# Moran.I

##### Moran's I Autocorrelation Index

This function computes Moran's I autocorrelation coefficient of
`x`

giving a matrix of weights using the method described by
Gittleman and Kot (1990).

- Keywords
- models, regression

##### Usage

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

##### 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:`alternative`

.

##### 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
```

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