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Log Odds and the Interpretation of Logit Models
Author(s) -
Norton Edward C.,
Dowd Bryan E.
Publication year - 2018
Publication title -
health services research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.706
H-Index - 121
eISSN - 1475-6773
pISSN - 0017-9124
DOI - 10.1111/1475-6773.12712
Subject(s) - odds , logit , odds ratio , statistics , logistic regression , econometrics , standard error , standard deviation , term (time) , diagnostic odds ratio , interpretation (philosophy) , mathematics , computer science , confidence interval , physics , quantum mechanics , programming language
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.