You must supply both the rates in the different areas as well as the weights (wij) between pairs of areas. The weights reflect how
‘connected’ you think two areas are, and usually reflect geographic proximity. Moran’s I is used to determine whether
‘connected’ areas are more similar to one another than would be expected under spatial randomness.
Weights can be specified in many ways, but usually are based on geographic adjacency, distance, or some other criteria reflecting the alternative spatial model.
In the absence of more detailed knowledge areas are often connected based on geographic adjacency. Two areas, i and j, are assigned a weight of 1 when they share a common border. Otherwise they are assigned a weight of 0. The alternative spatial model under this simple scheme states that rates in spatially contiguous areas are correlated. This is a reasonable model to use when you are interested in detecting contiguous areas with similar disease rates.
The weights themselves may be assigned values other than 0 or 1. A common scheme is to calculate weights based on geographic distance. For example, let dij be the geographic distance between areas i and j. Then the weight may be calculated as an inverse distance function:
The alternative spatial model then states that rates in nearby, not necessarily contiguous, areas are correlated. This is a reasonable model to use when you think processes on a large geographic scale may be causing rates in distant, as well as adjacent, areas to covary.
Finally, one may specify weights based on some other criteria reflecting the alternative spatial model. Obviously, there are many ways to specify the weights. The rule of thumb is to use a weighting scheme which reflects your alternative hypothesis.