There is a known connection between the multinomial and the Poisson likelihoods. This, in turn, means that a Poisson regression may be transformed into a logit model and vice versa. In this paper, I show the data transformations required to implement this transformation. Several examples are used as illustrations.
BakerS. G.1994. The multinomial-Poisson transformation. The Statistician43: 495–504.
2.
GuimarãesP., FigueiredoO., and WoodwardD.2003. A tractable approach to the firm location decision problem. Review of Economic and Statistics85(1): 201–204.
3.
HausmanJ., HallB., and GrilichesZ.1984. Economic models for count data with an application to the patents-R&D relationship. Econometrica52: 909–938.
4.
LangJ.1996. On the comparison of multinomial and Poisson log-linear models. Journal of the Royal Statistical Society, Series B, 58: 253–266.
5.
McFaddenD.1974. Conditional logit analysis of qualitative choice behavior. In Frontiers in Econometrics, ed. ZerembkaP., 105–142. New York: Academic Press.
6.
PalmgrenJ.1981. The Fisher information matrix for log linear models arguing conditionally on observed explanatory variables. Biometrika68: 563–566.