Combining Related and Sparse Data in Linear Regression Models

Meta-analysis has become a popular approach for studying systematic variation in parameter estimates across studies. This article discusses the use of meta-analysis results as prior information in a new study. Although hierarchical prior distributions in a traditional Bayesian framework are characterized by complete exchangeability, meta-analysis priors explicitly incorporate heterogeneity in prior vectors. This article discusses the nature of the meta-analysis priors, their properties, and how they can be integrated into a familiar recursive estimation framework to enhance the efficiency of parameter estimates in linear regression models. This approach has the added advantage that it can provide such estimates when (a) the design or data matrix is not of full rank or (b) when observations are too few to allow independent estimation. The methodology is illustrated using published and new meta-analysis results in market-response and diffusion-of-innovation models.

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