Restricted maximum likelihood estimates covariance matrix parameters from linear combinations of the data whose distribution does not involve the fixed mean coefficients. It differs from a restricted maximum-likelihood estimator obtained by maximizing an ordinary likelihood function under a null hypothesis.
For and a full-column-rank design matrix , take with and . Then , so restricted maximum likelihood maximizesChanging the orthonormal basis by an orthogonal matrix leaves this expression unchanged.
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Restricted Maximum Likelihood (REML) is a statistical technique used primarily in the estimation of variance components in mixed models. It is particularly useful in the context of linear mixed-effects models, where researchers are interested in both fixed effects and random effects. ### Key Features of REML: 1. **Variance Component Estimation**: REML is mainly used to estimate variance components associated with random effects. This is important when distinguishing between the effects of different sources of variability in the data.