Exponential Correlation Structure
This function is a constructor for the "corExp"
class,
representing an exponential spatial correlation structure. Letting
d denote the range and n denote the nugget
effect, the correlation between two observations a distance
r apart is exp(-r/d) when no nugget effect
is present and (1-n)*exp(-r/d) when a nugget
effect is assumed. Objects created using this constructor must later be
initialized using the appropriate Initialize
method.
corExp(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 "corExp"
, also inheriting from class
"corSpatial"
, representing an exponential 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, esp. p. 238.
sp1 <- corExp(form = ~ x + y + z) # Pinheiro and Bates, p. 238 spatDat <- data.frame(x = (0:4)/4, y = (0:4)/4) cs1Exp <- corExp(1, form = ~ x + y) cs1Exp <- Initialize(cs1Exp, spatDat) corMatrix(cs1Exp) cs2Exp <- corExp(1, form = ~ x + y, metric = "man") cs2Exp <- Initialize(cs2Exp, spatDat) corMatrix(cs2Exp) cs3Exp <- corExp(c(1, 0.2), form = ~ x + y, nugget = TRUE) cs3Exp <- Initialize(cs3Exp, spatDat) corMatrix(cs3Exp) # example lme(..., corExp ...) # Pinheiro and Bates, pp. 222-247 # p. 222 options(contrasts = c("contr.treatment", "contr.poly")) 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. 247 fm4BW.lme <- update(fm3BW.lme, correlation = corExp(form = ~ Time, nugget = TRUE)) anova(fm3BW.lme, fm4BW.lme)
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