A wide range ofstatistical model frameworks are available to ecologists, and more are being developed everyday. The choice of a particular framework in a particular situation should be dictated primarily by: (1) the purpose of the modeling exercise and (2) the nature of the data being used to quantify the model.
As stated in the 'Introduction', the purposes for which ecologists use statistical models include: to quantify the implications of alternative hypotheses, to distinguish or synthesize the effects of multiple influences, and to predict the outcomes of controlled or uncontrolled system changes. The various frameworks presented in this article might be more or less suitable for these purposes. For example, the simplicity and ease of interpretation of linear regression-based models makes it easy for researchers to quickly formulate alternative hypotheses stated in terms of the slopes and intercepts of the regression model. Structural equation modeling, on the other hand, is somewhat less intuitive to many ecologists, but can be more effective at resolving confounding factors in the attempt to represent causal relationships. By graphically representing causal relationships and translating them into conditional independence relations, BBNs assist modelers in the articulation of appropriate submodels. Separate development and later reassembly of these submodels provides a logical framework for predictive synthesis across subdisciplines. In general, by allowing the incorporation of prior knowledge and encouraging a fuller representation of uncertainty, the Bayesian methods are especially useful for the purpose of providing support to managers and decision makers.
Ideally, the way in which data are collected and recorded should be determined by their anticipated use. However, the reality is that most modeling exercises begin only after the relevant data are already in hand. Therefore, the modeling framework often has to be chosen to accommodate the format of the data, rather than vice versa. Throughout this article, the data type used in each model has been explicitly identified. For example, Table 1 provides an overview of how the use of discrete or continuous variables will dictate the linear regression-based modeling method that is appropriate. Similar concerns arise for nonlinear, nonregression-based frameworks as well. For example, using continuous variables in a BBN implies the use of continuous conditional probability density functions (PDFs) characterizing the relationships among nodes, while categorical variables require discrete probabilities (i.e., histograms). Different algorithms for prediction and inference have been developed for these two situations.
See a/so: Structural Dynamic Models.
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