# How to subset alternatives in nested multinomial logistic regression?

I am trying to predict whether or not captains in a particular groundfish fishery choose to fish on any given day and what variables may influence that decision. Originally I had planned on using vanilla logistic regression, where each captain decided to fish or not fish on any given day of the season in a particular fishery. However, this is not a realistic model as many vessels participate in multiple fisheries. Thus, I want to run a nested multinational logistic regression model with the structure at the bottom.

Note that Group 1 and 2 exist to avoid violating the IIA assumption.

Because each species has a different season and within each species captains have variable amounts of fishing quota lbs (when the quota is gone you can no longer fish even if the season is open), not all nodes are available at the same time. I would like to include a dummy variable for whether or not an individual node is an option, but I am not sure if that makes sense or even if this method (multinomial logistic) is still viable.

I could try something like this Coding of semi-numerical variables i.e whuber's response, but I have a lot more subsets and nests within those subsets.

Edit* I have since looked into, but at the moment have not implemented, a varying choice logit model. The description of the model can be found http://web.mit.edu/teppei/www/research/dchoice.pdf.

I am using R and was planning on using lmer4, but I am not sure if I will be able to.

## 2 Answers

Why use nested multinomial logit. If you use Group 1 and 2 to avoid IIA assumption , you can use multinomial probit instead of logit.

• I have since come across this, and this seems like it could be a good way to go. However, it would be nice to let the regressors vary across choice sets. This is allowed in the varying choice set logit model, although I am not sure if there is a nice package, like the MNP package, to implement it. – Trevor Gratz May 2 '14 at 21:43

The general term for the type of model you want is a choice model. Assuming your description of the problem is correct, the choices that you are trying to model are not Fish vs Don't fish, but instead the days of the week.

The second level of your hierarchy is not, I think, really a level of a hierarchy in terms of the choice. Rather, it is a characteristics of the fishing captain's environment, and so can be dealt with either via interactions, alternative specific effects, or, by estimating a separate model for each fish type. (A challenge with your question is that you are going to have to get across a whole field of research in order to model it; there are specialist books on this topic, and Hensher et al. is probably the simplest to get started with).

The issue of certain nodes not being available at the same time is not dealt with by dummy variables. Rather, it is dealt with by having different alternatives in the choice sets. For example, in transportation research, if modeling choice of transport options, only people with a car have the option of traveling by a car.

I can't see how you can model this in lmer. There are quite a few specialist choice modeling packages in R. People who estimate a lot of choice models for real-world problem solving (as opposed to academic publication) tend to choose between a latent class logit and a mixed logit (aka random parameters logit). Nested logit is a technique that had its day, 30 years ago. And, just to add to your challenge, this is one of those areas where R is not great, and you will find that some of the models will run for a very long time. Most practitioners will use specialized software that is a lot faster than R for this type of data, such as Stata, SAS, or more specialized packages, such as LIMDEP and Latent Gold.