Description Usage Arguments Value Note Author(s) References See Also Examples

The BB join count test for spatial autocorrelation using a spatial
weights matrix in weights list form for testing whether same-colour joins
occur more frequently than would be expected if the zones were labelled
in a spatially random way. The assumptions underlying the test are
sensitive to the form of the graph of neighbour relationships and other
factors, and results may be checked against those of `joincount.mc`

permutations.

1 2 3 4 |

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

`listw` |
a |

`zero.policy` |
default NULL, 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), "less" or "two.sided". |

`adjust.n` |
default TRUE, if FALSE the number of observations is not adjusted for no-neighbour observations, if TRUE, the number of observations is adjusted consistently (up to and including spdep 0.3-28 the adjustment was inconsistent - thanks to Tomoki NAKAYA for a careful bug report) |

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

`x` |
object to be printed |

`...` |
arguments to be passed through for printing |

A list with class `jclist`

of lists with class `htest`

for each of the k colours containing the following components:

`statistic` |
the value of the standard deviate of the join count statistic. |

`p.value` |
the p-value of the test. |

`estimate` |
the value of the observed statistic, its expectation and variance under non-free sampling. |

`alternative` |
a character string describing the alternative hypothesis. |

`method` |
a character string giving the method used. |

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

The derivation of the test (Cliff and Ord, 1981, p. 18) assumes that the weights matrix is symmetric. For inherently non-symmetric matrices, such as k-nearest neighbour matrices, `listw2U()`

can be used to make the matrix symmetric. In non-symmetric weights matrix cases, the variance of the test statistic may be negative.

Roger Bivand Roger.Bivand@nhh.no

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 20.

`joincount.mc`

, `joincount.multi`

, `listw2U`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
data(oldcol)
HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c("low","high"))
names(HICRIME) <- rownames(COL.OLD)
joincount.test(HICRIME, nb2listw(COL.nb, style="B"))
joincount.test(HICRIME, nb2listw(COL.nb, style="C"))
joincount.test(HICRIME, nb2listw(COL.nb, style="S"))
joincount.test(HICRIME, nb2listw(COL.nb, style="W"))
by(card(COL.nb), HICRIME, summary)
print(is.symmetric.nb(COL.nb))
coords.OLD <- cbind(COL.OLD$X, COL.OLD$Y)
COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4))
print(is.symmetric.nb(COL.k4.nb))
joincount.test(HICRIME, nb2listw(COL.k4.nb, style="B"))
cat("Note non-symmetric weights matrix - use listw2U()\n")
joincount.test(HICRIME, listw2U(nb2listw(COL.k4.nb, style="B")))
``` |

```
Loading required package: sp
Loading required package: Matrix
Join count test under nonfree sampling
data: HICRIME
weights: nb2listw(COL.nb, style = "B")
Std. deviate for low = 1.0141, p-value = 0.1553
alternative hypothesis: greater
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 = 1.22e-10
alternative hypothesis: greater
sample estimates:
Same colour statistic Expectation Variance
54.00000 27.22449 17.88838
Join count test under nonfree sampling
data: HICRIME
weights: nb2listw(COL.nb, style = "C")
Std. deviate for low = 1.0141, p-value = 0.1553
alternative hypothesis: greater
sample estimates:
Same colour statistic Expectation Variance
7.1810345 6.2500000 0.8428969
Join count test under nonfree sampling
data: HICRIME
weights: nb2listw(COL.nb, style = "C")
Std. deviate for high = 6.3307, p-value = 1.22e-10
alternative hypothesis: greater
sample estimates:
Same colour statistic Expectation Variance
11.4051724 5.7500000 0.7979712
Join count test under nonfree sampling
data: HICRIME
weights: nb2listw(COL.nb, style = "S")
Std. deviate for low = 2.5786, p-value = 0.00496
alternative hypothesis: greater
sample estimates:
Same colour statistic Expectation Variance
8.2425673 6.2500000 0.5971141
Join count test under nonfree sampling
data: HICRIME
weights: nb2listw(COL.nb, style = "S")
Std. deviate for high = 6.1736, p-value = 3.337e-10
alternative hypothesis: greater
sample estimates:
Same colour statistic Expectation Variance
10.4249914 5.7500000 0.5734265
Join count test under nonfree sampling
data: HICRIME
weights: nb2listw(COL.nb, style = "W")
Std. deviate for low = 4.6675, p-value = 1.524e-06
alternative hypothesis: greater
sample estimates:
Same colour statistic Expectation Variance
9.5190476 6.2500000 0.4905378
Join count test under nonfree sampling
data: HICRIME
weights: nb2listw(COL.nb, style = "W")
Std. deviate for high = 5.1205, p-value = 1.523e-07
alternative hypothesis: greater
sample estimates:
Same colour statistic Expectation Variance
9.2920635 5.7500000 0.4784979
HICRIME: low
Min. 1st Qu. Median Mean 3rd Qu. Max.
2.00 2.00 4.00 3.84 4.00 10.00
------------------------------------------------------------
HICRIME: high
Min. 1st Qu. Median Mean 3rd Qu. Max.
3.000 4.750 6.000 5.667 7.000 9.000
[1] TRUE
[1] FALSE
Join count test under nonfree sampling
data: HICRIME
weights: nb2listw(COL.k4.nb, style = "B")
Std. deviate for low = 4.3698, p-value = 6.217e-06
alternative hypothesis: greater
sample estimates:
Same colour statistic Expectation Variance
36.500000 25.000000 6.925749
Join count test under nonfree sampling
data: HICRIME
weights: nb2listw(COL.k4.nb, style = "B")
Std. deviate for high = 6.7293, p-value = 8.523e-12
alternative hypothesis: greater
sample estimates:
Same colour statistic Expectation Variance
40.500000 23.000000 6.762918
Note non-symmetric weights matrix - use listw2U()
Join count test under nonfree sampling
data: HICRIME
weights: listw2U(nb2listw(COL.k4.nb, style = "B"))
Std. deviate for low = 4.3698, p-value = 6.217e-06
alternative hypothesis: greater
sample estimates:
Same colour statistic Expectation Variance
36.500000 25.000000 6.925749
Join count test under nonfree sampling
data: HICRIME
weights: listw2U(nb2listw(COL.k4.nb, style = "B"))
Std. deviate for high = 6.7293, p-value = 8.523e-12
alternative hypothesis: greater
sample estimates:
Same colour statistic Expectation Variance
40.500000 23.000000 6.762918
```

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