There are two cases that are evaluated in the bivariate join count. The first being in-situ colocation (CLC) where xi = 1 and zi = 1. The second is the general form of the bivariate join count (BJC) that is used when there is no in-situ colocation.
The BJC case "is useful when x and z cannot occur in the same location, such as when x and z correspond to two different values of a single categorical variable" or "when x and z can co-locate, but do not" (Anselin and Li, 2019). Whereas the CLC case is useful in evaluating simultaneous occurrences of events.
The local bivariate join count statistic requires a binary weights list which can be generated with nb2listw(nb, style = "B")
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P-values are only reported for those regions that match the CLC or BJC criteria. Others will not have an associated p-value.
P-values are estimated using a conditional permutation approach. This creates a reference distribution from which the observed statistic is compared.