RandomFields (version 3.1.36)

# RMtrend: Trend Model

## Description

`RMtrend` is a pure trend model with covariance 0.

## Usage

`RMtrend(mean)`

## Arguments

mean
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(.)\$.

## Value

`RMtrend` returns an object of class `RMmodel`.

## Details

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`.

## References

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

`RMmodel`, `RFformula`, `RFsimulate`, `RMplus`

## Examples

```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!

```