I'm trying to decide whether to run a multinomial logit or a conditonal logit (McFadden, 1973). I have data from a choice-based conjoint study in which each of the respondent's choices was between a pair of products with varying characteristics, including price. Each of the characteristics is a continuous variable, if that matters. I want to estimate a marginal willingness to pay for each of the characteristics. Typical explanations of how the two models differ are as follows:
Multinomial logit models a choice as a function of the chooser's characteristics, whereas conditional logit models the choice as a function of the choices’ characteristics.
By this logic, I would lean towards a conditional logit given that I'm trying to estimate a marginal willingness to pay for each characteristic. On the other hand, the values I estimate for this depend entirely on the preferences of the respondents, so you could say that I'm really estimating something relating to the preferences of respondents, rather than anything innate about the choices' characteristics.
Does anybody have a more crisp understanding of the differences between the models and/or reflections on which would be more appropriate in this setting?