similarity.test: Compute the similarity test.

In spqdep: Testing for Spatial Independence of Qualitative Data in Cross Section

Compute the similarity test.

Description

This function compute the nonparametric test for spatial independence using symbolic analysis for categorical/qualitative spatial process.

Usage

similarity.test(formula = NULL, data = NULL, fx = NULL, listw = listw,
alternative = "two.sided", distr = "asymptotic", nsim = NULL, control = list())

Arguments

formula	a symbolic description of the factor (optional).
data	an (optional) data frame or a sf object containing the variable to testing for.
fx	a factor (optional).
listw	a listw object
alternative	a character string specifying the type of cluster, must be one of "High" (default), "Both" or "Low".
distr	A string. Distribution of the test "asymptotic" (default) or "bootstrap"
nsim	Number of permutations.
control	List of additional control arguments.

Details

This testing approach for spatial independence that extends some of the properties of the join count statistic. The premise of the tests is similar to the join count statistic in that they use the concept of similarity between neighbouring spatial entities (Dacey 1968; Cliff and Ord 1973, 1981). However, it differs by taking into consideration the number of joins belonging locally to each spatial unit, rather than the total number of joins in the entire spatial system. The approach proposed here is applicable to spatial and network contiguity structures, and the number of neighbors belonging to observations need not be constant.

We define an equivalence relation \sim in the set of locations S. An equivalence relation satisfies the following properties:

Reflexive: s_i \sim s_i for all s_i \in S,
Symmetric: If s_i \sim s_j, then s_j \sim s_i for all s_i,\ s_j \in S and
Transitive: If s_i \sim s_j and s_j \sim s_k, then s_i \sim s_k for all s_i, \ s_j, \ s_k \in S

We call the relation \sim a similarity relation. Then, the null hypothesis that we are interested in is

H_0: \{X_s\}_{s \in S} \ \ is\ \ iid

Assume that, under the null hypothesis, P(s_i \sim s_{ji}) = p_i for all s_{ji} \in N_{s_i}.
Define

I_{ij}=1 \ \ if \ \ s_i \sim s_{ji} \ \ ; 0 \ \ otherwise

Then, for a fixed degree d and for all location si with degree d, the variable d

Λ_{(d,i)}=∑_{j=1}^d I_{ij}

gives the number of nearest neighbours to si that are similar to si. Therefore, under the null hypothesis, H_0, Λ(d,i) follows a binomial distribution B(d, p_i).

Value

A object of the htest

data.name	a character string giving the names of the data.
statistic	Value of the similarity test
N	total number of observations.
Zmlc	Elements in the Most Likelihood Cluster.
alternative	a character string describing the alternative hypothesis.
p.value	p-value of the similarity test
similiarity.mc	values of the similarity test in each permutation.

Control arguments

seedinit	Numerical value for the seed (only for boot version). Default value seedinit=123

Author(s)

Fernando López	[e-mail]
Román Mínguez	[e-mail]
Antonio Páez	[e-mail]
Manuel Ruiz	[e-mail]

References

• Farber, S., Marin, M. R., & Paez, A. (2015). Testing for spatial independence using similarity relations. Geographical Analysis. 47(2), 97-120.

See Also

sp.runs.test, dgp.spq, Q.test, , scan.test

Examples

# Case 1:
N <- 100
cx <- runif(N)
cy <- runif(N)
listw <- spdep::knearneigh(cbind(cx,cy), k = 3)
p <- c(1/4,1/4,1/4,1/4)
rho <- 0.5
fx <- dgp.spq(p = p, listw = listw, rho = rho)
W <- (spdep::nb2mat(spdep::knn2nb(listw)) >0)*1
similarity <- similarity.test(fx = fx, data = FastFood.sf, listw = listw)
print(similarity)

# Case 2: test with formula, a sf object (points) and knn
data("FastFood.sf")
coor <- sf::st_coordinates(sf::st_centroid(FastFood.sf))
listw <- spdep::knearneigh(coor, k = 4)
formula <- ~ Type
similarity <- similarity.test(formula = formula, data = FastFood.sf, listw = listw)
print(similarity)

# Case 3:
data(provinces_spain)
listw <- spdep::poly2nb(as(provinces_spain,"Spatial"), queen = FALSE)
provinces_spain$Male2Female <- factor(provinces_spain$Male2Female > 100)
levels(provinces_spain$Male2Female) = c("men","woman")
formula <- ~ Male2Female
similarity <- similarity.test(formula = formula, data = provinces_spain, listw = listw)
print(similarity)

spqdep documentation built on March 28, 2022, 5:06 p.m.