Jann, Ben; Karlson, Kristian Bernt (2023). Estimation of marginal odds ratios (University of Bern Social Sciences Working Papers 44). Bern: University of Bern, Department of Social Sciences
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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.
Item Type: |
Working Paper |
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Division/Institute: |
03 Faculty of Business, Economics and Social Sciences > Social Sciences > Institute of Sociology |
UniBE Contributor: |
Jann, Ben |
Subjects: |
300 Social sciences, sociology & anthropology |
Series: |
University of Bern Social Sciences Working Papers |
Publisher: |
University of Bern, Department of Social Sciences |
Language: |
English |
Submitter: |
Ben Jann |
Date Deposited: |
11 Jan 2023 12:23 |
Last Modified: |
31 Jan 2023 15:21 |
JEL Classification: |
C01, C25, C87 |
BORIS DOI: |
10.48350/176998 |
URI: |
https://boris.unibe.ch/id/eprint/176998 |
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