the siren song of the linear model

Prepare for a really dorky blog entry.

I was very struck by Kendler, Kuhn, & Prescott's 2004 article--not necessarily because of their conclusions about risk factors for depressive episodes but because of how they got there. In other words, I appreciated their approach to various statistical issues, especially model building and the use of raw probabilities. Admittedly, I am still a quantitative infant, but I particularly appreciated their deliberate decision to compare additive versus multiplicative models of risk. It is often tempting to try to fit any dataset to a linear model, not for any theoretical reason, but simply for reasons of convenience. Much can be gained, however, from considering the implications of fitting data to different mathematical functions; in this case, for instance, fitting a multiplicative model of risk suggests processes that differ in important ways from the ones that would operate in an additive model of risk. Just because linear models are easy to construct and analyze does not mean that they are the best way to understand our data!

I also appreciated Kendler et al.'s discussion of their decision to use raw probabilities as opposed to transforming them, perhaps to log(raw probability). Using a logarithmic transformation may indeed have made the process of statistical analysis easier but it also would have disguised one of the most interesting features of these data, which is the nonlinear relationship between risk of a depressive episode and contextual threat X neuroticism. I agree with the "public health argument" and I also think that it would have been much more difficult to interpret log(hazard ratio) than it is to interpret the raw probabilities. Despite the statistical convenience that transformation to a log scale can provide, it can lead to results that are difficult to interpret. Here, sticking with the raw probabilities makes the patterns Kendler et al. wish to highlight much more clear.


P.S. Jim--you wanted me to remind you to get me the reference(s) on doing meta-analyses of single-case studies.