# mlink.test: Maximum Linkage spatial scan test In smerc: Statistical Methods for Regional Counts

## Maximum Linkage spatial scan test

### Description

mlink.test implements the Maximum Linkage spatial scan test of Costa et al. (2012). Starting with a single region as a current zone, new candidate zones are constructed by combining the current zone with the connected region that maximizes the resulting likelihood ratio test statistic, with the added constraint that the region has the maximum connections (i.e., shares a border with) with the regions in the current zone. This procedure is repeated until the population or distance upper bounds constraints are reached. The same procedure is repeated for each region. The clusters returned are non-overlapping, ordered from most significant to least significant. The first cluster is the most likely to be a cluster. If no significant clusters are found, then the most likely cluster is returned (along with a warning).

### Usage

mlink.test(
coords,
cases,
pop,
w,
ex = sum(cases)/sum(pop) * pop,
nsim = 499,
alpha = 0.1,
ubpop = 0.5,
ubd = 1,
longlat = FALSE,
cl = NULL
)


### Arguments

 coords An n \times 2 matrix of centroid coordinates for the regions in the form (x, y) or (longitude, latitude) is using great circle distance. cases The number of cases observed in each region. pop The population size associated with each region. w A binary spatial adjacency matrix for the regions. ex The expected number of cases for each region. The default is calculated under the constant risk hypothesis. nsim The number of simulations from which to compute the p-value. alpha The significance level to determine whether a cluster is signficant. Default is 0.10. ubpop The upperbound of the proportion of the total population to consider for a cluster. ubd A proportion in (0, 1]. The distance of potential clusters must be no more than ubd * m, where m is the maximum intercentroid distance between all coordinates. longlat The default is FALSE, which specifies that Euclidean distance should be used. If longlat is TRUE, then the great circle distance is used to calculate the intercentroid distance. cl A cluster object created by makeCluster, or an integer to indicate number of child-processes (integer values are ignored on Windows) for parallel evaluations (see Details on performance).

### Details

The maximum intercentroid distance can be found by executing the command: sp::spDists(as.matrix(coords), longlat = longlat), based on the specified values of coords and longlat.

### Value

Returns a smerc_cluster object.

Joshua French

### References

Costa, M.A. and Assuncao, R.M. and Kulldorff, M. (2012) Constrained spanning tree algorithms for irregularly-shaped spatial clustering, Computational Statistics & Data Analysis, 56(6), 1771-1783. <doi:10.1016/j.csda.2011.11.001>

print.smerc_cluster, summary.smerc_cluster, plot.smerc_cluster, scan.stat, scan.test

### Examples

data(nydf)
data(nyw)
coords <- with(nydf, cbind(longitude, latitude))
coords = coords, cases = floor(nydf$cases), pop = nydf$pop, w = nyw,