sepindex-class {covatest}

Class "sepindex"

Description

A class for the non separability index (r) for different spatial and temporal lags: \[r(\mathbf{h}, u, \Theta)= \rho(\mathbf{h}, u;\Theta)/ [\rho(\mathbf{h},0;\Theta)\rho(\mathbf{0},u;\Theta)]\] with \(\rho(\mathbf{h}, u;\Theta)>0\); \(\rho(\mathbf{h},0;\Theta)>0\) and \(\rho(\mathbf{0},u;\Theta)>0\). On the basis of this index, the type of non separability of the covariance function can be analyzed.

Usage

sepindex(vario_st, nt, ns, globalSill)

## S4 method for signature 'sepindex'
boxplot(x, ...)

## S4 method for signature 'sepindex'
show(object)

## S4 method for signature 'sepindex'
x[i, j, drop = FALSE]

## S4 method for signature 'sepindex'
summary(object)

Arguments

vario_st

object of class StVariogram, containing the spatio-temporal sample variogram, output from the function variogramST of the package gstat

nt

integer, the number of temporal lags in vario_st

ns

integer, the number of spatial lags in vario_st

globalSill

numeric, the value of the sample variance

x

object of class sepindex for methods boxplot and extract

...

any arguments that will be passed to the panel plotting functions

object

object of class sepindex for methods show and summary

i

index specifying elements to extract. Each row includes data for specific spatio-temporal lags

j

index specifying elements to extract. Set 1 for spatial lags (hs), 2 for temporal lags (ht) and 3 for the nonseparability index (SepIndex)

drop

logical, the argument is set, by default, equal to FALSE to preserve the structure of the object. It is advisable not to change this option

Slots

sep.index.ratio

the empirical non separability index ratio and the corresponding spatio-temporal lags

cov.st

the spatio-temporal sample covariance function and the corresponding spatio-temporal lags

cov.tm

the purely temporal sample covariance function and the corresponding temporal lags

cov.sp

the purely spatial sample covariance function and the corresponding spatial lags

References

Cappello, C., De Iaco, S., Posa, D., 2020, covatest: An R Package for Selecting a Class of Space-Time Covariance Functions. Journal of Statistical Software, 94(1) 1–42.

De Iaco, S., Posa, D., 2013, Positive and negative non-separability for space-time covariance models. Journal of Statistical Planning and Inference, 143 378–391.

Gräler, B., Pebesma, E.J., Heuvelink G., 2016, Spatio-Temporal Interpolation Using gstat. The R Journal, 8(1) 204–218.

Pebesma, E.J., 2004, Multivariable geostatistics in S: the gstat package. Computers & Geosciences, 30 683–691.

Rodriguez, A., Diggle, P.J., 2010, A class of convolution-based models for spatio-temporal processes with non-separable covariance structure. Scandinavian Journal of Statistics, 37(4) 553–567.

Examples

# --start define the STFDF rr_13-- #
library(sp)
library(spacetime)
#library(gstat)
data(air)
ls()
if (!exists("rural")) rural = STFDF(stations, dates, data.frame(PM10 =
as.vector(air)))
rr = rural[,"2005::2010"]
unsel = which(apply(as(rr, "xts"), 2, function(x) all(is.na(x))))
r5to10 = rr[-unsel,]
rr_13 <- r5to10[c("DEHE046","DESN049","DETH026","DENW063","DETH061","DEBY047",
"DENW065","DEUB029","DENW068","DENI019","DEHE051","DERP016","DENI051"),
"2005::2006"]
# --end define the STFDF rr_13-- #

#compute the Global Sill
C00_13 <- var(rr_13[,,"PM10"]@data[[1]], na.rm = TRUE)

#estimate the spatio-temporal variogram by using the function variogramST
#of the package gstat.
#For this aim see vv_13.Rd
data(vv_13)
nonsep.index <- sepindex(vario_st = vv_13, nt = 16, ns = 4, globalSill = C00_13)

##methods for sepindex

#1. show
nonsep.index

#2. summary
summary(nonsep.index)

#3. boxplot
boxplot(nonsep.index, ylab="Non-separability ratio")

#4. [ extract
nonsep.index[1:8, ] #selection of the first 8 rows
nonsep.index[1:8, 1:2] #selection of the first 2 columns