This is methodological interpretation of aggregate model output, not an individual prediction, diagnosis, or treatment recommendation.
Field-by-field
| Field | Interpretation |
|---|---|
| Estimate β | Change in log odds for the stated predictor change |
| Standard error | Estimated uncertainty of β under the model |
| z/Wald statistic | Estimate divided by its standard error |
| p-value | Null-model tail probability for the stated coefficient test |
| exp(β) | Conditional odds ratio |
| Confidence interval | Compatible coefficient or OR values under the interval method |
| Intercept | Log odds at reference categories and numeric predictor zeros |
R’s glm documentation identifies the binomial-logit model, while summary.glm documents coefficient and deviance fields.1 Software can report profile-likelihood or Wald intervals; name the method.
Coding controls the sentence
For a binary predictor, exp(β) compares the coded category with the reference. For a continuous predictor, it compares a one-unit increase unless rescaled. For an interaction, one main coefficient is conditional on the interacting variable’s reference value.
An OR above 1 means higher modeled odds, not higher probability by the same factor. Odds-ratio interpretation covers that distinction.
Suppose β = .69, so exp(β) ≈ 2. If baseline probability is .10, doubling the odds gives probability about .18, not .20; from a baseline of .50, doubling the odds gives about .67, not 1.00. The coefficient cannot be converted to one probability change without a baseline and the rest of the model.
For continuous predictors, check whether the unit is one year, 10 points, or one standard deviation. For splines and polynomials, one exponentiated coefficient does not represent a constant OR across the range. Predicted probabilities or contrasts at stated values are often clearer.
Model-level output
Deviance, likelihood-ratio tests, information criteria, pseudo-R², discrimination, and calibration answer different questions. Linear regression output gives the continuous-outcome counterpart; AUC interpretation covers ranking performance.
Inspect separation, sparse categories, influential observations, calibration, and validation. A converged model can still be unstable; large coefficients with huge standard errors are a warning to inspect the data and estimator rather than to report an extreme OR at face value.
A defensible reporting sentence
“The adjusted coefficient was β = .59 (SE .20), corresponding to OR 1.80 (95% CI [1.21, 2.68]) for a one-unit increase, conditional on the listed covariates. This is an odds comparison, not a 1.8-fold probability.”