Trend Model
RMtrend is a pure trend model with covariance 0.
RMtrend(mean)
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 |
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.
Using uncapsulated subtraction 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.
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
model1 <- RMexp(var=2, scale=1) + trend
dta <- RFsimulate(model1, 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=dta))
## model2 can be made explicit 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=dta))
## IMPORTANT: subtraction 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!Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.