# A collection of new posts on logit choice models

They’re only a little bit in Stan, but I thought there might be some interest here in a new collection of posts explaining logit models of discrete choice.

A simple choice model (what’s identifiable, what’s not?):
http://khakieconomics.github.io/2019/03/17/A-simple-model-of-choice.html

Putting it all together:
http://khakieconomics.github.io/2019/03/17/Putting-it-all-together.html

There’s a bunch to come in the coming days/months, but thought these would be more useful in the wild than on my laptop. In rough order I’m doing:

• Aggregate logit (using linear regression or multinomial likelihood conditional logit)
• Dealing with endogenous price-setting (using IVs or structural price-setting models)
• Random coefficients logit (choice level). There’s a post there showing how to do this but a new one is coming.
• Ranked choice RE logit.
• Aggregate random coefficients logit (have two posts on this but I’ve changed my approach)
• Policy simulations and welfare analysis. A new product, a price change, a merger.

If there are other things you want in a chapter about discrete choice, please let me know!

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Looks very very interesting. Thanks!

A question I have about choice models (not sure this is the right forum (or thread) to ask) is what happens when things can sell out. To be more specific: popular choices sell out. Suppose customers can chose between 10 different variants. Variants 1 and 2 are the most popular. But because most people prefer them, they’re sold out soon. So they will only be part of a few experiments. What impact does that have?

As a toy example: there are 10 variants, and the shop has only 5 of each. Variant 1 is the most popular, then variant 2. The other 8 are equally popular. If there is no error term, and all participants have the same preference, then the first 5 participants will buy variant 1, then 5 participants will buy variant 2 and then 40 participants will buy one of the other variants. So variant 1 only participates in 5 out of the 50 experiments, variant 2 only participates in 10 out of 50 experiments, and the other variants will participate in all 50 experiments. What impact does that have on the chance of knowing if 1 and 2 are the most popular? And what if there’s a bit of error.

Hey Uri –

The sold-out items aren’t in the choice-set, so as long as you exclude them you’re fine.

A much bigger source of trouble is when the products themselves are offered in one market but not another–this says something about the seller’s assumption of the profitability of offering the good. As far as I know, this is an open problem.

But the sold-out items are in the choice set, but just for the first couple of experiments (or choices, not sure what terminology is better), because after that they’re sold out…

A nice analogy is a problem that @shira’s model for https://twitter.com/DataProgress/status/1101141154656075779 brought up: what’s the outside good when contestants/choices drop out?

The trick here is to make a single choice (or outside good) in the first round be the outside good, then recast all choice attributes as difference from the attributes of that good. Then the choice to take the outside good in latter rounds is potentially the choice to buy one of the sold-out goods.

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Thanks for the interesting suggestion!

Hello Jim :
This is somewhat related to your BLP (aggregate data , random coefficients , endogenous prices. ).
I was wandering if you compared the results using the Bayesian approach (without instruments ) to a typical BLP approach (ala Nevo ).
Also, did you compare the estimates from the GMM style models to the Bayesian approach.
Thanks