Extensions of Multinomial Logit: The Hedonic Demand Model, the Non-Independent Logit Model, and the Ranked Logit Model

Economic models of multinomial discrete choice are based on the probability that the utility of a given discrete alternative will exceed the utility of all others. The unknown parameters of these utility functions are estimated by assuming utility maximization and analyzing choices actually observed. The Multinomial Logit Model follows from assuming constant utility function parameters and an independently distributed additive stochastic term that obeys the Type I extreme value distribution. Multinomial logit is computationally the simplest multinomial discrete choice model and is also the most frequently used. Three distinct enhancements of multinomial logit are presented and analyzed here. I also show how, in cases where conventional estimates of statistical dispersion are suspect, a variance component structure can be used to derive realistic estimates. The Hedonic Demand Model allows the utility function parameters to have a probability distribution across individuals. Empirical results demonstrate that the Hedonic Demand Model differs in economically important ways from multinomial logit. The Non-Independent Logit Model allows the additive stochastic term to have a variance components structure across alternatives. The Ranked Logit Model allows the analysis of data on individual rankings of the alternatives beyond just the first choice for a group of individuals or for a single individual. Empirical results are presented for both forms. Because all three enhancements are logit type models, in that the additive stochastic term has a Type I extreme value distribution, they are computationally feasible. I compare these logit type models to alternatives and show how technical aspects of logit type models give them good theoretical properties, notably a particular type of robustness. Due to their relative computational feasibility and robustness, these models can be valuable to practitioners who wish to allow for individual differences, to model correlations among alternative utilities, or to utilize data on choice rankings beyond the first.