Panel-data mixed logit: repeated choices under different circumstances

[Kees Maat]

Hi Statalist,

Using the panel-data mixed logit choice model – cmxtmixlogit – one can take into account repeated choices, such as repeated mode choices. I have two questions:

1. Because multiple respondents each make multiple choices, the choices are not independent of each other, as variation can not only be attributed to the choices, but also to the respondent. This model controls for that. Does this mean that this panel model is therefore a multilevel model?
2. Does this panel model assume that all choices are made under the same circumstances? What if we have choices for each season (or for good and bad weather). In that case, it can be assumed that the choices are different for each season; or different between good and bad weather. Can I use the panel model for that as well? What does that mean for the differences in coefficients between the seasons?

Thanks, Kees

[Hong Il Yoo]

You can say it's a 2-level model in the sense that there're random parameters that vary across individuals but remain constant within an individual, and there're type 1 extreme value errors that vary across individuals and choice tasks.

No the model does not assume that people make choices under the same circumstances. Let n, j, and t index individuals, alternatives and choice tasks. Each independent variable can vary across all or any subset of {n, j, t} so there is considerable flexibility in terms of describing how one choice scenario is different from another.

[Kees Maat]

Thanks for your answer.

So, the random variable is the one that varies not only between alternatives (j) (e.g. travel time) but also between moments in time (t) (e.g. temperature).

In Stata: cmxtmixlogit mode_choice, casevars (income) random (traveltime temperature).

This means that I also get a coefficient for temperature, based on the different values between the seasons.
Is that correct?

[Hong Il Yoo]

I'm afraid that it is not correct. I'd like to recommend William Greene's textbook chapter (in "Econometric Analysis") on conditional and random parameter logit models. His book does a much better job at explaining the model than I can do in a short post. Then you can refer to the Stata user manual entry on -cmxtmixlogit- for how to set up -indepvars- in -rand()- to estimate your desired model specification. Assuming that your -temperature- varies over both j and t, my guess is that the model specification that you have in mind is one that interacts -temperature- with seasonal dummies and includes the interaction terms in -rand()-.

[Kees Maat]

Your last sentence is indeed what I mean. Unfortunately, I do not see where I go wrong.

[Hong Il Yoo]

I wonder whether we're thinking of different things. So that we're on the same page, let's write out the random utility function explicitly. Your command line specifies U_{njt} = alpha_{j} * income_{nt} + beta1_{n} * traveltime_{njt} + beta2_{n} * temperature_{njt} + error_{njt} where alpha_{j} is a non-random coefficient and beta1_{n} & beta2_{n} are independently normally distributed random coefficients. So you're assuming that the marginal utility from temperature is equal to beta2_{n} and remains invariant within individual n across all seasons. Could you confirm if this is the model specification that you'd like to estimate?

[Kees Maat]

I understand. But how can I then specify the influence of season?

[Hong Il Yoo]

There're several different ways e.g., -rand(c.traveltime c.temperature c.temperature#1.winter)- where -winter- is a dummy indicator of winter months. You should keep in mind that random coefficient models are quite a different beast from the non-random coefficient models and think carefully through stochastic implications of your modelling decisions. For example, whether your base group is winter months or non-winter months is not a simple matter of reparameterisation and -rand(c.traveltime c.temperature c.temperature#1.winter)- vs -rand(c.traveltime c.temperature c.temperature#0.winter)- amounts to different stochastic specifications.

[Kees Maat]

Thanks a lot! I guess that I have to play with the parameters, to experience the implications of the different specifications.