Odds
Topic of Introduction to generalised linear models, part of Generalised linear models
Odds
| Type | Topic |
| Taught in | Introduction to generalised linear models |
| Part | Generalised linear models |
| Questions using it | 22 |
The ratio p/(1-p) of the probability of an event to the probability that it does not happen. Probability 0.8 is odds 4. Logistic regression models the log-odds as a linear function of the covariates.
In Introduction to generalised linear models
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 Bayesian hypotheses and model comparison · Standard errors, and models for counts · Categorical responses · Paired comparisons, and how far a fit is from the data · Smooth means · Additive smooths · Model selection for stochastic models · Statistical classifiers and discriminant analysis · Logistic regression · Ensembles, random forests, and boosting · Random slopes, and a binary mixed model · Marginal models, and two responses at once · Three species on one hillside
- Questions that use it (22) — An IQ threshold · Posterior odds (answer) · Odds ratios (answer) · A logistic rule in an unfamiliar setting (answer) · Q11 · Q21 · Q29 · Q35 (answer) · Q38 (answer) · Q40 (answer) · Q46 (answer) · Q53 (answer) · Q59 (answer) · Question 8 (answer) · Question 15 (answer) · Question 18 (answer) · Question 20 (answer) · Question 21 (answer) · C8 · C20 · C25 (answer) · C26 (answer)
- All 9 questions on Introduction to generalised linear models
See also
Interpreting a logistic regression · Logit link · Explanatory variable · Odds ratio · Proportional-odds model · Exponential family · Mean and variance of an exponential family · Generalised linear model