ApolloChoiceModelling forum

In this year's Choice Academy, instructors discussed that when price is distributed negative lognormal we may not expect the price coefficient to be negative in our mixed logit models (rather the sign and size are related to the level of price sensitivity). For example, when I run my mixed logit model price is estimated to be positive (mean=0.49; sd=1.39). When I estimate the unconditional for price (following it's distributional assumptions) it is negative (−4.30). However, it seems uncommon in DCE papers to have a positive price coefficient reported. Following this, I have two questions about how to handle when an estimated price coefficient in a mixed logit model.

First: When reporting results from the estimation, should I report the price coefficient with standard error in the main table and the unconditional below? Or should I be reporting the unconditional?

Second: If we also run the same model in WTP space (e.g., b_price(a1*attribute1 + a2*attribute2 + ... )) , the positive coefficient outside of the paratheses seems to flip the expected signs of all attributes (distributed normal) inside the parentheses. Again here, is there a best practice for how to proceed with a positive price coefficient?

Thanks for all you do!

Hi

your price coefficient is not positive. The parameters mu and sigma are for the mean and sd of the logarithm of the beta, i.e. the normal that’s inside the negative exponential

See e.g. https://people.math.ethz.ch/~stahel/log ... basics.htm

Stephane

Thanks for your response! Hoping you can clarify one point for me.

In my notes, I have written that when discussing the uncorrelated MMNL model in Apollo instructors said that "we don't necessarily expect the mean parameters to be negative because we are going to use a negative exponential around them. So a smaller - or negative - mean for the logarithm of the coefficient will simply mean that the actual coefficient will be smaller in absolute value."

Is it inappropriate to have a positive mu parameter for price?

Hi

the mean for the coefficient is negative as we have discussed. The fact that the mu inside your negative exponential is positive simply means that your coefficient has a median that is more negative than -1

Stephane

Perfect. Thanks for the clarification.