EBImoran.mc

0th

Percentile

Permutation test for empirical Bayes index

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.

Keywords
spatial
Usage
EBImoran.mc(n, x, listw, nsim, zero.policy = NULL, alternative = "greater", spChk=NULL, return_boot=FALSE, subtract_mean_in_numerator=TRUE)
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
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), 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()
return_boot
return an object of class boot from the equivalent permutation bootstrap rather than an object of class htest
subtract_mean_in_numerator
default TRUE, if TRUE subtract mean of z in numerator of EBI equation on p. 2157 in reference (consulted with Renato Assunção 2016-02-19); until February 2016 the default was FALSE agreeing with the printed paper.
Details

The statistic used is (m is the number of observations): $$EBI = \frac{m}{\sum_{i=1}^{m}\sum_{j=1}^{m}w_{ij}} \frac{\sum_{i=1}^{m}\sum_{j=1}^{m}w_{ij}z_i z_j}{\sum_{i=1}^{m}(z_i - \bar{z})^2} $$ where: $$z_i = \frac{p_i - b}{\sqrt{v_i}}$$ and: $$p_i = n_i / x_i$$ $$v_i = a + (b / x_i)$$ $$b = \sum_{i=1}^{m} n_i / \sum_{i=1}^{m} x_i $$ $$a = s^2 - b / (\sum_{i=1}^{m} x_i / m)$$ $$s^2 = \sum_{i=1}^{m} x_i (p_i - b)^2 / \sum_{i=1}^{m} x_i $$

Value

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

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

Aliases
  • EBImoran.mc
  • EBImoran
Examples
example(nc.sids)
EBImoran.mc(nc.sids$SID74, nc.sids$BIR74,
 nb2listw(ncCC89_nb, style="B", zero.policy=TRUE), nsim=999, zero.policy=TRUE)
sids.p <- nc.sids$SID74 / nc.sids$BIR74
moran.mc(sids.p, nb2listw(ncCC89_nb, style="B", zero.policy=TRUE),
 nsim=999, zero.policy=TRUE)
Documentation reproduced from package spdep, version 0.6-9, License: GPL (>= 2)

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