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
corRatio(value, form, nugget, metric, fixed)
- an optional vector with the parameter values in constrained form. If
valuecan have only one element, corresponding to the "range" of the rational quadratic correlation structure, which must be greater than zero. If
TRUE, meaning that a nugget effect is present,
valuecan 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
- a one sided formula of the form
~ S1+...+Sp, or
~ S1+...+Sp | g, specifying spatial covariates
Spand, 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.
- an optional logical value indicating whether a nugget effect is present. Defaults to
- 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
- 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.
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))
Documentation reproduced from R 3.0.1. License: GPL-2.