IDEAS home Printed from https://ideas.repec.org/a/spr/pharme/v33y2015i1p25-30.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s40273-014-0210-6
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s40273-014-0210-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. repec:zbw:rwidps:0039 is not listed on IDEAS
    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. Krinsky, Itzhak & Robb, A Leslie, 1990. "On Approximating the Statistical Properties of Elasticities: A Correction," The Review of Economics and Statistics, MIT Press, vol. 72(1), pages 189-190, February.
    5. 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.
    6. 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.
    7. Colin Vance, 2006. "Marginal Effects and Significance Testing with Heckman’s Sample Selection Model: A Methodological Note," RWI Discussion Papers 0039, Rheinisch-Westfälisches Institut für Wirtschaftsforschung.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Claudia T. Matthaeus-Kraemer & Norman Rose & Melissa Spoden & Mathias W. Pletz & Konrad Reinhart & Carolin Fleischmann-Struzek, 2023. "Urban–Rural Disparities in Case Fatality of Community-Acquired Sepsis in Germany: A Retrospective Cohort Study," IJERPH, MDPI, vol. 20(10), pages 1-12, May.
    2. 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.
    3. Aman Pushp & Rahul Singh Gautam & Vikas Tripathi & Jagjeevan Kanoujiya & Shailesh Rastogi & Venkata Mrudula Bhimavarapu & Neha Parashar, 2023. "Impact of Financial Inclusion on India’s Economic Development under the Moderating Effect of Internet Subscribers," JRFM, MDPI, vol. 16(5), pages 1-15, May.
    4. Sara Burcham & Wei-Wen Hsu & Sharon L. Larson & Jack Rubinstein & Susan M. Pinney, 2025. "Residential Proximity, Duration, and Health-Related Quality of Life: Insights from the Fernald Cohort," IJERPH, MDPI, vol. 22(5), pages 1-24, May.
    5. 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.
    6. 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.
    7. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yujin Jeong & Jordan I. Siegel & Sophie Yu‐Pu Chen & Whitney K. Newey, 2020. "A recentering approach for interpreting interaction effects from logit, probit, and other nonlinear models," Strategic Management Journal, Wiley Blackwell, vol. 41(11), pages 2072-2091, November.
    2. Zhang, Xumin & Khachatryan, Hayk, 2021. "Effects of perceived economic contributions on individual preferences for environmentally friendly residential landscapes," Land Use Policy, Elsevier, vol. 101(C).
    3. Zhifeng Gao & Ted C. Schroeder, 2009. "Consumer responses to new food quality information: are some consumers more sensitive than others?," Agricultural Economics, International Association of Agricultural Economists, vol. 40(3), pages 339-346, May.
    4. Ortega, David L. & Wang, H. Holly & Wu, Laping & Hong, Soo Jeong, 2015. "Retail channel and consumer demand for food quality in China," China Economic Review, Elsevier, vol. 36(C), pages 359-366.
    5. Chaikaew, Pasicha & Hodges, Alan W. & Grunwald, Sabine, 2017. "Estimating the value of ecosystem services in a mixed-use watershed: A choice experiment approach," Ecosystem Services, Elsevier, vol. 23(C), pages 228-237.
    6. Zawojska, Ewa & Czajkowski, Mikotaj, 2017. "Are preferences stated in web vs. personal interviews different? A comparison of willingness to pay results for a large multi-country study of the Baltic Sea eutrophication reduction," Annual Meeting, 2017, June 18-21, Montreal, Canada 258604, Canadian Agricultural Economics Society.
    7. Brox, James A. & Fader, Christina, 1996. "Production elasticity differences between just-in-time and non-just-in-time users in the automotive parts industry," The North American Journal of Economics and Finance, Elsevier, vol. 7(1), pages 77-90.
    8. Otrachshenko, Vladimir & Tyurina, Elena & Nagapetyan, Artur, 2022. "The economic value of the Glass Beach: Contingent valuation and life satisfaction approaches," Ecological Economics, Elsevier, vol. 198(C).
    9. Khan, Mohammed Tajuddin & Kishore, Avinash & Joshi, Pramod K., 2016. "Gender dimensions on farmers’ preferences for direct-seeded rice with drum seeder in India," IFPRI discussion papers 1550, International Food Policy Research Institute (IFPRI).
    10. Scaccia, Luisa & Marcucci, Edoardo & Gatta, Valerio, 2023. "Prediction and confidence intervals of willingness-to-pay for mixed logit models," Transportation Research Part B: Methodological, Elsevier, vol. 167(C), pages 54-78.
    11. Greene, William, 2007. "Functional Form and Heterogeneity in Models for Count Data," Foundations and Trends(R) in Econometrics, now publishers, vol. 1(2), pages 113-218, August.
    12. Joachim Marti, 2012. "Assessing preferences for improved smoking cessation medications: a discrete choice experiment," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 13(5), pages 533-548, October.
    13. Torres, Marcelo de O. & Felthoven, Ronald G., 2014. "Productivity growth and product choice in catch share fisheries: The case of Alaska pollock," Marine Policy, Elsevier, vol. 50(PA), pages 280-289.
    14. Glaser, Lewrene K. & Thompson, Gary D., 2000. "Demand For Organic And Conventional Beverage Milk," 2000 Annual Meeting, June 29-July 1, 2000, Vancouver, British Columbia 36346, Western Agricultural Economics Association.
    15. Cheng, Haotian & Zhang, Tong & Lambert, Dayton M. & Feuz, Ryan, 2023. "An empirical comparison of conjoint and best-worst scaling case III methods," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 106(C).
    16. Jakus, Paul M. & Dowell, Paula & Murray, Matthew N., 2000. "The Effect Of Fluctuating Water Levels On Reservoir Fishing," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 25(2), pages 1-13, December.
    17. Kallas, Z. & Gómez-Limón, J.A., 2007. "Valoración De La Multifuncionalidad Agraria: Una Aplicación A Través Del Método De Los Experimentos De Elección/Agricultural Multifunctionality Valuation: A Case Study Using The Choice Experiment," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 25, pages 107-144, Abril.
    18. Kerstin K Zander & Gillian B Ainsworth & Jürgen Meyerhoff & Stephen T Garnett, 2014. "Threatened Bird Valuation in Australia," PLOS ONE, Public Library of Science, vol. 9(6), pages 1-9, June.
    19. Concu, Giovanni B., 2007. "Investigating distance effects on environmental values: a choice modelling approach," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 51(2), pages 1-20.
    20. Sheng Gong & Jason.S. Bergtold & Elizabeth Yeager, 2021. "Assessing the joint adoption and complementarity between in-field conservation practices of Kansas farmers," Agricultural and Food Economics, Springer;Italian Society of Agricultural Economics (SIDEA), vol. 9(1), pages 1-24, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:pharme:v:33:y:2015:i:1:p:25-30. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.