R: Trend Model

RMtrend {RandomFields} | R Documentation

## 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(.),…,Z_p(.)); the i-th component of `mean` is interpreted as constant mean of Z_i(.).

### 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`.

### Value

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

### Note

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`.

### Author(s)

Marco Oesting, oesting@math.uni-mannheim.de

Martin Schlather, schlather@math.uni-mannheim.de http://ms.math.uni-mannheim.de/de/publications/software

### References

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

### See Also

`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!

[Package RandomFields version 3.1.50 Index]