Working correlation
Topic of Marginal models, and two responses at once, part of Correlated data
Working correlation
| Type | Topic |
| Taught in | Marginal models, and two responses at once |
| Part | Correlated data |
| Questions using it | 2 |
The correlation structure assumed within a cluster when fitting generalised estimating equations, such as independence or exchangeable. It need not be correct: the sandwich variance protects the standard errors, though a closer working correlation gives more efficient estimates.
In Marginal models, and two responses at once
That is the attraction. We specify a mean that has an interpretation as a population average, a variance that depends on that mean, and a working association within each cluster. The working association does not have to be right. After the fit, a sandwich estimator replaces the model-based variance of \hat{\boldsymbol{\beta}} by one that uses the empirical residuals. If the mean is correctly specified, \hat{\boldsymbol{\beta}} is consistent, and so is the sandwich variance, even when the working correlation is wrong. The rate depends on how wrong it was. The guarantee is asymptotic in the number of clusters and, in the theory, in the size of each cluster. A handful of clusters, or one cluster with almost all the data, is not a setting in which the robust column should be trusted blindly.
Used in
- Taught in Marginal models, and two responses at once
- Also used in Three species on one hillside
- Questions that use it (2) — C39 · C40 (answer)
- All 6 questions on Marginal models, and two responses at once
See also
Generalised estimating equations · Marginal model · Sandwich estimator · Correlation · Exchangeability · Standard error · Marginal and conditional effects · Warp-breaks data