Dan Lakeland writes:

I am working with some biologists on a model for time-to-response for animals under certain conditions. The model(s) ultimately are defined in terms of a differential equation that relates a (hidden) concentration of a metabolic product to the (cumulative) probability that an animal will respond within a given time by changing its behavior.

Now mostly, in my experience, statistical models are models for averages, or particular quantiles of the dataset (medians etc). Most models attempt to predict something (like time to response) from something else (like say measured amounts of a drug). In this case, rather than predicting individual response times, we’re trying to predict shape of a distribution from measured exposure to a certain environment.

In this case, we are tempted to use some measure of the goodness of fit to try to guess what is going on internally within the animal. For ease of computation, I’m fitting this model with maximum likelihood methods initially (a Bayesian approach may come later if time allows).

What is your opinion on model selection methods in this type of scenario? Your book index has “model selection and why we avoid it” which sounds unhelpful, but the section on model selection was actually more helpful than the index implied. Is there anything you can add in this context?

My reply: I’m not quite sure what your question is, but maybe, if I can translate it into the social-science examples with which I’m more familiar, I can imagine you’re doing something like predicting what percentage of people will respond a certain way to an advertisement, or how low a price would have to be before half the people would buy something. Framed that way, these sorts of models are pretty common. In section 6.8 of ARM, we discuss the relation between certain models for individuals and for groups.