PROC MIXED

Uses REML, and Newton-Rhapson, first iteration uses Fisher scoring.

Syntax

PROC MIXED (options); CLASS ... MODEL ... RANDOM ... REPEATED ... LSMEANS...

Convergence

Check model has converged, and criterion is close to 0. If -2 Res Log Like value is very large and negative, likely that covariance matrix is singular: results will be invalid, respecify model omitting random effects. If Hessian matrix not positive definite, may have reached local maxima and will need to try grid search

Asymptotic covariance matrix of estimates

Gives rough indication of correlation between variance components. Only asymptotically normal and only accurate with large DF. Using empirical option gives empirical estimates instead.

MODEL statement

MODEL dependent = fixed effects / options Use . for interactions. Need to define non-linear terms in DATA statement.

Useful options:

• DDFM = satterthwaite, use Satterthwaite approximation for
• calculating degrees of freedom
• SOLUTION, output fixed effects estimates
• CL, give confidence intervals for fixed effect estimates

Random statement

Used to specify random effects/coefficients $\mathbf{\beta}$ , and form of variance matrix $\mathbf{G}$ .

RANDOM random effects / options

Useful options:

• SOLUTION: print random effects solution
• G: print $\mathbf{G}$ matrix
• V: print $\mathbf{V}$ matrix
• GROUP = effect: estimate separate $\mathbf{G}$ matrix for
• each group
• SUBJECT = blocking effect TYPE = covariance pattern: specify
• block diagonal form for $\mathbf{G}$ matrix (eg. for random coefficients
• model: SUBJECT=patient TYPE=UN)

REPEATED statement

Specifies correlation structure of residual matrix $\mathbf{R}$ , used for covariance pattern models.

REPATED repeated effect / SUBJECT = blocking effect TYPE = pattern options

Covariance types:

• UN: unrestricted
• TOEP: toeplitz
• AR(1): first-order autoregressive
• CS: compound symmetry
• SP (sptype): spatial structure based on Euclidean distance
• function

Useful options:

• GROUP: estimate separate covariance pattern for each group
• R = subjects: print $\mathbf{R}$ matrix for subjects
• RCORR = subjects: print correlation matrix

When REPEATED statement is used alone, the residual DF is incorrect for between patient comparisons of fixed effects. If compound symmetry structure required, can fit subjects (nested in treatment) as RANDOM effects.

LSMEANS statement

Calculates least squares mean estimates of specified fixed effects. LSMEANS fixed effects / options

Useful options:

• CL: give confidence intervals
• DIFF: print difference estimates
• PDIFF: prints p-values for difference estimates