smerc (version 1.3)

tango.test: Tango's clustering detection test

Description

tango.test performs a test for clustering proposed by Tango (1995). The test uses Tango's chi-square approximation for significance testing by default, but also uses Monto Carlo simulation when nsim > 0.

Usage

tango.test(cases, pop, w, nsim = 0)

Arguments

cases

The number of cases observed in each region.

pop

The population size associated with each region.

w

An \(n \times n\) weights matrix.

nsim

The number of simulations for which to perform a Monto Carlo test of significance. Counts are simulated according to a multinomial distribution with sum(cases) total cases and class probabilities pop/sum(pop). sum(cases) .

Value

Returns a list of class tango with elements:

tstat

Tango's index

tstat.chisq

The approximately chi-squared statistic proposed by Tango that is derived from tstat

dfc

The degrees of freedom of tstat.chisq

pvalue.chisq

The p-value associated with tstat.chisq

tstat.sim

The vector of test statistics from the simulated data if nsim > 0

pvalue.sim

The p-value associated with the Monte Carlo test of significance when nsim > 0

Additionally, the goodness-of-fit gof and spatial autocorrelation sa components of the Tango's index are provided (and for the simulated data sets also, if appropriate).

Details

The dweights function can be used to construct a weights matrix w using the method of Tango (1995), Rogerson (1999), or a basic style.

References

Tango, T. (1995) A class of tests for detecting "general" and "focused" clustering of rare diseases. Statistics in Medicine. 14, 2323-2334.

Rogerson, P. (1999) The Detection of Clusters Using A Spatial Version of the Chi-Square Goodness-of-fit Test. Geographical Analysis. 31, 130-147

Tango, T. (2010) Statistical Methods for Disease Clustering. Springer.

Waller, L.A. and Gotway, C.A. (2005). Applied Spatial Statistics for Public Health Data. Hoboken, NJ: Wiley.

See Also

dweights

Examples

# NOT RUN {
data(nydf)
coords = as.matrix(nydf[,c("x", "y")])
w = dweights(coords, kappa = 1)
results = tango.test(nydf$cases, nydf$pop, w, nsim = 49)
# }