What are hierarchical models?

A hierarchical model is a model where for each term in the model, all lower order terms contained in it must also be in the model. For example, suppose there is a model with four factors: A, B, C, and D. If the term A * B * C is in the model then the terms A, B, C, A*B, A*C, and B*C must also be in the model, though any terms with D do not have to be in the model. The hierarchical structure applies to nesting as well. If B (A) is in the model, then A must be also.

A model is non-hierarchical if it does not contain all of the lower order terms for each term in the model.

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