Overview (MIXED command)

The MIXED procedure fits a variety of mixed linear models. The mixed linear model expands the general linear model used in the GLM procedure in that the data are permitted to exhibit correlation and non-constant variability. The mixed linear model, therefore, provides the flexibility of modeling not only the means of the data but also their variances and covariances.

The MIXED procedure is also a flexible tool for fitting other models that can be formulated as mixed linear models. Such models include multilevel models, hierarchical linear models, and random coefficient models.

Important changes to MIXED compared to previous versions

Specifying how degrees of freedom are computed for significance tests. Prior to version 26, SATTERTHWAITE method was the only method available for specifying how degrees of freedom are computed for significance tests. Starting with version 26, the RESIDUAL and KENWARDROGER methods are also available for specifying how degrees of freedom are computed for significance tests.

Independence of random effects. Prior to version 11.5, random effects were assumed to be independent. If you are using MIXED syntax jobs from a version prior to 11.5, be aware that the interpretation of the covariance structure may have changed.

Default covariance structures. Prior to version 11.5, the default covariance structure for random effects was ID, and the default covariance structure for repeated effects was VC.

Interpretation of VC covariance structure. Prior to version 11.5, the variance components (VC) structure was a diagonal matrix with heterogenous variances. Now, when the variance components structure is specified on a RANDOM subcommand, a scaled identity (ID) structure is assigned to each of the effects specified on the subcommand. If the variance components structure is specified on the REPEATED subcommand, it will be replaced by the diagonal (DIAG) structure. Note that the diagonal structure has the same interpretation as the variance components structure in versions prior to 11.5.

Basic features

Covariance structures. Various structures are available. Use multiple RANDOM subcommands to model a different covariance structure for each random effect.

Standard errors. Appropriate standard errors will be automatically calculated for all hypothesis tests on the fixed effects, and specified estimable linear combinations of fixed and random effects.

Subject blocking. Complete independence can be assumed across subject blocks.

Choice of estimation method. Two estimation methods for the covariance parameters are available.

Tuning the algorithm. You can control the values of algorithm-tuning parameters with the CRITERIA subcommand.

Optional output. You can request additional output through the PRINT subcommand. The SAVE subcommand allows you to save various casewise statistics back to the active dataset.

Basic specification

  • The basic specification is a variable list identifying the dependent variable, the factors (if any) and the covariates (if any).
  • By default, MIXED adopts the model that consists of the intercept term as the only fixed effect and the residual term as the only random effect.

Subcommand order

  • The variable list must be specified first.
  • Subcommands can be specified in any order.

Syntax rules

  • For many analyses, the MIXED variable list, the FIXED subcommand, and the RANDOM subcommand are the only specifications needed.
  • A dependent variable must be specified.
  • Empty subcommands are silently ignored.
  • Multiple RANDOM subcommands are allowed. However, if an effect with the same subject specification appears in multiple RANDOM subcommands, only the last specification will be used.
  • Multiple TEST subcommands are allowed.
  • All subcommands, except the RANDOM and the TEST subcommands, should be specified only once. If a subcommand is repeated, only the last specification will be used.
  • The following words are reserved as keywords in the MIXED procedure: BY, WITH, and WITHIN.