# Compares Dissimilarity Indices for Gradient Detection

### Description

Rank correlations between dissimilarity indices and gradient separation.

### Usage

1 2 3 4 |

### Arguments

`grad` |
The gradient variable or matrix. |

`veg` |
The community data matrix. |

`indices` |
Dissimilarity indices compared, partial matches to
alternatives in |

`stepacross` |
Use |

`method` |
Correlation method used. |

`metric` |
Metric to evaluate the gradient separation. See Details. |

`...` |
Other parameters to |

### Details

A good dissimilarity index for multidimensional scaling should have
a high rank-order similarity with gradient separation. The function
compares most indices in `vegdist`

against gradient
separation using rank correlation coefficients in
`cor`

. The gradient separation between each point is
assessed using given `metric`

. The default is to use Euclidean
distance of continuous variables scaled to unit variance, or to use
Gower metric for mixed data using function
`daisy`

when `grad`

has factors. The other
alternatives are Mahalanabis distances which are based on
`grad`

matrix scaled so that columns are orthogonal
(uncorrelated) and have unit variance, or Manhattan distances of
`grad`

variables scaled to unit range.

The `indices`

argument can accept any dissimilarity
indices besides the ones calculated by the
`vegdist`

function. For this, the argument value
should be a (possibly named) list of functions.
Each function must return a valid 'dist' object with dissimilarities,
similarities are not accepted and should be converted into dissimilarities
beforehand.

### Value

Returns a named vector of rank correlations.

### Note

There are several problems in using rank correlation coefficients.
Typically there are very many ties when *n(n-1)/2* gradient
separation values are derived from just *n* observations.
Due to floating point arithmetics, many tied values differ by
machine epsilon and are arbitrarily ranked differently by
`rank`

used in `cor.test`

. Two indices
which are identical with certain
transformation or standardization may differ slightly
(magnitude *10^{-15}*) and this may lead into third or fourth decimal
instability in rank correlations. Small differences in rank
correlations should not be taken too seriously. Probably this method
should be replaced with a sounder method, but I do not yet know
which... You may experiment with `mantel`

,
`anosim`

or even `protest`

.

Earlier version of this function used `method = "kendall"`

, but
that is far too slow in large data sets.

The functions returning dissimilarity objects should be self contained,
because the `...`

argument passes additional parameters
to `stepacross`

and not to the functions supplied
via the `indices`

argument.

### Author(s)

Jari Oksanen, with additions from Peter Solymos

### References

Faith, F.P., Minchin, P.R. and Belbin,
L. (1987). Compositional dissimilarity as a robust measure of
ecological distance. *Vegetatio* 69, 57-68.

### See Also

`vegdist`

, `stepacross`

,
`no.shared`

, `monoMDS`

,
`cor`

, `Machine`

, and for
alternatives `anosim`

, `mantel`

and
`protest`

.

### Examples

1 2 3 4 5 6 7 8 9 10 | ```
data(varespec)
data(varechem)
## The variables are automatically scaled
rankindex(varechem, varespec)
rankindex(varechem, wisconsin(varespec))
## Using non vegdist indices as functions
funs <- list(Manhattan=function(x) dist(x, "manhattan"),
Gower=function(x) cluster:::daisy(x, "gower"),
Ochiai=function(x) designdist(x, "1-J/sqrt(A*B)"))
rankindex(scale(varechem), varespec, funs)
``` |