A clarification of the phi mixing model

The authors review a deterministic model proposed for the analysis of two-way contingency tables that arise in counts of pairwise interactions. This model decomposes the table into the sum of two matrices with special forms: in one the contacts are distributed selectively, in the other they are distributed at random. We show that this model has several inherent problems. The decomposition is not unique, which compromises estimation and interpretation of the parameters; the deterministic framework provides no basis for estimation or hypothesis testing; and the assumption of decomposibility is supported by neither empirical evidence nor theoretical considerations. We show that generalized linear models provide a suitable alternative once the probability process is specified and the overparameterization is removed.