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. 2018 Apr;53(2):859-878.
doi: 10.1111/1475-6773.12712. Epub 2017 May 30.

Log Odds and the Interpretation of Logit Models

Edward C Norton  1   2 , Bryan E Dowd  3
Affiliations

Log Odds and the Interpretation of Logit Models

Edward C Norton et al. Health Serv Res. 2018 Apr.

Abstract

Objective: We discuss how to interpret coefficients from logit models, focusing on the importance of the standard deviation (σ) of the error term to that interpretation.

Study design: We show how odds ratios are computed, how they depend on the standard deviation (σ) 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.

Keywords: Logit; marginal effects; odds ratio; probit; risk ratio.

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Figures

Figure 1
Figure 1
Scaled Response Functions for Logit, Probit, LPM [Color figure can be viewed at wileyonlinelibrary.com]
Figure 2
Figure 2
Conditional Marginal Effects of Age with 95% CIs [Color figure can be viewed at wileyonlinelibrary.com]
Figure 3
Figure 3
Marginal Effects as a Function of P and Log Odds (β/σ) [Color figure can be viewed at wileyonlinelibrary.com]
Figure 4
Figure 4
Log Odds as a Function of P and Marginal Effects [Color figure can be viewed at wileyonlinelibrary.com]
See this image and copyright information in PMC

References

    1. Ai, C. , and Norton E. C.. 2003. “Interaction Terms in Logit and Probit Models.” Economics Letters 80 (1): 123–9.
    1. Allison, P. D. 1999. “Comparing Logit and Probit Coefficients across Groups.” Sociological Methods and Research 28 (2): 186–208.
    1. Altman, D. G. , Deeks J. J., and Sackett D. L.. 1998. “Odds Ratios Should Be Avoided When Events Are Common.” British Medical Journal 317 (7168): 1318. - PMC - PubMed
    1. Angrist, J. D. 2001. “Estimation of Limited Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice.” Journal of Business and Economic Statistics 19 (1): 2–28.
    1. Ben‐Akiva, M. , and Morikawa T.. 1990. “Estimation of Switching Models from Revealed Preferences and Stated Intentions.” Transportation Research A 24 (6): 485–95.

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