nlme (version 3.1-86)

corSpher: Spherical Correlation Structure

Description

This function is a constructor for the 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.

Usage

corSpher(value, form, nugget, metric, fixed)

Value

an object of class corSpher, also inheriting from class corSpatial, representing a spherical spatial correlation structure.

References

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.

See Also

Initialize.corStruct, summary.corStruct, dist

Examples

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))

Run the code above in your browser using DataCamp Workspace