Multinomial–Poisson Transformation

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Modeling Movie Life Cycles and Market Share (2005, methodology): “Hence, instead of modeling this directly as a logit model, we use a Poisson transform approximation (Baker 1995; Technical Appendix).”
Poisson, Poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory. (2005, methodology): “Although this type of model provides good statistical fit, it is not commonly used in practice since the likelihood function can be very difficult to compute (Baker, 1994).”