Given a spatial weights matrix and degree of autocorrelation, returns autocorrelated data.

`sim_sar(m = 1, mu = rep(0, nrow(w)), w, rho, sigma = 1, ...)`

## Arguments

- m
The number of samples required. Defaults to `m=1`

to return an `n`

-length vector; if `m>1`

, an `m x n`

matrix is returned (i.e. each row will contain a sample of correlated values).

- mu
An `n`

-length vector of mean values. Defaults to a vector of zeros with length equal to `nrow(w)`

.

- w
Row-standardized `n x n`

spatial weights matrix.

- rho
Spatial autocorrelation parameter in the range (-1, 1). Typically a scalar value; otherwise an n-length numeric vector.

- sigma
Scale parameter (standard deviation). Defaults to `sigma = 1`

. Typically a scalar value; otherwise an n-length numeric vector.

- ...
further arguments passed to `MASS::mvrnorm`

.

## Value

If `m = 1`

a vector of the same length as `mu`

, otherwise an `m x length(mu)`

matrix with one sample in each row.

## Details

Calls `MASS::mvrnorm`

internally to draw from the multivariate normal distribution. The covariance matrix is specified following the simultaneous autoregressive (SAR) model.

## Examples

```
data(georgia)
w <- shape2mat(georgia, "W")
x <- sim_sar(w = w, rho = 0.5)
aple(x, w)
x <- sim_sar(w = w, rho = 0.7, m = 10)
dim(x)
apply(x, 1, aple, w = w)
```