Song Qian sent me this paper, to appear in the journal Ecology, on ecological applications of multilevel analysis of variance. Here’s the abstract:
A Bayesian representation of the analysis of variance by Gelman (2005) is introduced with ecological examples. These examples demonstrate typical situations we encounter in ecological studies. Compared to the conventional methods, the multilevel approach is more flexible in model formulation, easier to setup, and easier to present. Because the emphasis is on estimation, multilevel model results are more informative than the results from a significance test. The improved capacity is largely due to the changed computation methods. In our examples, we show that (1) the multilevel model is able to discern a treatment effect that is too weak for the conventional approach, (2) the graphical presentation associated with the multilevel method is more informative, and (3) the multilevel model can incorporate all sources of uncertainty to accurately describe the true relationship between the outcome and potential predictors.
I like the method (of course) and also the graphical displays. The next step is to move beyond exchangeable models, especially for interactions.
Do they provide example code/a how-to? As an ecologist, I think I can safely say that many in the field are slow to adopt new methods unless there is a very well laid out THIS IS HOW YOU DO IT – i.e., R or SAS code. Otherwise, folk will usually look at it, and move on. While statistics are how we ultimately quantitatively draw conclusions, ecologists as a whole (particularly field ecologists) are often reluctant to invest the time to move beyond what they learn in stats 101, which, in this field, is all ANOVA/Simple Linear Regression with decisions made by p values. This is changing (hurray Burnham and Anderson, Gotelli and Ellison, Jim Clark, and Ben Boelker's books!), but, if one wants to make inroads with newer methodologies, they have to make it easy. Ecologists have more than enough other things on their day to day research plates (designing well controlled experiments that will survive natural conditions, worrying about artefacts, coming to grips with the natural history of the systems they are working in, etc.) But, given point (1) from their abstract, this is something that, if folk know how to do it, will be very very attractive, as we're a field of finding biologically significant needles in the haystack of natural variability.