# corPagel

##### Pagel's ``lambda'' Correlation Structure

The correlation structure from the present model is derived from the Brownian motion model by multiplying the off-diagonal elements (i.e., the covariances) by \(\lambda\). The variances are thus the same than for a Brownian motion model.

- Keywords
- models

##### Usage

```
corPagel(value, phy, form = ~1, fixed = FALSE)
# S3 method for corPagel
corMatrix(object, covariate = getCovariate(object),
corr = TRUE, ...)
# S3 method for corPagel
coef(object, unconstrained = TRUE, …)
```

##### Arguments

- value
the (initial) value of the parameter \(\lambda\).

- phy
an object of class

`"phylo"`

.- 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.

- fixed
a logical specifying whether

`gls`

should estimate \(\lambda\) (the default) or keep it fixed.- object
an (initialized) object of class

`"corPagel"`

.- 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).

- corr
a logical value specifying whether to return the correlation matrix (the default) or the variance-covariance matrix.

- unconstrained
a logical value. If

`TRUE`

(the default), 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.- …
further arguments passed to or from other methods.

##### Value

an object of class `"corPagel"`

, the coefficients from an object
of this class, or the correlation matrix of an initialized object of
this class. In most situations, only `corPagel`

will be called
by the user.

##### References

Freckleton, R. P., Harvey, P. H. and M. Pagel, M. (2002) Phylogenetic
analysis and comparative data: a test and review of evidence.
*American Naturalist*, **160**, 712--726.

Pagel, M. (1999) Inferring the historical patterns of biological
evolution. *Nature*, **401**,877--884.

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