Saturated model
Topic of Paired comparisons, and how far a fit is from the data, part of Generalised linear models
Saturated model
| Type | Topic |
| Taught in | Paired comparisons, and how far a fit is from the data |
| Part | Generalised linear models |
| Questions using it | 3 |
A model with one parameter per observation, so that its fitted means equal the data. It fits perfectly and predicts nothing; the deviance of any other model is measured from it.
In Paired comparisons, and how far a fit is from the data
McCullagh and Nelder’s sentence is the right one: fitting a model replaces the data y_1,\ldots,y_n by fitted means \hat\mu_1,\ldots,\hat\mu_n that depend on fewer parameters than there are observations. A model with n parameters can repeat the sample exactly and then cannot predict anything else. The saturated fit is the baseline you compare with, not the fit you report.
Used in
- Taught in Paired comparisons, and how far a fit is from the data
- Also used in Logistic regression · Ensembles, random forests, and boosting
- Questions that use it (3) — Q34 (answer) · Question 19 (answer) · C29
- All 4 questions on Paired comparisons, and how far a fit is from the data
See also
Deviance · Residual deviance · Null deviance · Scaled deviance · Deviance residual · Bradley–Terry model · Three links, one cholesterol slope · Analysis of deviance · Residuals in a GLM