krig(x, Y, cov.function, lambda=NA, cost=1, knots, weights=rep(1, length(Y)), m=2, return.matrices=T, nstep.cv=50, scale.type="user", x.center=rep(0, ncol(x)), x.scale=rep(1, ncol(x)), rho=NA, sigma2=NA, ...)
x
| Matrix of independent variables. |
Y
| Vector of dependent variables. |
cov.function
| Covariance function for data in the form of an S-PLUS function (see exp.cov). |
lambda
| Smoothing parameter that is the ratio of the error variance (sigma**2) to the scale parameter of the covariance function. If omitted this is estimated by GCV. |
cost
| Cost value used in GCV criterion. Corresponds to a penalty for increased number of parameters. |
knots
| Subset of data used in the fit. |
weights
| Weights are proportional to the reciprocal variance of the measurement error. The default is no weighting i.e. vector of unit weights. |
m
| A polynomial function of degree (m-1) will be included in the model as the drift (or spatial trend) component. |
return.matrices
| Matrices from the decompositions are returned. The default is T. |
nstep.cv
| Number of grid points for minimum GCV search. |
scale.type
| The independent variables and knots are scaled to the specified scale.type. By default the scale type is "unit.sd", whereby the data is scaled to have mean 0 and standard deviation 1. Scale type of "range" scales the data to the interval (0,1) by forming (x-min(x))/range(x) for each x. Scale type of "user" allows specification of an x.center and x.scale by the user. The default for "user" is mean 0 and standard deviation 1. Scale type of "unscaled" does not scale the data. |
x.center
| Centering values are subtracted from each column of the x matrix. |
x.scale
| Scale values that divided into each column after centering. |
rho
| Scale factor for covariance. |
sigma2
| Variance of e. |
...
| Optional arguments. Theta can be specified. If the cov.parameters are specified this list is assumed to be arguments to the covariance function. |
WARNING: The covariance functions often have a nonlinear parameter that controls the strength of the correlations as a function of separation, usually refered to as the range parameter. This parameter must be specified in the call to krig and will not be estimated.
call
| Call to the function |
y
| Vector of dependent variables. |
x
| Matrix of independent variables. |
weights
| Vector of weights. |
knots
| Locations used to define the basis functions. |
transform
| List of components used in centering and scaling data. |
np
| Total number of parameters in the model. |
nt
| Number of parameters in the null space. |
matrices
| List of matrices from the decompositions (D, G, u, X, qr.T). |
gcv.grid
| Matrix of values used in the GCV grid search. The first column is the grid of lambda values used in the search, the second column is the trace of the A matrix, the third column is the GCV values and the fourth column is the estimated variance. |
cost
| Cost value used in GCV criterion. |
m
| Order of the polynomial space: highest degree polynomial is (m-1). |
eff.df
| Effective degrees of freedom of the model. |
fitted.values
| Predicted values from the fit. |
residuals
| Residuals from the fit. |
lambda
| Value of the smoothing parameter used in the fit. |
yname
| Name of the response. |
cov.function
| Covariance function of the model. |
beta
| Estimated coefficients in the ridge regression format |
d
| Esimated coefficients for the polynomial basis functions that span the null space |
fitted.values.null
| Fitted values for just the polynomial part of the estimate |
trace
| Effective number of parameters in model. |
c
| Estimated coefficients for the basis functions derived from the covariance. |
coefficients
| Same as the beta vector. |
just.solve
| Logical describing if the data has been interpolated using the basis functions. |
shat
| Estimated standard deviation of the measurement error (nugget effect). |
sigma2
| Estimated variance of the measurement error (shat**2). |
rho
| Scale factor for covariance. COV(h(x),h(x')) = rho*cov.function(x,x') |
mean.var
| Normalization of the covariance function used to find rho. |
best.model
| Vector containing the value of lambda, the estimated variance of the measurement error and the scale factor for covariance used in the fit. |
#2-d example krig(ozone$x, ozone$y, exp.cov) -> fit # fitting a surface to ozone # measurements. plot(fit) # plots fit and residuals # data using a Gaussian covariance # first make up covariance function test.cov <- function(x1,x2){exp(-(rdist(x1,x2)/.5)**2)} krig(flame$x, flame$y, test.cov) -> fit.flame surface(fit.flame)