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Model Hierarchy

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Definition

Model Hierarchy is based on the principle that if a model contains a higher-order effect then it must also include the lower-order effects contained within that higher-order effect. Thus, a model containing the second-order effect AB must also include the Main Effects A and B, keeping the 'family' of factor effects together. This principle, although not always necessary, ensures good statistical properties of the model such as internal consistency.

In general, model hierarchy is more of an issue if the model is constructed for explanatory rather than prediction purposes. In either case however it might help to examine the diagnostics and fit of both, the hierarchical and non-hierarchical Models and base the final decision on their comparison.