Restricted maximum likelihood
Topic of Random intercepts, part of Correlated data
Restricted maximum likelihood
| Type | Topic |
| Taught in | Random intercepts |
| Part | Correlated data |
| Questions using it | 1 |
REML estimates variance components from the likelihood of contrasts that do not involve the fixed effects. It corrects the downward bias of maximum likelihood for variances, as the divisor n-1 does for a sample variance, and it is the default for linear mixed models.
In Random intercepts
From Random intercepts
The estimation, for a normal mixed model, is not the closed form \hat{\boldsymbol{\beta}}=({\color{blue}\boldsymbol{X}}^\top{\color{blue}\boldsymbol{X}})^{-1}{\color{blue}\boldsymbol{X}}^\top{\boldsymbol{y}}, because the covariance is not a multiple of the identity and it depends on variance parameters that themselves depend on \boldsymbol{\beta}. Restricted maximum likelihood, which removes the fixed mean before estimating the variances, is the stable version of that loop. The next chapter is the one in which we fit the model and read the variances.
Used in
- Taught in Random intercepts
- Also used in Random slopes, and a binary mixed model
- Questions that use it (1) — Question 22 (answer)
- All 1 questions on Random intercepts
See also
Variance · Likelihood function · Fixed and random effects · Maximum likelihood · Linear mixed model · Random intercept model · Intraclass correlation · Repeated measures