Mixed Logit Model


#41

@jeremy.koster - Could you provide some summary stats re: your data? How often do fisherman choose the same spots? Do the same people go to the same places or do they alternate? Do they often go to particular places around the same time or do they scatter across the 10 possible sites? If they coalesce in particular places at one (or a few) at a time, is there a pattern to which these places are (e.g. weather, fish migration patterns, etc.)?

There are a number of likely helpful models in economics for your problem, but which one depends on the answers to the above. I’d be happy to suggest something more concrete upon hearing more :)


#42

Thanks, Jim. If you and Bob or others know researchers who are well-versed in good models for these data and open to dabbling in an anthropological problem, I’d be glad to connect them with the lead investigators on the project. I’d love to see more choice models in anthropology, which doesn’t have much experience with such approaches.


#43

Thanks shoshievass,

As a disclaimer, the data were collected by a researcher in Grenada, and I am not the one who is best-positioned to summarize the data. That said, the basic details are that all fishing activities by approximately 13 boat captains were documented for about one year. The captains have the option of choosing from about 9 fishing sites, but there are rules about the order in which boats can fish at these sites, largely determined by queuing according to time of arrival. The outcomes (n = 998) of each fishing episode are known (in terms of how much fish were caught by boat j) – which is a positively skewed distribution – along with the date and time and the length of the fishing episode. But there is no way to know what the expected productivity of unexploited sites would be at time t. The sites are all close enough that weather should be similar across sites, but there may be ecological aspects of the bays that mean some sites are more or less productive at different times.

After fishing at a site, captains have the option of getting in line for another turn at that site, or switching to a different site. Based on what I’ve seen of the data, these decisions could be reconstructed (with some moderate coarseness in the time frames at which these decisions were documented). I haven’t looked too closely at summary statistics, but according to the researchers, it seems common for captains to cluster together at productive sites . . . unless things get too crowded, at which point some will disperse to look for less crowded sites. (Fortunately, it seems that there is no fishing by other captains who were not in the study population, so the distribution of boats at any particular time is knowable, albeit with some measurement uncertainty.)


#44

@richard_mcelreath, author of Statistical Rethinking, is an anthropologist. He’ll probably know what’s up in Anthro, though this seems like a very generic kind of sequential choice problem, which is hardly to say that it’s easy (any inference involving projected discrete choice can get hard due to combinatorics and require dynamic programming algorithms rather than brute force).


#45

Thanks, Bob.

Actually, Richard is a co-author of mine, and these data arrived on my desk via another mutual colleague from our corner of anthropology. In general, choice models are not widely used in our field, but it’s possible that some of my colleagues may have connections to ecologists who have done work on analogous topics (perhaps including the Hidden Markov models that you had recommended previously).


#46

I guess that’s not too surprising given that we’re not exactly all here at random.


#47

I’ll respond properly as soon as I get a chance! (Probably over the weekend - sorry; a bit of a hectic time for me!)