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Category Archives: RubMaps review

4. Model selection using the Schwarz criterion

Nevertheless, Goldberg et al. innovated an important contribution in two key respects. Firstly, their piecewise model is defined by a small number of discrete phases or periods. This brings the advantage of directly modelling the timing and intensity of population events (the date at which the model changed from one phase to the other), and a simple description of the population behaviour in each phase. Secondly and most importantly, the authors raised the point that a model comparison is required. They test various models, both simpler (one phase) and more complex (up to six phases) in various permutations of logistic and exponential phases. We construct a continuous piecewise model, calculate likelihoods and use the BIC to select the most appropriate number of phases. Finally, we use a GOF test to show the data are plausible under the best model.

3. Continuous piecewise linear modelling

The goal in population modelling is usually to identify specific demographic events. Typically, the objective is to estimate the date of some event that marks a change in the trajectory of the population levels, such as the start of a rapid decline or increase in population levels (perhaps from disease, migration or changes in carrying capacity) and provide a simple description of the population behaviour between these events, such as a growth rate. A CPL model lends itself well to these objectives since its parameters are the coordinates of the hinge points, which are the relative population size (y) and timing (x) of these events.

We choose the number of linear phases (or number of hinge points joining these phases) systematically as part of a model selection process.

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