Linear regression on clustering result

Question

I've got a data about mammal body weight responses to increasing air temperature. I want to know whether there are some mammals that respond to the increasing air temperatures differently. Hence, I was going to preform a affinity propagation clustering method on the responses of body weight to temperature, which would get me a number of groups. Now, I want to know what influences whether a certain individual is assigned to a certain group - i.e. what influences the differences in mammal body weight responses to increasing air temperatures? I've got a lot of additional data to explain this, like longevity, habitat parameters, competition etc. So I thought to then construct a linear model to explain growth in each of the clusters (i.e. what are the predictors of mammal body response in each cluster).

Is this statistically sound? I feel like it may be a little bit of a weird way to do it, but I can't think of anything else. Any help would be greatly appreciated, thank you!

Answer 1

Instead of jumping right into separate linear models for each of your pre-defined groups based on body-weight responses to air temperature, step back and do exploratory data analysis. Look at and play with all the data, see how much the multiple predictors themselves might account for the differences among species, without pre-grouping. You might find that there are clusters of values of predictors that could fundamentally account for what you sense to be different groups with respect to the weight/temperature relationship.

When you build a model, start with a single model that incorporates all species. If possible, go back closer to raw data with body weight itself (often best on a log scale for allometry) as the outcome and air temperature as one of the multiple predictors. Include species as a predictor too, treated as random effects if there are more than a handful. Allow for species to differ not only in their intercepts with respect to weight but also in their coefficients for the weight/temperature relationship. Build as rich a model as you have data for (including interactions among predictors that your knowledge of the subject matter suggests might be important), without overfitting.

Then see if there are substantial amounts of variance in the weight/temperature relationship that isn't explained by predictors other than species. I can't say how this will all turn out. You might end up with the same groups that you have already identified, but your progression through the analysis should show how much of the grouping has to do with groupings of the predictors and how much remains unexplained.