corSpher
class,
representing a spherical spatial correlation structure. Letting
$d$ denote the range and $n$ denote the nugget
effect, the correlation between two observations a distance
$r < d$ apart is $1-1.5(r/d)+0.5(r/d)^3$ when no
nugget effect is present and $(1-n)
(1-1.5(r/d)+0.5(r/d)^3)$
when a nugget effect is assumed. If $r \geq d$ the
correlation is zero. Objects created using this constructor must later
be initialized using the appropriate Initialize
method.corSpher(value, form, nugget, metric, fixed)
nugget
is FALSE
, value
can
have only one element, corresponding to the "range" of the
spherical correlation structure, which must be great~ S1+...+Sp
, or
~ S1+...+Sp | g
, specifying spatial covariates S1
through Sp
and, optionally, a grouping factor g
.
When a grouping factor is presenFALSE
."euclidean"
for the root sum-of-squares of distances;
"maximum"
for the maximum difference; and "manhattan
FALSE
, in which case
the coefficients are allowed to vary.corSpher
, also inheriting from class
corSpatial
, representing a spherical spatial correlation
structure.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.
Initialize.corStruct
,
summary.corStruct
,
dist
sp1 <- corSpher(form = ~ x + y)
# example lme(..., corSpher ...)
# 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
fm6BW.lme <- update(fm3BW.lme,
correlation = corSpher(form = ~ Time))
# example gls(..., corSpher ...)
# Pinheiro and Bates, pp. 261, 263
fm1Wheat2 <- gls(yield ~ variety - 1, Wheat2)
# p. 262
fm2Wheat2 <- update(fm1Wheat2, corr =
corSpher(c(28, 0.2),
form = ~ latitude + longitude, nugget = TRUE))
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