R

Moran.I {ape}

calsalmon April 18, 2014
Moran’s I Autocorrelation Index
Package:

ape

Version:

3.0-11

Description

This function computes Moran’s I autocorrelation coefficient of x giving a matrix of weights using the method described by Gittleman and Kot (1990).

Usage

Moran.I(x, weight, scaled = FALSE, na.rm = FALSE,
          alternative = "two.sided")

Arguments

x
a numeric vector.
weight
a matrix of weights.
scaled
a logical indicating whether the coefficient should be scaled so that it varies between -1 and +1 (default to FALSE).
na.rm
a logical indicating whether missing values should be removed.
alternative
a character string specifying the alternative hypothesis that is tested against the null hypothesis of no phylogenetic correlation; must be of one “two.sided”, “less”, or “greater”, or any unambiguous abbrevation of these.

Details

The matrix weight is used as “neighbourhood” weights, and Moran’s I coefficient is computed using the formula: with

  • yi = observations
  • wij = distance weight
  • n = number of observations
  • S0 = \code{sum_{i=1..n} sum{j=1..n} wij}

 

The null hypothesis of no phylogenetic correlation is tested assuming normality of I under this null hypothesis. If the observed value of I is significantly greater than the expected value, then the values of xare positively autocorrelated, whereas if Iobserved < Iexpected, this will indicate negative autocorrelation.

Values

A list containing the elements:

observed
the computed Moran’s I.
expected
the expected value of I under the null hypothesis.
sd
the standard deviation of I under the null hypothesis.
p.value
the P-value of the test of the null hypothesis against the alternative hypothesis specified inalternative.

References

Gittleman, J. L. and Kot, M. (1990) Adaptation: statistics and a null model for estimating phylogenetic effects. Systematic Zoology, 39, 227–241.

See Also

weight.taxo

Examples

 

tr <- rtree(30)
x <- rnorm(30)
## weights w[i,j] = 1/d[i,j]:
w <- 1/cophenetic(tr)
## set the diagonal w[i,i] = 0 (instead of Inf...):
diag(w) <- 0
Moran.I(x, w)
Moran.I(x, w, alt = "l")
Moran.I(x, w, alt = "g")
Moran.I(x, w, scaled = TRUE) # usualy the same

 

Author(s)

Julien Dutheil julien.dutheil@univ-montp2.fr and Emmanuel Paradis

Documentation reproduced from package ape, version 3.0-11. License: GPL (>= 2)