funs.overall.nnct {nnspat} | R Documentation |
Dixon's Overall Test of Segregation for NNCT
Description
Two functions: overall.nnct.ct
and overall.nnct
.
Both functions are objects of class "Chisqtest"
but with different arguments (see the parameter list below).
Each one performs hypothesis tests of deviations of
cell counts from the expected values under RL or CSR for all cells (i.e., entries) combined in the NNCT.
That is, each test is Dixon's overall test of segregation based on NNCTs for k \ge 2
classes.
This overall test is based on the chi-squared approximation of the corresponding quadratic form
and are due to Dixon (1994, 2002).
Both functions exclude the last column of the NNCT (in fact any column will do and last column
is chosen without loss of generality), to avoid ill-conditioning of the covariance matrix (for its inversion
in the quadratic form).
Each function yields the test statistic, p
-value and df
which is k(k-1)
, description of the
alternative with the corresponding null values (i.e., expected values) of NNCT entries, sample estimates (i.e., observed values) of the entries in NNCT.
The functions also provide names of the test statistics, the description of the test and the data set used.
The null hypothesis is that all N_{ij}
entries are equal to their expected values under RL or CSR.
See also (Dixon (1994, 2002); Ceyhan (2010, 2017)) and the references therein.
Usage
overall.nnct.ct(ct, covN)
overall.nnct(dat, lab, ...)
Arguments
ct |
A nearest neighbor contingency table, used in |
covN |
The |
dat |
The data set in one or higher dimensions, each row corresponds to a data point,
used in |
lab |
The |
... |
are for further arguments, such as |
Value
A list
with the elements
statistic |
The overall chi-squared statistic |
stat.names |
Name of the test statistic |
p.value |
The |
df |
Degrees of freedom for the chi-squared test, which is |
estimate |
Estimates of the parameters, NNCT, i.e., matrix of the observed |
est.name , est.name2 |
Names of the estimates, former is a longer description of the estimates than the latter. |
null.value |
Matrix of hypothesized null values for the parameters which are expected values of the
the |
null.name |
Name of the null values |
method |
Description of the hypothesis test |
ct.name |
Name of the contingency table, |
data.name |
Name of the data set, |
Author(s)
Elvan Ceyhan
References
Ceyhan E (2010).
“On the use of nearest neighbor contingency tables for testing spatial segregation.”
Environmental and Ecological Statistics, 17(3), 247-282.
Ceyhan E (2017).
“Cell-Specific and Post-hoc Spatial Clustering Tests Based on Nearest Neighbor Contingency Tables.”
Journal of the Korean Statistical Society, 46(2), 219-245.
Dixon PM (1994).
“Testing spatial segregation using a nearest-neighbor contingency table.”
Ecology, 75(7), 1940-1948.
Dixon PM (2002).
“Nearest-neighbor contingency table analysis of spatial segregation for several species.”
Ecoscience, 9(2), 142-151.
See Also
overall.seg.ct
, overall.seg
, overall.tct.ct
and overall.tct
Examples
n<-20 #or try sample(1:20,1)
Y<-matrix(runif(3*n),ncol=3)
ipd<-ipd.mat(Y)
cls<-sample(1:2,n,replace = TRUE) #or try cls<-rep(1:2,c(10,10))
ct<-nnct(ipd,cls)
W<-Wmat(ipd)
Qv<-Qvec(W)$q
Rv<-Rval(W)
varN<-var.nnct(ct,Qv,Rv)
covN<-cov.nnct(ct,varN,Qv,Rv) #default is byrow
overall.nnct(Y,cls)
overall.nnct.ct(ct,covN)
overall.nnct(Y,cls,method="max")
#cls as a factor
na<-floor(n/2); nb<-n-na
fcls<-rep(c("a","b"),c(na,nb))
ct<-nnct(ipd,fcls)
overall.nnct(Y,fcls)
overall.nnct.ct(ct,covN)
#############
n<-40
Y<-matrix(runif(3*n),ncol=3)
ipd<-ipd.mat(Y)
cls<-sample(1:4,n,replace = TRUE) #or try cls<-rep(1:2,c(10,10))
ct<-nnct(ipd,cls)
W<-Wmat(ipd)
Qv<-Qvec(W)$q
Rv<-Rval(W)
varN<-var.nnct(ct,Qv,Rv)
covN<-cov.nnct(ct,varN,Qv,Rv)
overall.nnct(Y,cls)
overall.nnct.ct(ct,covN)