| corRatio {nlme} | R Documentation |
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 (r/d)^2/(1+(r/d)^2) when no nugget effect
is present and
(1-n)*(r/d)^2/(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 nugget is FALSE, value can
have only one element, corresponding to the "range" of the
rational quadratic correlation structure, which must be greater than
zero. If nugget is TRUE, meaning that a nugget effect
is present, value can contain one or two elements, the first
being the "range" and the second the "nugget effect" (one minus the
correlation between two observations taken arbitrarily close
together); the first must be greater than zero and the second must be
between zero and one. Defaults to numeric(0), which results in
a range of 90% of the minimum distance and a nugget effect of 0.1
being assigned to the parameters when object is initialized. |
form |
a one sided formula of the form ~ S1+...+Sp, or
~ S1+...+Sp | g, specifying spatial covariates S1
through Sp and, optionally, a grouping factor g.
When a grouping factor is present in form, the correlation
structure is assumed to apply only to observations within the same
grouping level; observations with different grouping levels are
assumed to be uncorrelated. Defaults to ~ 1, which corresponds
to using the order of the observations in the data as a covariate,
and no groups. |
nugget |
an optional logical value indicating whether a nugget
effect is present. Defaults to FALSE. |
metric |
an optional character string specifying the distance
metric to be used. The currently available options are
"euclidean" for the root sum-of-squares of distances;
"maximum" for the maximum difference; and "manhattan"
for the sum of the absolute differences. Partial matching of
arguments is used, so only the first three characters need to be
provided. Defaults to "euclidean". |
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 FALSE, in which case
the coefficients are allowed to vary. |
an object of class corRatio, also inheriting from class
corSpatial, representing a rational quadratic spatial correlation
structure.
Jose Pinheiro Jose.Pinheiro@pharma.novartis.com 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. (1997) "Modern Applied Statistics with S-plus", 2nd 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.
Initialize.corStruct,
summary.corStruct,
dist
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))