Log Odds and the Interpretation of Logit Models

Key takeaways

(file:///C:\Users\scott\Downloads\HESR-53-859.pdf)

Bibliography: Norton, E.C., Dowd, B.E., 2018. Log Odds and the Interpretation of Logit Models. Health Serv Res 53, 859–878. https://doi.org/10.1111/1475-6773.12712

Authors:: Edward C. Norton, Bryan E. Dowd

Collections:: To Read

First-page: 859

Abstract

Objective. We discuss how to interpret coefficients from logit models, focusing on the importance of the standard deviation (r) of the error term to that interpretation. Study Design. We show how odds ratios are computed, how they depend on the standard deviation (r) of the error term, and their sensitivity to different model specifications. We also discuss alternatives to odds ratios. Principal Findings. There is no single odds ratio; instead, any estimated odds ratio is conditional on the data and the model specification. Odds ratios should not be compared across different studies using different samples from different populations. Nor should they be compared across models with different sets of explanatory variables. Conclusions. To communicate information regarding the effect of explanatory variables on binary {0,1} dependent variables, average marginal effects are generally preferable to odds ratios, unless the data are from a case–control study.

Citations

content: "@nortonLogOddsInterpretation2018" -file:@nortonLogOddsInterpretation2018

Reading notes

Imported on 2024-05-07 21:17

⭐ Important

& Researchers often struggle with how to estimate a model with a binary {0,1} dependent variable and present the results in a meaningful way. (p. 859)
& More recent critiques have identified a more serious problem with odds ratios. Allison (1999) explained why odds ratios cannot be compared across samples. Mood (2010) extended this work nicely to show that odds ratios cannot be interpreted as absolute effects, nor can they be compared across models or across groups within models (p. 860)
& An odds ratio estimated from a multivariate logit model is conditional on the sample and on the model specification (Allison 1999; Mood 2010). A study that aims or claims to estimate the odds ratio, even in a single dataset, is misguided. (p. 865)
& Third, it is not possible to compare odds ratios from different studies that use different datasets or even subpopulations within the same dataset, even if Interpretation of Logit Models 86 (p. 865)
& they have the same model specification (Allison 1999; Mood 2010) (p. 866)
& One popular alternative to the odds ratio is the marginal or incremental effect (sometimes these are called partial effects) of an explanatory variable on the probability that yi equals 1 versus 0. (p. 867)
& The marginal effect is less sensitive to changes in the model specification than the odds ratio. First, this has been proved rigorously for the case of independent omitted variables for the logit, probit, and multinomial logit models (Lee 1982; Yatchew and Griliches 1985; Wooldridge 2010). (p. 867)
& Second, unlike the odds ratio, the change in the marginal effect (ME) with respect to a change in sigma has parts that can be either positive or negative, depending on the baseline probability where the change is evaluated. (p. 867)
& The researcher should report the magnitude of the results that best answers the research question (p. 873)