Heteroscedasticity in mixed logit model

[JvB]

Hi Michiel,

I was wondering if there is a possibilty of heteroskedasticity in mixed logit estimations that bias the results (I have a mixed logit with some random parameters and an error component for the panel effect)? And if yes, where could heteroskedasticity come from and is there anything I can do about it? I´ve read that most researchers do not check for heteroskedasticity in their data as there is nothing that can be done about it anyways?
Your advice is highly appreciated.

Thanks and best,
Julia

[Michiel Bliemer]

It depends on the source of the heteroskedasticity, but in many cases you can account for it in model estimation. The utility function looks something like:

U = lambda * (b1*x1 + b2*x2 + ...)

where usually one normalises lambda =1.

In a heteroskedastic model, you can account for observed heteroskedasticity by making lambda a function of characteristics of the data collection, the respondent, or other characteristics.

For example, if you have respondents with and without dementia, you could use
lambda = 1 + a*dementia, or
lambda = a^dementia
where you estimate parameter a.

As another example, to account for learning or fatigue effects in a choice experiment, you could use
lambda = 1 + a1*choicetasknr + a2*choicetasknr^2
where you estimate parameters a1 and a2.

To account for differences in choice task complexity in your data, you could define lambda as the entropy term, see the work of Swait. There are many other forms of lambda that you could define to account for heteroskedasticity in your data, so it is not true that "nothing can be done about it".

Michiel