A function to compute joint-count test for binomial and multinomial (asymptotic and permutation distributions).

A function to compute joincount tests for spatial qualitative data. This function is a wrapper of joincount.multi and joincount.test in spdep package.

Usage

jc.test(formula = NULL,
               data = NULL,
               fx = NULL,
               listw = NULL,
               na.action,
               zero.policy = NULL,
               distr = "asymptotic",
               alternative = "greater",
               control =list())

Arguments

formula: a symbolic description of the factor(s).
data: an (optional) data frame or a sf object with points/multipolygons geometry containing the variable(s) to be tested.
fx: a factor or a matrix of factors in columns
listw: A listw object created for example by nb2listw from spdep package; if nb2listw not given, the spatial weights are built using the object given in listw argument (usually an sf object). Default = NULL.
na.action: A function (default options("na.action")), can also be na.omit or na.exclude. It may be necessary to set zero.policy to TRUE because this subsetting may create no-neighbour observations.
zero.policy: Similar to the corresponding parameter of lagsarlm function in spatialreg package. If TRUE assign zero to the lagged value of zones without neighbours. Default = NULL.
distr: character. Distribution type "asymptotic" (default) or "mc".
alternative: character string specifying the alternative hypothesis, must be one of "greater" (default), or "less".
control: list of additional arguments.

Value

An spjctest object. This type of object is a list of htest objects. The length of the list is the number of factor variables included in the formula or the number of columns in fx. Each element of the list can be a jclist object, for binomial factors, or a jcmulti object for multinomial factors. See joincount.test or joincount.multi for additional details.

Control arguments

`nsim`	number of permutations used in the Monte Carlo distribution. Default `nsim` = 999.
`seedinit`	seed to select the initial element during the simulations. Default `seedinit` = 1111.
`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. See `joincount.multi` for aditional information.
`spChk`	should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use get.spChkOption(). See `joincount.multi` for aditional information.
`sampling`	default nonfree, may be free. See `joincount.test` for additional information.
`queen`	default TRUE. Defines the neighborhood criteria for sf objects.
`style`	defines the style for `listw`. Default = B (binary).
`knn`	chooses the number of neighboors when this criteria is used. Default `knn` = 5.

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, pp. 19-20.
Upton, G., Fingleton, B. 1985 Spatial data analysis by example: point pattern and qualitative data, Wiley, pp. 158–170.

Author

Fernando López	fernando.lopez@upct.es
Román Mínguez	roman.minguez@uclm.es
Antonio Páez	paezha@gmail.com
Manuel Ruiz	manuel.ruiz@upct.es

Examples


## Case 1
## Multinomial + Binomial using a sf multipolygon
# \donttest{
data("provinces_spain")
# sf::sf_use_s2(FALSE)
provinces_spain$Mal2Fml <- factor(provinces_spain$Mal2Fml > 100)
levels(provinces_spain$Mal2Fml) = c("men","woman")
provinces_spain$Older <- cut(provinces_spain$Older, breaks = c(-Inf,19,22.5,Inf))
levels(provinces_spain$Older) = c("low","middle","high")
f1 <- ~ Older + Mal2Fml
jc1 <- jc.test(formula = f1,
               data = provinces_spain,
               distr = "mc",
               alternative = "greater",
               zero.policy = TRUE)
#> although coordinates are longitude/latitude, st_intersects assumes that they
#> are planar
#> Warning: some observations have no neighbours;
#> if this seems unexpected, try increasing the snap argument.
#> Warning: neighbour object has 4 sub-graphs;
#> if this sub-graph count seems unexpected, try increasing the snap argument.
summary(jc1)


  JoinCount Spatial Tests (Monte Carlo)
    
pairs
      pvalue
      Joincount
      Expected
      Variance
    
Older - multinomial - alternative: greater - Monte-Carlo simulation of
        join-count statistic (nonfree sampling)
    
high:high
0.44800
14
13.81
9.83
low:low
0.65200
7
8.18
6.43
middle:middle
0.59500
13
13.80
10.40
low:high
0.41500
24
23.01
16.06
middle:high
0.59200
28
29.20
18.35
middle:low
0.35600
25
22.99
14.59
Jtot
0.38800
77
75.20
21.25
Mal2Fml - binomial - alternative: greater - Monte-Carlo simulation of join-count statistic
    
men-men
0.50250
60
60.21
22.75
woman-woman
0.02100
13
7.16
6.08

provinces_spain$Coast <- factor(provinces_spain$Coast)
levels(provinces_spain$Coast) = c("no","yes")
f2 <- ~ Mal2Fml + Coast
jc2 <- jc.test(formula = f2,
               data = provinces_spain,
               distr = "mc",
               zero.policy = TRUE)
#> although coordinates are longitude/latitude, st_intersects assumes that they
#> are planar
#> Warning: some observations have no neighbours;
#> if this seems unexpected, try increasing the snap argument.
#> Warning: neighbour object has 4 sub-graphs;
#> if this sub-graph count seems unexpected, try increasing the snap argument.
summary(jc2)


