SIMULATION STUDY OF HIERARCHICAL REGRESSION

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Abstract
Hierarchical regression – which attempts to improve standard regression estimates by adding a second‐stage ‘prior’ regression to an ordinary model – provides a practical approach to evaluating multiple exposures. We present here a simulation study of logistic regression in which we compare hierarchical regression fitted by a two‐stage procedure to ordinary maximum likelihood. The simulations were based on case‐control data on diet and breast cancer, where the hierarchical model uses a second‐stage regression to pull conventional dietary‐item estimates toward each other when they have similar levels of food constituents. Our results indicate that hierarchical modelling of continuous covariates offers worthwhile improvement over ordinary maximum‐likelihood, provided one does not underspecify the second‐stage standard deviations.

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