Restricted Maximum Likelihood

Question

Why don't we use restricted maximum likelihood to estimate parameters in non-mixed models?

You use it: REML is for estimating variance parameters, and in non-mixed models there is only one such, $\sigma^2$. When dividing by $n-1$ to get a variance estimate, you are using REML. See http://stats.stackexchange.com/questions/48671/what-is-restricted-maximum-likelihood-and-when-should-it-be-used — kjetil b halvorsen, May 04 '15 at 17:02

score 3 · Accepted Answer · answered May 04 '15 at 17:54

For REML under fixed effects the variance estimator equivalent to $S^2=\frac{\sum_{i=1}^n (y_i - x_i \hat{\beta})^2}{n-p}$ where $\hat{\beta}$ is the OLS estimator, but as a bonus with OLS you also get to use Gauss-Markov Theorem for $\hat{\beta}$.

With REML you don't get any coefficient estimates.

Restricted Maximum Likelihood

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