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))

[Package *nlme* version 3.1-80 Index]