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

Key takeaways

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Reading notes

Imported on 2024-05-07 21:16

⭐ Important

• & nlike 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 (p. 332)
• & Although marginal effects are gaining popularity over odds ratios, they do not necessarily align with much sociological research in which relative inequality is a key concept (e.g., in stratification research, political sociology, medical sociology, or demography). Indeed, many sociologists still prefer the odds ratio precisely because it is a relative measure and because it is insensitive to the marginal distribution of the dependent variable (Mare 1981; Erikson and Goldthorpe 1992). (p. 333)
• & In contrast, the magnitude of a marginal effect depends on the distribution of the binary outcome (Mare 1981:76; Holm, Ejrnæs, and Karlson 2015), a property that makes it difficult to directly compare effect sizes among, say, populations with different overall outcome rates (p. 333)
• & Marginal and conditional odds ratios are equally valid estimands, and their respective uses should depend on the research question. However, from a mathematical perspective, the difference between them arises from what statisticians call noncollapsibility: “Noncollapsibility of the OR [odds ratio] derives from the fact that when the expected probability of outcome is modeled as a nonlinear function of the exposure, the marginal effect cannot be expressed as a weighted average of the conditional effects” (Pang et al. 2016:1926). (p. 335)
• & Because MOR and COR both are valid estimands, there is no a priori argument for choosing one over the other. However, although we agree with the general point that the choice of estimand should depend on the research question, for most practical purposes we find that the MOR estimand is superior to COR estimands. (p. 336)
• & First, the MOR has an interpretation equivalent to an average marginal effect on the probability scale: it is a population-averaged effect focusing on the average “population response” to a treatment of interest. (p. 336)
• & increasing reporting of average marginal effects in sociological research, the MOR presents itself as a notable alternative or complement to the reporting of AMEs. (p. 336)
• & because MORs are unaffected by noncollapsibility, they can be used for comparing coefficients from same-sample models including different covariates (i.e., for mediation analyses or effect decompositions (p. 336)
• & ORs are straightforward to compare across different studies or populations as their magnitude does not depend in arbitrary ways on the conditioning set (p. 336)