EBImoran.mc {spdep}R Documentation

Permutation test for empirical Bayes index

Description

An empirical Bayes index modification of Moran's I for testing for spatial autocorrelation in a rate, typically the number of observed cases in a population at risk. The index value is tested by using nsim random permutations of the index for the given spatial weighting scheme, to establish the rank of the observed statistic in relation to the nsim simulated values.

Usage

EBImoran.mc(n, x, listw, nsim, zero.policy = FALSE, 
 alternative = "greater", spChk=NULL)

Arguments

n a numeric vector of counts of cases the same length as the neighbours list in listw
x a numeric vector of populations at risk the same length as the neighbours list in listw
listw a listw object created for example by nb2listw
nsim number of permutations
zero.policy 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), or "less"
spChk should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use get.spChkOption()

Details

The statistic used is (m is the number of observations):

EBI = (n sum_i sum_j w_ij z_i z_ji) / (S0 sum_i (z_i - zbar)^2)

where:

z_i = (p_i - b) / sqrt(v_i)

and:

p_i = n_i / x_i

v_i = a + (b / x_i)

sum_i n_i / sum_i x_i

a = s^2 - b / (sum_i x_i / m)

s^2 = sum_i x_i (p_i - b)^2 / sum_i x_i

Value

A list with class htest and mc.sim containing the following components:

statistic the value of the observed Moran's I.
parameter the rank of the observed Moran's I.
p.value the pseudo p-value of the test.
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, and the number of simulations.
res nsim simulated values of statistic, final value is observed statistic
z a numerical vector of Empirical Bayes indices as z above

Author(s)

Roger Bivand Roger.Bivand@nhh.no

References

Assunção RM, Reis EA 1999 A new proposal to adjust Moran's I for population density. Statistics in Medicine 18, pp. 2147–2162

See Also

moran, moran.mc, EBest

Examples

data(nc.sids)
EBImoran.mc(spNamedVec("SID74", nc.sids), spNamedVec("BIR74", nc.sids),
 nb2listw(ncCC89.nb, style="B", zero.policy=TRUE), nsim=999,
 zero.policy=TRUE)
sids.p <- nc.sids$SID74 / nc.sids$BIR74
names(sids.p) <- rownames(nc.sids)
moran.mc(sids.p, nb2listw(ncCC89.nb, style="B", zero.policy=TRUE),
 nsim=999, zero.policy=TRUE)

[Package spdep version 0.3-12 Index]