# Permutation test for same colour join count statistics

`joincount.mc.Rd`

A permutation test for same colour join count statistics calculated by using nsim random permutations of fx for the given spatial weighting scheme, to establish the ranks of the observed statistics (for each colour) in relation to the nsim simulated values.

## Usage

```
joincount.mc(fx, listw, nsim, zero.policy=attr(listw, "zero.policy"),
alternative="greater", spChk=NULL)
```

## Arguments

- fx
a factor of the same length as the neighbours and weights objects in listw

- listw
a

`listw`

object created for example by`nb2listw`

- nsim
number of permutations

- zero.policy
default

`attr(listw, "zero.policy")`

as set when`listw`

was created, if attribute not set, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA- alternative
a character string specifying the alternative hypothesis, must be one of "greater" (default), "two.sided", or "less".

- spChk
should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use

`get.spChkOption()`

## Value

A list with class `jclist`

of lists with class `htest`

and `mc.sim`

for each of the k colours containing the following components:

- statistic
the value of the observed statistic.

- parameter
the rank of the observed statistic.

- method
a character string giving the method used.

- data.name
a character string giving the name(s) of the data.

- p.value
the pseudo p-value of the test.

- alternative
a character string describing the alternative hypothesis.

- estimate
the mean and variance of the simulated distribution.

- res
nsim simulated values of statistic, the final element is the observed statistic

## Author

Roger Bivand Roger.Bivand@nhh.no

## Examples

```
data(oldcol)
HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c("low","high"))
names(HICRIME) <- rownames(COL.OLD)
joincount.mc(HICRIME, nb2listw(COL.nb, style="B"), nsim=99, alternative="two.sided")
#>
#> Monte-Carlo simulation of join-count statistic
#>
#> data: HICRIME
#> weights: nb2listw(COL.nb, style = "B")
#> number of simulations + 1: 100
#>
#> Join-count statistic for low = 34, rank of observed statistic = 88.5,
#> p-value = 0.23
#> alternative hypothesis: two.sided
#> sample estimates:
#> mean of simulation variance of simulation
#> 28.96970 18.19295
#>
#>
#> Monte-Carlo simulation of join-count statistic
#>
#> data: HICRIME
#> weights: nb2listw(COL.nb, style = "B")
#> number of simulations + 1: 100
#>
#> Join-count statistic for high = 54, rank of observed statistic = 100,
#> p-value < 2.2e-16
#> alternative hypothesis: two.sided
#> sample estimates:
#> mean of simulation variance of simulation
#> 26.83838 20.13688
#>
joincount.test(HICRIME, nb2listw(COL.nb, style="B"), alternative="two.sided")
#>
#> Join count test under nonfree sampling
#>
#> data: HICRIME
#> weights: nb2listw(COL.nb, style = "B")
#>
#> Std. deviate for low = 1.0141, p-value = 0.3105
#> alternative hypothesis: two.sided
#> sample estimates:
#> Same colour statistic Expectation Variance
#> 34.00000 29.59184 18.89550
#>
#>
#> Join count test under nonfree sampling
#>
#> data: HICRIME
#> weights: nb2listw(COL.nb, style = "B")
#>
#> Std. deviate for high = 6.3307, p-value = 2.44e-10
#> alternative hypothesis: two.sided
#> sample estimates:
#> Same colour statistic Expectation Variance
#> 54.00000 27.22449 17.88838
#>
```