corExp  R Documentation 
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 (1n) \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.
JosÃ© 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, SpringerVerlag.
Littel, Milliken, Stroup, and Wolfinger (1996) "SAS Systems for Mixed Models", SAS Institute.
Pinheiro, J.C., and Bates, D.M. (2000) "MixedEffects Models in S and SPLUS", Springer, esp. p. 238.
corClasses
,
Initialize.corStruct
,
summary.corStruct
,
dist
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. 222247
# 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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