joincount.test: BB join count statistic for k-coloured factors
In spdep: Spatial Dependence: Weighting Schemes, Statistics and Models
Description
Usage
Arguments
Value
Note
Author(s)
References
See Also
Examples
Description
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.
Usage
1
2
3
4
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
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 get.spChkOption()
x
object to be printed
...
arguments to be passed through for printing
Value
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.
Note
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.
Author(s)
Roger Bivand Roger.Bivand@nhh.no
References
Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 20.
See Also
joincount.mc, joincount.multi, listw2U
Examples
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")))
Example output
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
spdep documentation built on Aug. 19, 2017, 3:01 a.m.
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Description Usage Arguments Value Note Author(s) References See Also Examples
Description
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.
Usage
1 2 3 4 |
Arguments
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 |
Value
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. |
Note
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.
Author(s)
Roger Bivand Roger.Bivand@nhh.no
References
Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 20.
See Also
joincount.mc, joincount.multi, listw2U
Examples
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")))
|
Example output
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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