Journal
BIOMETRICS
Volume 56, Issue 3, Pages 915-921Publisher
INTERNATIONAL BIOMETRIC SOC
DOI: 10.1111/j.0006-341X.2000.00915.x
Keywords
Bayesian statistics; causal inference; empirical Bayes estimators; epidemiologic methods; hierarchical regression; mixed models; multilevel modeling; random-coefficient regression; relative risk; risk assessment; shrinkage; variance components
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Regression models with random coefficients arise naturally in both frequentist and Bayesian approaches to estimation problems. They are becoming widely available in standard computer packages under the headings of generalized linear mixed models, hierarchical models, and multilevel models. I here argue that such models offer a more scientifically defensible framework for epidemiologic analysis than the fixed-effects models now prevalent in epidemiology. The argument invokes an antiparsimony principle attributed to L. J. Savage, which is that models should be rich enough to reflect the complexity of the relations under study. It also invokes the countervailing principle that you cannot estimate anything if you try to estimate everything (often used to justify parsimony). Regression with random coefficients offers a rational compromise between these principles as well as an alternative to analyses based on standard variable-selection algorithms and their attendant distortion of uncertainty assessments. These points are illustrated with an analysis of data on diet, nutrition, and breast cancer.
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