Statistical Prediction
Statistical models help ecologists use the patterns they find in their data to make predictions. Such predictions are needed to explore the implications of alternative hypotheses, anticipate the outcomes of possible experimental designs, and provide decision support to ecosystem managers. A wide range of model frameworks are appropriate for prediction depending on the nature of the data. This article starts with the most restricted and familiar setting – linear regression analysis – and proceeds by considering increasingly general, regression-based techniques which sequentially drop some limiting assumptions. These include generalized linear models, quantile regression, nonlinear regression, and generalized additive models. Some special cases of regression, such as correlated data models, structural equation models, classification and regression trees, and artificial neural networks, are also described. Nonregression-based methods are presented next, including hierarchical models, Bayesian models, and belief networks. These methods are generally better able to deal with situations of multiple plausible models or overparametrized model formulations. The article concludes by discussing issues of model-based prediction, including multimodel averaging.
