Modeling binary (presence/absence, alive/dead) variables in ecological models is commonplace. A surprisingly thorny set of problems accompany interpretation and comparison of coefficients from such models. The more complex the hypothesis being represented, the more compelling is the case for coefficient standardization. There exist a variety of disparate approaches to standardization used in various fields of investigation. In this talk, we review the issues, approaches taken in a wide range of fields, and reveal the fundamental challenges. Simulation studies allow us to reveal problems and evaluate proposed solutions.
Results/Conclusions
We show that the fundamental problems facing the interpretation of raw coefficients from binary responses models arise from the fact that the underlying true effect is not identifiable. This means that most coefficient comparisons of interest cannot be safely made without some form of standardization. Two approaches to standardization are examined, one based on a latent-linear perspective and the other from an observed-empirical perspective. The traditional recipe for standardization using standard deviations is examined carefully and potential problems quantified. The ratio of standard deviation to empirical range for binary predictors is roughly 0.5 while for Gaussian variables, the number is in the realm of 0.20 to 0.15 depending on sample size. Skewed distributions can exhibit ratios down to 0.05; thus, standard deviations are a very inconsistent basis for coefficient interpretation, as their relationship to the range of a variable can vary 10-fold. An alternative recipe using user-defined “relevant” ranges is shown to make standardized coefficients more directly interpretable using a variety of ecological examples.