| Moran.I {ape} | R Documentation |
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
|
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 |
Author(s)
Julien Dutheil dutheil@evolbio.mpg.de 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
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