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Log Odds and the Interpretation of Logit Models
Edward C Norton1,2, Bryan E Dowd3
1Department of Health Management and Policy, Department of Economics, University of Michigan, Ann Arbor, MI.
Health Services Research
|June 1, 2017
Summary
Interpreting logit model coefficients requires understanding the error term's standard deviation. Odds ratios are conditional and vary with data and model specification, making average marginal effects often preferable.
Area of Science:
- Statistics
- Biostatistics
- Econometrics
Background:
- Logit models are widely used for binary outcomes.
- Interpretation of coefficients, particularly odds ratios, can be complex.
- The standard deviation of the error term influences coefficient interpretation.
Purpose of the Study:
- To clarify the interpretation of coefficients in logit models.
- To examine the dependence of odds ratios on the error term's standard deviation and model specification.
- To discuss alternatives to odds ratios for reporting results.
Main Methods:
- Analysis of logit model coefficient interpretation.
- Demonstration of odds ratio computation and its dependency on standard deviation (σ).
- Evaluation of odds ratio sensitivity to varying model specifications.
Main Results:
- Odds ratios are not absolute; they are conditional on data and model.
- Comparison of odds ratios across different studies or models is unreliable.
- The standard deviation (σ) of the error term is crucial for accurate interpretation.
Conclusions:
- Average marginal effects are generally superior to odds ratios for reporting variable effects on binary outcomes.
- Odds ratios may be appropriate in specific contexts, such as case-control studies.
- Careful consideration of model specification is essential when using odds ratios.
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