# corGrafen

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##### Grafen's (1989) Correlation Structure

Grafen's (1989) covariance structure. Branch lengths are computed using Grafen's method (see compute.brlen). The covariance matrice is then the traditional variance-covariance matrix for a phylogeny.

Keywords
models
##### Usage
corGrafen(value, phy, form=~1, fixed = FALSE)
# S3 method for corGrafen
coef(object, unconstrained = TRUE, ...)
# S3 method for corGrafen
corMatrix(object,
covariate = getCovariate(object), corr = TRUE, ...)
##### Arguments
value

The $\rho$ parameter

phy

An object of class phylo representing the phylogeny (branch lengths are ignored) to consider

object

An (initialized) object of class corGrafen

corr

a logical value. If 'TRUE' the function returns the correlation matrix, otherwise it returns the variance/covariance matrix.

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.

form

a one sided formula of the form ~ t, or ~ t | g, specifying the taxa covariate t and, optionally, a grouping factor g. A covariate for this correlation structure must be character valued, with entries matching the tip labels in the phylogenetic tree. 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.

covariate

an optional covariate vector (matrix), or list of covariate vectors (matrices), at which values the correlation matrix, or list of correlation matrices, are to be evaluated. Defaults to getCovariate(object).

unconstrained

a logical value. If 'TRUE' the coefficients are returned in unconstrained form (the same used in the optimization algorithm). If 'FALSE' the coefficients are returned in "natural", possibly constrained, form. Defaults to 'TRUE'

some methods for these generics require additional arguments. None are used in these methods.

##### Value

An object of class corGrafen or the rho coefficient from an object of this class or the correlation matrix of an initialized object of this class.

##### References

Grafen, A. (1989) The phylogenetic regression. Philosophical Transactions of the Royal society of London. Series B. Biological Sciences, 326, 119--157.

corClasses, compute.brlen, vcv.phylo.