Rational Quadratic Correlation Structure
This function is a constructor for the corRatio
class,
representing a rational quadratic spatial correlation structure. Letting
d denote the range and n denote the nugget
effect, the correlation between two observations a distance
r apart is 1/(1+(r/d)^2) when no nugget effect
is present and (1-n)/(1+(r/d)^2) when a
nugget effect is assumed. Objects created using this constructor need
to be later initialized using the appropriate Initialize
method.
corRatio(value, form, nugget, metric, fixed)
value |
an optional vector with the parameter values in
constrained form. If |
form |
a one sided formula of the form |
nugget |
an optional logical value indicating whether a nugget
effect is present. Defaults to |
metric |
an optional character string specifying the distance
metric to be used. The currently available options are
|
fixed |
an optional logical value indicating whether the
coefficients should be allowed to vary in the optimization, or kept
fixed at their initial value. Defaults to |
an object of class corRatio
, also inheriting from class
corSpatial
, representing a rational quadratic spatial correlation
structure.
José Pinheiro and Douglas Bates bates@stat.wisc.edu
Cressie, N.A.C. (1993), "Statistics for Spatial Data", J. Wiley & Sons.
Venables, W.N. and Ripley, B.D. (2002) "Modern Applied Statistics with S", 4th Edition, Springer-Verlag.
Littel, Milliken, Stroup, and Wolfinger (1996) "SAS Systems for Mixed Models", SAS Institute.
Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models in S and S-PLUS", Springer.
sp1 <- corRatio(form = ~ x + y + z) # example lme(..., corRatio ...) # Pinheiro and Bates, pp. 222-249 fm1BW.lme <- lme(weight ~ Time * Diet, BodyWeight, random = ~ Time) # p. 223 fm2BW.lme <- update(fm1BW.lme, weights = varPower()) # p 246 fm3BW.lme <- update(fm2BW.lme, correlation = corExp(form = ~ Time)) # p. 249 fm5BW.lme <- update(fm3BW.lme, correlation = corRatio(form = ~ Time)) # example gls(..., corRatio ...) # Pinheiro and Bates, pp. 261, 263 fm1Wheat2 <- gls(yield ~ variety - 1, Wheat2) # p. 263 fm3Wheat2 <- update(fm1Wheat2, corr = corRatio(c(12.5, 0.2), form = ~ latitude + longitude, nugget = TRUE))
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