Estimated generalized least squares (GLS) method is the default estimation method for fixed effects in PROC MIXED. Estimation is more difficult in the mixed model than in the general linear model since, in addition to estimating β, it is also necessary to estimate γ, and parameters in the G and R matrices.

Least squares is no longer the best estimation method. Generalized least squares (GLS) is more appropriate. GLS minimizes (y-Xb)'V^-1(y-Xb). However, this requires knowledge of V and, therefore, knowledge of G and R. Lacking such information, one approach is to use estimated GLS, in which you insert some reasonable estimate for V into the minimization problem. PROC MIXED uses a likelihood-based method, such as ML or REML, to estimate G and R and therefore V.

This is further discussed in "Mixed Models Theory" in the MIXED documentation and the book SAS System for Mixed Models.

To provide your own estimate of V through the G and R matrices, use the PARMS statement and specify the PDATA= and NOITER options. Also, specify the NOPROFILE option in the PROC MIXED statement to prevent MIXED from estimating the residual variance.

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