CKrige {constrainedKriging} | R Documentation |

Function for constrained, covariance-matching constrained and universal (external drift kriging) point or block (of any shape) kriging in a global neighbourhood and for isotropic covariance models.

CKrige( formula, data, locations, object, ...) ## S4 method for signature 'formula,data.frame,formula,preCKrigePolygons' CKrige(formula, data, locations, object, method = 2, ex.out = F) ## S4 method for signature 'formula,data.frame,formula,preCKrigePoints' CKrige(formula, data, locations, object, method = 2, ex.out = F)

`formula` |
formula of the linear regression model in the form |

`data` |
a data frame with the values of the covariates, the names of the
covariates used in the formula object must match the column
names of |

`locations` |
a |

`object` |
either an object of the class “ |

`...` |
two further arguments to control the spatial interpolation method and the output |

`method` |
numeric value to choose the kriging method |

`ex.out` |
logical value, if |

The `CKrige`

function depends always on a `preCKrige`

output object that contains the parameter of the isotropic covariance model as well
as the covariates of the prediction targets.

By default, `CKrige`

returns an object of
the class `SpatialPointsDataFrame`

or

`SpatialPolygonsDataFrame`

depending whether the input object for the `object`

argument is of the
class “`preCKrigePoints`

” or “`preCKrigePolygons`

”.

The data frame of the returned object contains the following columns independent of the selected kriging method:

`prediction` |
numeric vector with the kriging prediction of the chosen method |

`prediction.se` |
numeric vector with the root mean square error (kriging standard error) |

The data frame contains 3 additional columns with constrained kriging
parameters, if the argument `method = 2`

of the `CKrige`

function:

`sqrt.P` |
numeric vector with sqrt( Var[ target point or block ] - Var[ fitted values ] ) |

`sqrt.Q` |
numeric vector with sqrt( Var[ universal kriging predictor ] - Var[ fitted values ] ) |

`K` |
numeric vector with |

The data frame contains 3 additional columns with covariance-matching
constrained kriging parameters, if the argument
`method = 3`

of the `CKrige`

function:

`P1.11` |
numeric vector, first element of the matrix P1 = ( Cov[target point or block] - Cov[fitted values] )^(1/2) |

`Q1.11` |
numeric vector, first element of the matrix Q1 = ( Cov[universal kriging predictor] - Cov[fitted values] )^(1/2) |

`K.11` |
numeric vector, first element of the matrix K = O1^-1P1[1,1] |

The `CKrige`

function returns a list with the following components if
the argument `ex.out = T`

and the argument `method`

is either `1`

or `2`

:

`object` |
either an object of the class |

`krig.method` |
numeric scalar, number of the chosen kriging method 1, 2 or 3. |

`parameter` |
list with 2 components. First component |

`sk.weights` |
if argument |

`inv.Sigma` |
matrix, inverse covariance matrix of the data |

`residuals` |
numeric vector with the Generalized Least Square residuals of the linear regression. |

The list of the extended output contains the additional component `CMCK.par`

if the argument `method = 3`

. The
`CMCK.par`

component is a list of lists with CMCK parameters, in particular `P1`

list of the P1 matrices,
`Q1`

list of the Q1 matrices and `K`

list of the K matrices.

`print`

and `summary`

methods for the different `CKrige`

output objects are available.

Christoph Hofer, christoph.hofer@alumni.ethz.ch

See main help page of the constrainedKriging package.

## Not run: # load data data(meuse,meuse.blocks) # approximation of block variance # pixel area = 75m x 75m # exponential covariance function with measurement error = 0, nugget = 0.05, # part. sill = 0.15 and range parameter = 192.5 preCK=preCKrige(newdata=meuse.blocks,model= covmodel("exponential",0,0.05,0.15,192.5),pwidth=75,pheight=75) # block prediction by constrained kriging on the log scale CK=CKrige(formula=log(zinc)~sqrt(dist),data=meuse, locations=~x+y,object=preCK,ex.out=TRUE) # backtransformation to the original scale for the CK prediction beta=CK$parameter$beta.coef M=meuse.blocks@data$M c1 <- 0.2 c2 <- beta[2]^2 * meuse.blocks@data$M CK$object@data$Zn=exp(CK$object@data$prediction + 0.5*(0.2+beta[2]^2*M-unlist(preCK@covmat))) # U: upper limits of the relative 95 # U multiplied by the predictions CK$object@data$Zn gives # the upper limits of the 95 CK$object@data$U=exp(CK$object@data$prediction +1.96*CK$object@data$prediction.se) /CK$object@data$Zn # plots with spplot, generic function in the sp package # the plot shows the constrained kriging predictions on # the orginal scale # function ck.colors(n) create a rainbow-like color vector breaks <- seq(0, 1850, by = 185) spplot(CK$object,zcol="Zn",at=breaks,col.regions=ck.colors(10), colorkey=list(labels=list(at=breaks,labels=breaks))) # plot of the factor to get the upper bound of the 97.5 breaks=seq(1,3.2,by=0.2) spplot(CK$object,zcol="U",at=breaks,col.regions=ck.colors(11), colorkey=list(labels=list(at=breaks,labels=breaks))) ## End(Not run)

[Package *constrainedKriging* version 0.2.4 Index]