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Combining Related and Sparse Data in Linear Regression Models

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  • Vanhonacker, Wilfried R
  • Lehmann, Donald R
  • Sultan, Fareena

Abstract

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 (1) the design or data matrix is not of full rank or (2) 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.

Suggested Citation

  • Vanhonacker, Wilfried R & Lehmann, Donald R & Sultan, Fareena, 1990. "Combining Related and Sparse Data in Linear Regression Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(3), pages 327-335, July.
    • Handle: RePEc:bes:jnlbes:v:8:y:1990:i:3:p:327-35
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    Cited by:

    1. Kremer, Sara T.M. & Bijmolt, Tammo H.A. & Leeflang, Peter S.H. & Wieringa, Jaap E., 2008. "Generalizations on the effectiveness of pharmaceutical promotional expenditures," International Journal of Research in Marketing, Elsevier, vol. 25(4), pages 234-246.
    2. Jonathan Lee & Peter Boatwright & Wagner A. Kamakura, 2003. "A Bayesian Model for Prelaunch Sales Forecasting of Recorded Music," Management Science, INFORMS, vol. 49(2), pages 179-196, February.
    3. T. D. Stanley, 1998. "New Wine in Old Bottles: A Meta‐Analysis of Ricardian Equivalence," Southern Economic Journal, John Wiley & Sons, vol. 64(3), pages 713-727, January.
    4. Stanley, T. D., 2000. "An empirical critique of the Lucas critique," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 29(1), pages 91-107.
    5. Raymond J.G.M. Florax & Henri L.F. de Groot & Ruud A. de Mooij, 2002. "Meta-analysis: A Tool for Upgrading Inputs of Macroeconomic Policy Models," Tinbergen Institute Discussion Papers 02-041/3, Tinbergen Institute.

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