corSymm {nlme} | R Documentation

## General Correlation Structure

### Description

This function is a constructor for the `corSymm` class, representing a general correlation structure. The internal representation of this structure, in terms of unconstrained parameters, uses the spherical parametrization defined in Pinheiro and Bates (1996). Objects created using this constructor must later be initialized using the appropriate `Initialize` method.

### Usage

    corSymm(value, form, fixed)

### Arguments

`value` | an optional vector with the parameter values. Default is `numeric(0)`, which results in a vector of zeros of appropriate dimension being assigned to the parameters when `object` is initialized (corresponding to an identity correlation structure).

`form`

a one sided formula of the form `~ t`, or `~ t | g`, specifying a time covariate `t` and, optionally, a grouping factor `g`. A covariate for this correlation structure must be integer valued. 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.

`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.

### Value

an object of class `corSymm` representing a general correlation structure.

### Author(s)

Jose Pinheiro Jose.Pinheiro@pharma.novartis.com and Douglas Bates bates@stat.wisc.edu

### References

Pinheiro, J.C. and Bates., D.M. (1996) "Unconstrained Parametrizations for Variance-Covariance Matrices", Statistics and Computing, 6, 289-296.

Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models in S and S-PLUS", Springer.

### See Also

`Initialize.corSymm`, `summary.corSymm`

### Examples

    ## covariate is observation order and grouping factor is Subject
    cs1 <- corSymm(form = ~ 1 | Subject)

    # Pinheiro and Bates, p. 225
    cs1CompSymm <- corCompSymm(value = 0.3, form = ~ 1 | Subject)
    cs1CompSymm <- Initialize(cs1CompSymm, data = Orthodont)
    corMatrix(cs1CompSymm)

    # Pinheiro and Bates, p. 226
    cs1Symm <- corSymm(value =
            c(0.2, 0.1, -0.1, 0, 0.2, 0),
                       form = ~ 1 | Subject)
    cs1Symm <- Initialize(cs1Symm, data = Orthodont)
    corMatrix(cs1Symm)

    # 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))

    # example gls(..., corSymm ... )
    # Pinheiro and Bates, p. 251
    fm1Orth.gls <- gls(distance ~ Sex * I(age - 11), Orthodont,
                       correlation = corSymm(form = ~ 1 | Subject),
                       weights = varIdent(form = ~ 1 | age))

[Package nlme version 3.1-89 Index]