Trend Model

RMtrend is a pure trend model with covariance 0.

models, spatial
numeric or RMmodel. If it is numerical, it should be a vector of length $p$, where $p$ is the number of variables taken into account by the corresponding multivariate random field $(Z_1(.),\ldots,Z_p(.))$; the $i$-th component of mean is interpreted as constant mean of $Z_i(.)$.

Note that this function refers to trend surfaces in the geostatistical framework. Fixed effects in the mixed models framework are also being implemented, see RFformula.


RMtrend returns an object of class RMmodel.


Using uncapsulated substraction to build up a covariance function is ambiguous, see the examples below. Best to define the trend separately, or to use R.minus.


Chiles, J. P., Delfiner, P. (1999) Geostatistics: Modelling Spatial Uncertainty. New York: John Wiley & Sons.

See Also

RMmodel, RFformula, RFsimulate, RMplus

  • RMtrend
  • trend
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again

## first simulate some data with a sine and a mean as trend
repet <- 100
x <- seq(0, pi, len=10)
trend <- 2 * sin(R.p(new="isotropic")) + 3
model <- RMexp(var=2, scale=1) + trend
data <- RFsimulate(model, x=x, n=repet)

## now, let us estimate variance, scale, and two parameters of the trend
model2 <- RMexp(var=NA, scale=NA) + NA * sin(R.p(new="isotropic")) + NA

print(RFfit(model2, data=data))

## model2 can be made explicite by enclosing the trend parts by
## 'RMtrend'
model3 <- RMexp(var=NA, scale=NA) + NA *
          RMtrend(sin(R.p(new="isotropic"))) + RMtrend(NA)
print(RFfit(model2, data=data))

## IMPORTANT:  substraction is not a way to combine definite models
##             with trends
trend <- -1
(model0 <- RMexp(var=0.4) + trend) ## exponential covariance with mean -1
(model1 <- RMexp(var=0.4) + -1)    ## same as model0
(model2 <- RMexp(var=0.4) + RMtrend(-1)) ## same as model0
(model3 <- RMexp(var=0.4) - 1) ## this is a purely deterministic model
                               ## with exponential trend
plot(RFsimulate(model=model0, x=x, y=x)) ## exponential covariance
                               ##           and mean -1
plot(RFsimulate(model=model1, x=x, y=x)) ## dito
plot(RFsimulate(model=model2, x=x, y=x)) ## dito
plot(RFsimulate(model=model3, x=x, y=x)) ## purely deterministic model!

Documentation reproduced from package RandomFields, version 3.1.36, License: GPL (>= 3)

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