MoranI: Moran's I Autocorrelation Index

In ape: Analyses of Phylogenetics and Evolution

Moran's I Autocorrelation Index

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:

I = \frac{n}{S_0} \frac{\sum_{i=1}^n\sum_{j=1}^n w_{i,j}(y_i - \overline{y})(y_j - \overline{y})}{\sum_{i=1}^n {(y_i - \overline{y})}^2}

with

• y_i = observations

• w_{i,j} = distance weight

• n = number of observations

• S_0 = \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 x are positively autocorrelated, whereas if Iobserved < Iexpected, this will indicate negative autocorrelation.

Value

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 in alternative.

Author(s)

Julien Dutheil [e-mail] and Emmanuel Paradis

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

ape documentation built on May 29, 2024, 10:50 a.m.