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Marginal Odds Ratios: What They Are, How to Compute Them, and Why Sociologists Might Want to Use Them

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  • Karlson, Kristian Bernt

  • Ben Jann

Abstract

As sociologists are increasingly turning away from using odds ratios, reporting average marginal effects is becoming more popular. We aim to restore the use of odds ratios in sociological research by introducing marginal odds ratios. Unlike conventional odds ratios, marginal odds ratios are not affected by omitted covariates in arbitrary ways. Marginal odds ratios thus behave like average marginal effects but retain the relative effect interpretation of the odds ratio. We argue that marginal odds ratios are well suited for much sociological inquiry and should be reported as a complement to the reporting of average marginal effects. We define marginal odds ratios in terms of potential outcomes, show their close relationship to average marginal effects, and discuss their potential advantages over conventional odds ratios. We also briefly discuss how to estimate marginal odds ratios and present examples comparing marginal odds ratios to conventional odds ratios and average marginal effects.

Suggested Citation

  • 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.
    • Handle: RePEc:bss:wpaper:45
    DOI: 10.48350/178165
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    References listed on IDEAS

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    1. Jouni Kuha & Colin Mills, 2020. "On Group Comparisons With Logistic Regression Models," Sociological Methods & Research, , vol. 49(2), pages 498-525, May.
    2. J. S. Cramer, 2007. "Robustness of Logit Analysis: Unobserved Heterogeneity and Mis‐specified Disturbances," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 69(4), pages 545-555, August.
    3. Anders Holm & Mette Ejrnæs & Kristian Karlson, 2015. "Comparing linear probability model coefficients across groups," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(5), pages 1823-1834, September.
    4. 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.
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    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

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