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The test is essentially a goodness-of-fit test comparing two spatial models for the case subject locations, a null spatial model developed from control locations and a model that incorporates distance from the focus.
The spatial pattern of control subject locations, also called intensity or density, is modeled as an inhomogeneous spatial Poisson point process. In this case, the process is inhomogeneous because the intensity varies with location (x):
Where rho ( 
) is the overall number of events per unit area, 
is the spatial variation in intensity of the control locations with position irrespective of the focus, d is the distance from x to the focus, and f(d) is a function describing the change in intensity of the process with distance from the focus.
Diggle terms f(d) a raised incidence function. To separate this concept from the epidemiological definition of incidence, we will use the phrase raised density model. The null hypothesis is f(d) = 1, no change in density of cases with respect to the focus. The alternative hypothesis is a higher relative density of cases near the focus.
ClusterSeer offers one raised density function, from Diggle (1990):
where d2 is the squared distance between the location under consideration and the focus. The raised intensity of cases, represented by the value of f(d), decreases away from the focus (see graph).
First, parameter estimates are optimized through maximum likelihood estimation and the fit of the case data to the model is compared with a generalized likelihood ratio test.
