# corMartins

##### Martins's (1997) Correlation Structure

Martins and Hansen's (1997) covariance structure: $$V_{ij} = \gamma \times e^{-\alpha t_{ij}}$$ where \(t_{ij}\) is the phylogenetic distance between taxa \(i\) and \(j\) and \(\gamma\) is a constant.

- Keywords
- models

##### Usage

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

##### Arguments

- value
The \(\alpha\) parameter

- phy
An object of class

`phylo`

representing the phylogeny (with branch lengths) to consider- object
An (initialized) object of class

`corMartins`

- 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, ok 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 `corMartins`

or the alpha coefficient from an object of this class
or the correlation matrix of an initialized object of this class.

##### References

Martins, E. P. and Hansen, T. F. (1997) Phylogenies and the comparative
method: a general approach to incorporating phylogenetic information
into the analysis of interspecific data. *American Naturalist*,
**149**, 646--667.

##### See Also

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