  JoinCount Spatial Tests (Monte Carlo)
    
pairs
      pvalue
      Joincount
      Expected
      Variance
    
Mal2Fml - binomial - alternative: greater - Monte-Carlo simulation of join-count statistic
    
men-men
0.53300
60
60.32
22.94
woman-woman
0.01750
13
7.15
5.88
Coast - binomial - alternative: greater - Monte-Carlo simulation of join-count statistic
    
no-no
0.00100
64
36.75
20.15
yes-yes
0.93050
14
19.04
12.64
# }

# Case 2:
## Multinomial using a sf multipoint
data("FastFood.sf")
# sf::sf_use_s2(FALSE)
f1 <- ~ Type
jc3 <- jc.test(formula = f1,
               data = FastFood.sf,
               distr = "asymptotic",
               control = list(knn = 6))
#> Warning: neighbour object has 4 sub-graphs
 summary(jc3)


  JoinCount Spatial Tests (asymptotic)
    
pairs
      z-value
      pvalue
      Joincount
      Expected
      Variance
    
Type - multinomial - alternative: greater - Join count test under nonfree sampling
    
H:H
−4.14
0.99998
210.5
258.05
132.09
P:P
−1.70
0.95580
292.5
313.38
150.13
S:S
−4.05
0.99997
256.0
305.14
147.60
P:H
1.44
0.07503
596.0
570.72
308.52
S:H
3.02
0.00126
616.0
563.18
305.44
S:P
2.17
0.01482
660.0
620.53
329.37
Jtot
5.19
0.00000
1872.0
1,754.43
513.30

# Examples function joincount.test
data(oldcol, package = "spdep")
HICRIME <- cut(COL.OLD$CRIME, breaks = c(0,35,80), labels = c("low","high"))
names(HICRIME) <- rownames(COL.OLD)
jc4 <- jc.test(fx = HICRIME,
               listw = spdep::nb2listw(COL.nb,
               style="B"))
summary(jc4)


  JoinCount Spatial Tests (asymptotic)
    
pairs
      z-value
      pvalue
      Joincount
      Expected
      Variance
    
fx - binomial - alternative: greater - Join count test under nonfree sampling
    
high-high
6.33
0.00000
54
27.22
17.89
low-low
1.01
0.15527
34
29.59
18.90
high-low
−6.09
1.00000
28
59.18
26.23
 jc5 <- jc.test(fx = HICRIME,
                listw = spdep::nb2listw(COL.nb, style="B"),
                distr = "mc")
 summary(jc5)


  JoinCount Spatial Tests (Monte Carlo)
    
pairs
      pvalue
      Joincount
      Expected
      Variance
    
fx - binomial - alternative: greater - Monte-Carlo simulation of join-count statistic
    
high-high
0.00100
54
27.08
17.39
low-low
0.16050
34
29.65
18.06
 HICRIME <- cut(COL.OLD$CRIME, breaks = c(0, 35, 80),
                labels = c("low","high"))
 names(HICRIME) <- rownames(COL.OLD)
 jc6 <- jc.test(fx = HICRIME,
                listw = spdep::nb2listw(COL.nb,
                                 style = "B"))
summary(jc6)


  JoinCount Spatial Tests (asymptotic)
    
pairs
      z-value
      pvalue
      Joincount
      Expected
      Variance
    
fx - binomial - alternative: greater - Join count test under nonfree sampling
    
high-high
6.33
0.00000
54
27.22
17.89
low-low
1.01
0.15527
34
29.59
18.90
high-low
−6.09
1.00000
28
59.18
26.23

pairs	pvalue	Joincount	Expected	Variance
JoinCount Spatial Tests (Monte Carlo)
Older - multinomial - alternative: greater - Monte-Carlo simulation of join-count statistic (nonfree sampling)
high:high	0.44800	14	13.81	9.83
low:low	0.65200	7	8.18	6.43
middle:middle	0.59500	13	13.80	10.40
low:high	0.41500	24	23.01	16.06
middle:high	0.59200	28	29.20	18.35
middle:low	0.35600	25	22.99	14.59
Jtot	0.38800	77	75.20	21.25
Mal2Fml - binomial - alternative: greater - Monte-Carlo simulation of join-count statistic
men-men	0.50250	60	60.21	22.75
woman-woman	0.02100	13	7.16	6.08

pairs	z-value	pvalue	Joincount	Expected	Variance
JoinCount Spatial Tests (asymptotic)
Type - multinomial - alternative: greater - Join count test under nonfree sampling
H:H	−4.14	0.99998	210.5	258.05	132.09
P:P	−1.70	0.95580	292.5	313.38	150.13
S:S	−4.05	0.99997	256.0	305.14	147.60
P:H	1.44	0.07503	596.0	570.72	308.52
S:H	3.02	0.00126	616.0	563.18	305.44
S:P	2.17	0.01482	660.0	620.53	329.37
Jtot	5.19	0.00000	1872.0	1,754.43	513.30

pairs	z-value	pvalue	Joincount	Expected	Variance
JoinCount Spatial Tests (asymptotic)
fx - binomial - alternative: greater - Join count test under nonfree sampling
high-high	6.33	0.00000	54	27.22	17.89
low-low	1.01	0.15527	34	29.59	18.90
high-low	−6.09	1.00000	28	59.18	26.23

pairs	pvalue	Joincount	Expected	Variance
JoinCount Spatial Tests (Monte Carlo)
fx - binomial - alternative: greater - Monte-Carlo simulation of join-count statistic
high-high	0.00100	54	27.08	17.39
low-low	0.16050	34	29.65	18.06