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A Primer on Marginal Effects—Part I: Theory and Formulae

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  • Eberechukwu Onukwugha
  • Jason Bergtold
  • Rahul Jain

Abstract

Marginal analysis evaluates changes in an objective function associated with a unit change in a relevant variable. The primary statistic of marginal analysis is the marginal effect (ME). The ME facilitates the examination of outcomes for defined patient profiles while measuring the change in original units (e.g., costs, probabilities). The ME has a long history in economics; however, it is not widely used in health services research despite its flexibility and ability to provide unique insights. This paper, the first in a two-part series, introduces and illustrates the calculation of the ME for a variety of regression models often used in health services research. Part One includes a review of prior studies discussing MEs, followed by derivation of ME formulas for various regression models including linear, logistic, multinomial logit model (MLM), generalized linear model (GLM) for continuous data, GLM for count data, two-part model, sample selection (two-stage) model, and parametric survival model. Prior theoretical papers in health services research reported the derivation and interpretation of ME primarily for the linear and logistic models, with less emphasis on count models, survival models, MLM, two-part models, and sample selection models. These additional models are relevant for health services research studies examining costs and utilization. Part Two of the series will focus on the methods for estimating and interpreting the ME in applied research. The illustration, discussion, and application of ME in this two-part series support the conduct of future studies applying the marginal concept. Copyright Springer International Publishing Switzerland 2015

Suggested Citation

  • Eberechukwu Onukwugha & Jason Bergtold & Rahul Jain, 2015. "A Primer on Marginal Effects—Part I: Theory and Formulae," PharmacoEconomics, Springer, vol. 33(1), pages 25-30, January.
  • Handle: RePEc:spr:pharme:v:33:y:2015:i:1:p:25-30
    DOI: 10.1007/s40273-014-0210-6
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    References listed on IDEAS

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    2. Anderson, Soren & Newell, Richard G., 2003. "Simplified marginal effects in discrete choice models," Economics Letters, Elsevier, vol. 81(3), pages 321-326, December.
    3. Ai, Chunrong & Norton, Edward C., 2003. "Interaction terms in logit and probit models," Economics Letters, Elsevier, vol. 80(1), pages 123-129, July.
    4. K. Ishak & Noemi Kreif & Agnes Benedict & Noemi Muszbek, 2013. "Overview of Parametric Survival Analysis for Health-Economic Applications," PharmacoEconomics, Springer, vol. 31(8), pages 663-675, August.
    5. Krinsky, Itzhak & Robb, A Leslie, 1986. "On Approximating the Statistical Properties of Elasticities," The Review of Economics and Statistics, MIT Press, vol. 68(4), pages 715-719, November.
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    2. Ana Claudia Sant'Anna & Jason S. Bergtold & Aleksan Shanoyan & Gabriel Granco & Marcellus M. Caldas, 2018. "Examining the relationship between vertical coordination strategies and technical efficiency: Evidence from the Brazilian ethanol industry," Agribusiness, John Wiley & Sons, Ltd., vol. 34(4), pages 793-812, October.
    3. Ajax Persaud & Javid Zare, 2023. "Institutional varieties, governance quality, and firm‐level innovation in emerging economies: Case of India," Growth and Change, Wiley Blackwell, vol. 54(1), pages 234-259, March.
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    5. Bergtold, Jason S. & Ramsey, Steven M., 2015. "Neural Network Estimators of Binary Choice Processes: Estimation, Marginal Effects and WTP," 2015 AAEA & WAEA Joint Annual Meeting, July 26-28, San Francisco, California 205649, Agricultural and Applied Economics Association.
    6. Jason S. Bergtold & Elizabeth A. Yeager & Allen M. Featherstone, 2018. "Inferences from logistic regression models in the presence of small samples, rare events, nonlinearity, and multicollinearity with observational data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(3), pages 528-546, February.

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