# corGrafen

##### 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.

##### See Also

*Documentation reproduced from package ape, version 5.4, License: GPL-2 | GPL-3*