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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?

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    $\begingroup$ Hi: Sections 6.2 and 6.3 at this link hopefully explain it clearly. I didn't read it but I am somewhat familiar with the author's writings and remember liking them. data.princeton.edu/wws509/notes/c6s2.html $\endgroup$ – mark leeds Aug 7 '18 at 18:13
  • $\begingroup$ @markleeds I like this resource also. My issue is that the estimated coefficients should represent measures of how much users value attributes, so it's hard for me to conceptualize how one can hope to measure the value of attributes separately from consumers' preferences or consumers' preferences separately from the value of attributes. Maybe this is more obvious in other settings? This confusion notwithstanding, since my independent variables are on attributes of the good, I think I'll just push forward with a conditional logit. Thanks for the reference. $\endgroup$ – Shane Aug 7 '18 at 22:03
  • $\begingroup$ Hi Shane: I've never used conditional logit so, although your question sounds interesting, I can't help you. You may want to take a chance and email German who made that site. I emailed someone recently, never expecting them to reply and they did reply with a valuable response. Good luck. $\endgroup$ – mark leeds Aug 8 '18 at 12:24

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