RANDOM Subcommand (MIXED command)
The RANDOM
subcommand specifies the random effects in the mixed model.
- Depending on the covariance type specified, random
effects specified in one
RANDOM
subcommand may be correlated. - One covariance G matrix will be constructed for each
RANDOM
subcommand. The dimension of the random effect covariance G matrix is equal to the sum of the levels of all random effects in the subcommand. - When the variance components (
VC
) structure is specified, a scaled identity (ID
) structure will be assigned to each of the effects specified. This is the default covariance type for theRANDOM
subcommand. - Note that the
RANDOM
subcommand in theMIXED
procedure is different in syntax from theRANDOM
subcommand in theGLM
andVARCOMP
procedures. - Use a separate
RANDOM
subcommand when a different covariance structure is assumed for a list of random effects. If the same effect is listed on more than oneRANDOM
subcommand, it must be associated with a differentSUBJECT
combination. - Specify a list of terms to be included in the model, separated by commas or spaces.
- No random effects are included in the mixed model
unless a
RANDOM
subcommand is specified correctly. - Specify the keyword
INTERCEPT
to include the intercept as a random effect. TheMIXED
procedure does not include the intercept in theRANDOM
subcommand by default. TheINTERCEPT
term must be specified first on theRANDOM
subcommand. - To include a main-effect term, enter the name of
the factor on the
RANDOM
subcommand. - To include an interaction-effect term among factors,
use the keyword
BY
or the asterisk (*) to join factors involved in the interaction. For example,A*B*C
means a three-way interaction effect of A, B, and C, where A, B, and C are factors. The expressionA BY B BY C
is equivalent toA*B*C
. Factors inside an interaction effect must be distinct. Expressions such asA*C*A
andA*A
are invalid. - To include a nested-effect term, use the keyword
WITHIN
or a pair of parentheses on theRANDOM
subcommand. For example,A(B)
means that A is nested within B, where A and B are factors. The expressionA WITHIN B
is equivalent toA(B)
. Factors inside a nested effect must be distinct. Expressions such asA(A)
andA(B*A)
are invalid. - Multiple-level nesting is supported. For example,
A(B(C))
means that B is nested within C, and A is nested within B(C). When more than one pair of parentheses is present, each pair of parentheses must be enclosed or nested within another pair of parentheses. Thus,A(B)(C)
is invalid. - Nesting within an interaction effect is valid. For
example,
A(B*C)
means that A is nested within B*C. - Interactions among nested effects are allowed. The
correct syntax is the interaction followed by the common nested effect
inside the parentheses. For example, the interaction between A and B within levels of C should be
specified as
A*B(C)
instead ofA(C)*B(C)
. - To include a covariate term in the model, enter the
name of the covariate on the
FIXED
subcommand. - Covariates can be connected using the keyword
BY
or the asterisk (*). For example,X*X
is the product of X and itself. This is equivalent to entering a covariate whose values are the squared values of X. - Factor and covariate effects can be connected in
many ways. Suppose that A and B are factors and X and Y are covariates. Examples
of valid combinations of factor and covariate effects are
A*X
,A*B*X
,X(A)
,X(A*B)
,X*A(B)
,X*Y(A*B)
, andA*B*X*Y
. - No effects can be nested within a covariate effect.
Suppose that A and B are factors and X and Y are covariates. The effects
A(X)
,A(B*Y)
,X(Y)
, andX(B*Y)
are invalid. - The following options, which are specific for the random effects, can be entered after the
effects. Use the vertical bar (|) to precede the options.
SUBJECT(varname*varname*… ). Identify the subjects. Complete independence is assumed across subjects, thus producing a block-diagonal structure in the covariance matrix of the random effect with identical blocks. Specify a list of variable names (of any type) connected by asterisks. The number of subjects is equal to the number of distinct combinations of values of the variables. A case will not be used if it contains a missing value on any of the subject variables.
COVTYPE(type). Covariance structure. Specify the covariance structure of the identical blocks for the random effects (see Covariance Structure List (MIXED command)). The default covariance structure for random effects is
VC
.SOLUTION. Specifies to display the random-effects parameter estimates.
- If the
REPEATED
subcommand is specified, the variables in theRANDOM
subject list must be a subset of the variables in theREPEATED
subject list. - Random effects are considered independent of each other, and a separate covariance matrix is computed for each effect.
Example
MIXED SCORE BY SCHOOL CLASS
/RANDOM = INTERCEPT SCHOOL CLASS.