PROC HPMIXED: RANDOM Statement :: SAS/STAT(R) 9.2 User's Guide, Second Edition

The HPMIXED Procedure

RANDOM Statement

RANDOM random-effects </ options> ;

The RANDOM statement defines the random effects in the mixed model. It can be used to specify traditional variance component models (as in the VARCOMP procedure) and to specify random coefficients. The random effects can be classification or continuous. Multiple RANDOM statements are possible. Random effects specified in a RANDOM statement could be correlated with each other for certain types of covariance structures (see the TYPE= option). It is, however, assumed that random effects specified using different RANDOM statements are not correlated.

Using notation from the section Model Assumptions, the purpose of the RANDOM statement is to define the $\text{[math]}$ matrix of the mixed model, the random effects in the $\text{[math]}$ vector, and the structure of $\text{[math]}$ . The $\text{[math]}$ matrix is constructed exactly like the $\text{[math]}$ matrix for the fixed effects, and the $\text{[math]}$ matrix is constructed to correspond to the effects constituting $\text{[math]}$ . The structure of $\text{[math]}$ is defined by using the TYPE= option.

You can specify INTERCEPT (or INT) as a random effect. PROC HPMIXED does not include the intercept in the RANDOM statement by default, as it does in the MODEL statement.

You can specify the following options in the RANDOM statement after a slash (/).

ALPHA=number

requests that a t-type confidence interval with confidence level $\text{[math]}$ be constructed for the predictors of random effects in this statement. The value of number must be between 0 and 1 exclusively; the default is 0.05. Specifying the ALPHA= option implies the CL option.

CL

requests that t-type confidence limits be constructed for each of the predictors of random effects in this statement. The confidence level is 0.95 by default; this can be changed with the ALPHA= option. The CL option implies the SOLUTION option.

GROUP=effect

defines an effect specifying heterogeneity in the covariance structure of $\text{[math]}$ . All observations having the same level of the group effect have the same covariance parameters. Each new level of the group effect produces a new set of covariance parameters with the same structure as the original group. You should exercise caution in defining the group effect, because strange covariance patterns can result from its misuse. Also, the group effect can greatly increase the number of estimated covariance parameters, which can adversely affect the optimization process.

Continuous variables are permitted as arguments to the GROUP= option. PROC HPMIXED does not sort by the values of the continuous variable; rather, it considers the data to be from a new group whenever the value of the continuous variable changes from the previous observation. Using a continuous variable decreases execution time for models with a large number of groups and also prevents the production of a large "Class Levels Information" table.

NOFULLZ

eliminates the columns in $\text{[math]}$ corresponding to missing levels of random effects involving CLASS variables. By default, these columns are included in $\text{[math]}$ . It is sufficient to specify the NOFULLZ option in any RANDOM statement.

SOLUTION

requests that the solution for the random-effects parameters be produced. Using notation from the section Model Assumptions, these estimates are the empirical best linear unbiased predictors (BLUPs) $\text{[math]}$ . They can be useful for comparing the random effects from different experimental units and can also be treated as residuals in performing diagnostics for your mixed model.

The numbers displayed in the SE Pred column of the "Solution for Random Effects" table are not the standard errors of the $\text{[math]}$ displayed in the Estimate column; rather, they are the standard errors of predictions $\text{[math]}$ , where $\text{[math]}$ is the ith BLUP and $\text{[math]}$ is the ith random-effect parameter.

SUBJECT=effect

identifies the subjects in your mixed model. Complete independence is assumed across subjects; thus, for the RANDOM statement, the SUBJECT= option produces a block-diagonal structure in $\text{[math]}$ with identical blocks. The $\text{[math]}$ matrix is modified to accommodate this block-diagonality. In fact, specifying a subject effect is equivalent to nesting all other effects in the RANDOM statement within the subject effect.

Continuous variables are permitted as arguments to the SUBJECT= option. PROC HPMIXED does not sort by the values of the continuous variable; rather, it considers the data to be from a new subject whenever the value of the continuous variable changes from the previous observation. Using a continuous variable decreases execution time for models with a large number of subjects and also prevents the production of a large "Class Levels Information" table.

TYPE=covariance-structure

specifies the covariance structure of $\text{[math]}$ for G-side effects.

The TYPE=VC (variance components) option is the default structure. Another structure available in this experimental release is CHOL.

Note: This procedure is experimental.

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