The Validity of Poisson Assumptions in a Combined Loglinear/MDS Mapping Model

The validity of assuming a Poisson loglinear model as the generating process for citations from one journal into another has been questioned on the grounds that the expected citation rate may fluctuate, and that the citations may not be independent events. These objections are discussed. It is shown that fluctuation in generating rate is not a problem because the number of events generated by a Poisson process of fluctuating rate has the same probability distribution as for a Poisson process of the average rate sustained over the same period. It is also shown that nonindependence of citations would create no systematic bias, although it could lower the estimation efficiency by overweighting nonindependent citation patterns. There is no possibility of distinguishing variation in Poisson rate from nonindependence of citations because every citation series is a single sample from a unique process and can be equally well explained by either assumption. Accordingly, parsimony supports the choice of the Poisson model. Citation data are analyzed to confirm that the Poisson rate does vary with time. Nontransitivity is considered as another possible objection to the Poisson loglinear citation mapping model, and is shown not to be a major problem in the data set analyzed.