Basic Use of the Information-Theoretic Approach

Abstract

Model building and data analysis in the biological sciences somewhat presuppose that the investigator has some advanced education in the quantitative sciences, and statistics in particular. This requirement also implies that a researcher has substantial knowledge of statistical null hypothesis-testing approaches. Such investigators, including ourselves over the past several years, often find it difficult to understand the information-theoretic approach, only because it is conceptually so very different from the testing approach that is so familiar. Relatively speaking, the concepts and practical use of the information-theoretic approach are simpler than those of statistical hypothesis testing, and much simpler than some of the Bayesian approaches to data analysis (e.g., Laud and Ibrahim 1995 and Carlin and Chib 1995). The prevailing philosophy has been to use some test or criterion or statistic to select a model, from a set of models, that is somehow "best" in some particular sense. Inference is then entirely conditional on this selected model. We believe that approach should be merely the beginning, and an inadequate or humble beginning at that. There is much more to the model selection problem than this initial solution. Substantive information is contained in the differences (i), since they are free from arbitrary (and unknown) constants and are directly interpretable in many cases. Both the i and Akaike weights (w i) allow scientific hypotheses, carefully represented by models, to be ranked. The discrete likelihood of model i, given the data (L(g i |x)), provides a powerful way to assess the relative support for the alternative models. The w i provide a