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Estimation of marginal odds ratios

Author

Listed:
  • Ben Jann
  • Karlson, Kristian Bernt
Abstract
Coefficients from logistic regression are affected by noncollapsibility, which means that the comparison of coefficients across models may be misleading. Several strategies have been proposed in the literature to respond to these difficulties, the most popular of which is to report average marginal effects (on the probability scale) rather than odds ratios. Average marginal effects (AMEs) have many desirable properties but at least in part they throw the baby out with the bathwater. The size of an AME strongly depends on the marginal distribution of the dependent variable; for events that are very likely or very unlikely the AME necessarily has to be small because the probability space is bounded. Logistic regression, in contrast, estimates odds ratios which are free from such flooring and ceiling effects. Hence, odds ratios may be more appropriate than AMEs for comparison of effect sizes in many applications. Yet, logistic regression estimates conditional odds ratios, which are not comparable across different specifications. In this paper, we aim to remedy the declining popularity of the odds ratio by introducing an estimand that we term the "marginal odds ratio"; that is, logit coefficients that have properties similar to AMEs, but which retain the odds ratio interpretation. We define the marginal odds ratio theoretically in terms of potential outcomes, both for binary and continuous treatments, we develop estimation methods using three different approaches (G-computation, inverse probability weighting, RIF regression), and we present an example that illustrates the usefulness and interpretation of the marginal odds ratio.

Suggested Citation

  • Ben Jann & Karlson, Kristian Bernt, 2023. "Estimation of marginal odds ratios," University of Bern Social Sciences Working Papers 44, University of Bern, Department of Social Sciences, revised 17 Jan 2023.
    • Handle: RePEc:bss:wpaper:44
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    File URL: https://boris.unibe.ch/176998/8/jann-karlson-2023-mor.pdf
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    References listed on IDEAS

    as
    1. Sergio Firpo & Nicole M. Fortin & Thomas Lemieux, 2009. "Unconditional Quantile Regressions," Econometrica, Econometric Society, vol. 77(3), pages 953-973, May.
    2. Richard Williams, 2006. "Generalized ordered logit/partial proportional odds models for ordinal dependent variables," Stata Journal, StataCorp LP, vol. 6(1), pages 58-82, March.
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    Cited by:

    1. Karlson, Kristian Bernt & Ben Jann, 2023. "Marginal Odds Ratios: What They Are, How to Compute Them, and Why Sociologists Might Want to Use Them," University of Bern Social Sciences Working Papers 45, University of Bern, Department of Social Sciences.

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    More about this item

    Keywords

    marginal odds ratio; noncollapsibility; logistic regression; G-computation; inverse probability weighting; recentered influence functions;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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