usage

plane(measure = Euclid_dist(dim = 2L))

Arguments

Details

A 2D plane is initialised using ameasure object. By default, the measure object (measure) is the Euclidean distance in 2 dimensions,Euclid_dist.

Examples

P <- plane()print(type(P))print(sp::dimensions(P))

Plot predictions from FRK analysis

Description

This function acts as a wrapper aroundplot_spatial_or_ST. It plots the fields of theSpatial*DataFrame orSTFDF object corresponding to prediction and prediction uncertainty quantification. It also uses the@data slot ofSRE object to plot the training data set(s), and generates informative, latex-style legend labels for each of the plots.

Usage

plot(x, y, ...)## S4 method for signature 'SRE,list'plot(x, y, ...)## S4 method for signature 'SRE,STFDF'plot(x, y, ...)## S4 method for signature 'SRE,SpatialPointsDataFrame'plot(x, y, ...)## S4 method for signature 'SRE,SpatialPixelsDataFrame'plot(x, y, ...)## S4 method for signature 'SRE,SpatialPolygonsDataFrame'plot(x, y, ...)

Arguments

Value

A list ofggplot objects consisting of the observed data, predictions, and standard errors. This list can then be supplied to, for example,ggpubr::ggarrange().

Examples

## See example in the help file for SRE

Plot a Spatial*DataFrame or STFDF object

Description

Takes an object of classSpatial*DataFrame orSTFDF, and plots requested data columns usingggplot2

Usage

plot_spatial_or_ST(  newdata,  column_names,  map_layer = NULL,  subset_time = NULL,  palette = "Spectral",  plot_over_world = FALSE,  labels_from_coordnames = TRUE,  ...)## S4 method for signature 'STFDF'plot_spatial_or_ST(  newdata,  column_names,  map_layer = NULL,  subset_time = NULL,  palette = "Spectral",  plot_over_world = FALSE,  labels_from_coordnames = TRUE,  ...)## S4 method for signature 'SpatialPointsDataFrame'plot_spatial_or_ST(  newdata,  column_names,  map_layer = NULL,  subset_time = NULL,  palette = "Spectral",  plot_over_world = FALSE,  labels_from_coordnames = TRUE,  ...)## S4 method for signature 'SpatialPixelsDataFrame'plot_spatial_or_ST(  newdata,  column_names,  map_layer = NULL,  subset_time = NULL,  palette = "Spectral",  plot_over_world = FALSE,  labels_from_coordnames = TRUE,  ...)## S4 method for signature 'SpatialPolygonsDataFrame'plot_spatial_or_ST(  newdata,  column_names,  map_layer = NULL,  subset_time = NULL,  palette = "Spectral",  plot_over_world = FALSE,  labels_from_coordnames = TRUE,  ...)

Arguments

Value

A list ofggplot objects corresponding to the providedcolumn_names. This list can then be supplied to, for example,ggpubr::ggarrange().

See Also

plot

Examples

## See example in the help file for FRK

Plotting themes

Description

Formats a ggplot object for neat plotting.

Usage

LinePlotTheme()EmptyTheme()

Details

LinePlotTheme() createsggplot object with a white background, a relatively large font, and grid lines.EmptyTheme() on the other hand creates aggplot object with no axes or legends.

Value

Object of classggplot

Examples

## Not run: X <- data.frame(x=runif(100),y = runif(100), z = runif(100))LinePlotTheme() + geom_point(data=X,aes(x,y,colour=z))EmptyTheme() + geom_point(data=X,aes(x,y,colour=z))## End(Not run)

real line

Description

Initialisation of the real-line (1D) manifold.

Usage

real_line(measure = Euclid_dist(dim = 1L))

Arguments

Details

A real line is initialised using ameasure object. By default, the measure object (measure) describes the distance between two points as the absolute difference between the two coordinates.

Examples

R <- real_line()print(type(R))print(sp::dimensions(R))

Removes basis functions

Description

Takes an object of classBasis and returns an object of classBasis with selected basis functions removed

Usage

remove_basis(Basis, rmidx)## S4 method for signature 'Basis,ANY'remove_basis(Basis, rmidx)## S4 method for signature 'Basis,SpatialPolygons'remove_basis(Basis, rmidx)

Arguments

See Also

auto_basis for automatically constructing basis functions andshow_basis for visualising basis functions

Examples

library(sp)df <- data.frame(x = rnorm(10),                 y = rnorm(10))coordinates(df) <- ~x+yG <- auto_basis(plane(),df,nres=1)data.frame(G) # Print info on basis## Removing basis functions by indexG_subset <- remove_basis(G, 1:(nbasis(G)-1))data.frame(G_subset)## Removing basis functions using SpatialPolygonsx <- 1poly <- Polygon(rbind(c(-x, -x), c(-x, x), c(x, x), c(x, -x), c(-x, -x)))polys <- Polygons(list(poly), "1")spatpolys <- SpatialPolygons(list(polys))G_subset <- remove_basis(G, spatpolys)data.frame(G_subset)

Show basis functions

Description

Generic plotting function for visualising the basis functions.

Usage

show_basis(basis, ...)## S4 method for signature 'Basis'show_basis(basis, g = ggplot() + theme_bw() + xlab("") + ylab(""))## S4 method for signature 'TensorP_Basis'show_basis(basis, g = ggplot())

Arguments

Details

The functionshow_basis adapts its behaviour to the manifold being used. Withreal_line, the 1D basis functions are plotted with colour distinguishing between the different resolutions. Withplane, only local basis functions are supported (at present). Each basis function is shown as a circle with diameter equal to thescale parameter of the function. Linetype distinguishes the resolution. Withsphere, the centres of the basis functions are shown as circles, with larger sizes corresponding to coarser resolutions. Space-time basis functions of subclassTensorP_Basis are visualised by showing the spatial basis functions and the temporal basis functions in two separate plots.

See Also

auto_basis for automatically constructing basis functions.

Examples

library(ggplot2)library(sp)data(meuse)coordinates(meuse) = ~x+y # change into an sp objectG <- auto_basis(manifold = plane(),data=meuse,nres = 2,regular=2,prune=0.1,type = "bisquare")## Not run: show_basis(G,ggplot()) + geom_point(data=data.frame(meuse),aes(x,y))

sphere

Description

Initialisation of the 2-sphere, S2.

Usage

sphere(radius = 6371)

Arguments

Details

The 2D surface of a sphere is initialised using aradius parameter. The default value of the radiusR isR=6371 km, Earth's radius, while the measure used to compute distances on the sphere is the great-circle distance on a sphere of radiusR.

Examples

S <- sphere()print(sp::dimensions(S))

Type of manifold

Description

Retrieve slottype from object

Usage

type(.Object)## S4 method for signature 'manifold'type(.Object)

Arguments

See Also

real_line,plane,sphere,STplane andSTsphere for constructing manifolds.

Examples

S <- sphere()print(type(S))

World map

Description

This world map was extracted from the packagemaps v.3.0.1 byrunningggplot2::map_data("world"). To reduce the data size, only every third point ofthis data frame is contained inworldmap.

Usage

worldmap

Format

A data frame with 33971 rows and 6 variables:

long

longitude coordinate

lat

latitude coordinate

group

polygon (region) number

order

order of point in polygon boundary

region

region name

subregion

subregion name

References

Original S code by Becker, R.A. and Wilks, R.A. This R version is byBrownrigg, R. Enhancements have been made by Minka, T.P. and Deckmyn, A. (2015)maps: Draw Geographical Maps, R package version 3.0.1.