Interpreting a logistic regression
Section of Introduction to generalised linear models, part of Generalised linear models
Interpreting a logistic regression
| Type | Section |
| Taught in | Introduction to generalised linear models |
| Part | Generalised linear models |
| Questions using it | 1 |
Two covariates are enough. If you can say what \beta_1 and \beta_2 mean here, you can say it for twenty: \log\frac{p}{1-p}=\beta_0+\beta_1 x_1+\beta_2 x_2. Hold x_2 fixed and increase x_1 by one unit. The log-odds increase by \beta_1. Equivalently, the odds p/(1-p) are multiplied by e^{\beta_1}. The same sentence with the labels swapped is the interpretation of \beta_2. Log-odds are not a quantity anyone should be expected to feel. Odds are usually as far as a collaborator needs to go: “the odds of disease are multiplied by e^{\beta_1}.”
The intercept is the log-odds when every covariate is zero, and p=\frac{e^{\beta_0}}{1+e^{\beta_0}} is the corresponding probability. That baseline is meaningful only when setting every covariate to zero is a real, or at least a hypothetical, situation. Otherwise it is an algebraically correct description of a point off the edge of the data.
Used in
- Taught in Introduction to generalised linear models
- Also used in Categorical responses · Smooth means · Logistic regression · Neural units · High-dimensional analysis · Three species on one hillside
- Questions that use it (1) — Question 21
- All 9 questions on Introduction to generalised linear models
See also
Binary logistic regression · Logit link · Odds ratio · Heart-failure data · Odds · Exponential family · Mean and variance of an exponential family · Generalised linear model