makes the convergence criterion absolute. By default, it is relative (divided by the current objective function value). See the CONVF, CONVG, and CONVH options in this section for a description of various convergence criteria.

requests that confidence limits be constructed for the covariance parameter estimates with confidence level . The value of number must be between 0 and 1; the default is 0.05.

The ANOVAF option computes F tests in models with REPEATED statement and without RANDOM statement by a method similar to that of Brunner, Domhof, and Langer (2002). The method consists of computing special F statistics and adjusting their degrees of freedom. The technique is a generalization of the Greenhouse-Geiser adjustment in MANOVA models (Greenhouse and Geiser 1959). For more details, see the section F Tests With the ANOVAF Option.

produces the asymptotic correlation matrix of the covariance parameter estimates. It is computed from the corresponding asymptotic covariance matrix (see the description of the ASYCOV option, which follows). For ODS purposes, the name of the "Asymptotic Correlation" table is "AsyCorr."

requests that the asymptotic covariance matrix of the covariance parameters be displayed. By default, this matrix is the observed inverse Fisher information matrix, which equals , where is the Hessian (second derivative) matrix of the objective function. See the section Covariance Parameter Estimates for more information about this matrix. When you use the SCORING= option and PROC MIXED converges without stopping the scoring algorithm, PROC MIXED uses the expected Hessian matrix to compute the covariance matrix instead of the observed Hessian. For ODS purposes, the name of the "Asymptotic Covariance" table is "AsyCov."

requests confidence limits for the covariance parameter estimates. A Satterthwaite approximation is used to construct limits for all parameters that have a lower boundary constraint of zero. These limits take the form

where , is the Wald statistic , and the denominators are quantiles of the -distribution with degrees of freedom. See Milliken and Johnson (1992) and Burdick and Graybill (1992) for similar techniques.

For all other parameters, Wald -scores and normal quantiles are used to construct the limits. Wald limits are also provided for variance components if you specify the NOBOUND option. The optional =WALD specification requests Wald limits for all parameters.

The confidence limits are displayed as extra columns in the "Covariance Parameter Estimates" table. The confidence level is by default; this can be changed with the ALPHA= option.

requests the relative function convergence criterion with tolerance number. The relative function convergence criterion is

where is the value of the objective function at iteration k. To prevent the division by , use the ABSOLUTE option. The default convergence criterion is CONVH, and the default tolerance is 1E8.

requests the relative gradient convergence criterion with tolerance number. The relative gradient convergence criterion is

where is the value of the objective function, and is the th element of the gradient (first derivative) of the objective function, both at iteration k. To prevent division by , use the ABSOLUTE option. The default convergence criterion is CONVH, and the default tolerance is 1E8.

requests the relative Hessian convergence criterion with tolerance number. The relative Hessian convergence criterion is

where is the value of the objective function, is the gradient (first derivative) of the objective function, and is the Hessian (second derivative) of the objective function, all at iteration .

If is singular, then PROC MIXED uses the following relative criterion:

To prevent the division by , use the ABSOLUTE option. The default convergence criterion is CONVH, and the default tolerance is 1E8.

produces asymptotic standard errors and Wald -tests for the covariance parameter estimates.

names the SAS data set to be used by PROC MIXED. The default is the most recently created data set.

has the same effect as the DDFM=BW option in the MODEL statement.

computes the estimated variance-covariance matrix of the fixed-effects parameters by using the asymptotically consistent estimator described in Huber (1967), White (1980), Liang and Zeger (1986), and Diggle, Liang, and Zeger (1994). This estimator is commonly referred to as the "sandwich" estimator, and it is computed as follows:

Here, , is the number of subjects, and matrices with an subscript are those for the th subject. You must include the SUBJECT= option in either a RANDOM or REPEATED statement for this option to take effect.

When you specify the EMPIRICAL option, PROC MIXED adjusts all standard errors and test statistics involving the fixed-effects parameters. This changes output in the following tables (listed in Table 56.22): Contrast, CorrB, CovB, Diffs, Estimates, InvCovB, LSMeans, Slices, SolutionF, Tests1–Tests3. The OUTP= and OUTPM= data sets are also affected. Finally, the Satterthwaite and Kenward-Roger degrees of freedom methods are not available if you specify the EMPIRICAL option.

displays a table of various information criteria. The criteria are all in smaller-is-better form, and are described in Table 56.3.

Here denotes the maximum value of the (possibly restricted) log likelihood, the dimension of the model, and the number of observations. In SAS 6 of SAS/STAT software, equals the number of valid observations for maximum likelihood estimation and for restricted maximum likelihood estimation, where equals the rank of . In later versions, equals the number of effective subjects as displayed in the "Dimensions" table, unless this value equals 1, in which case equals the number of levels of the first random effect you specify in a RANDOM statement. If the number of effective subjects equals 1 and you have no RANDOM statements, then reverts to the SAS 6 values. For AICC (a finite-sample corrected version of AIC), equals the SAS 6 values of , unless this number is less than , in which case it equals .

For restricted likelihood estimation, equals , the effective number of estimated covariance parameters. In SAS 6, when a parameter estimate lies on a boundary constraint, then it is still included in the calculation of , but in later versions it is not. The most common example of this behavior is when a variance component is estimated to equal zero. For maximum likelihood estimation, equals .

For ODS purposes, the name of the "Information Criteria" table is "InfoCrit."

is a default option. The creation of the "Model Information," "Dimensions," and "Number of Observations" tables can be suppressed by using the NOINFO option.

Note that in SAS 6 this option displays the "Model Information" and "Dimensions" tables.

displays the parameter values at each iteration and enables the writing of notes to the SAS log pertaining to "infinite likelihood" and "singularities" during Newton-Raphson iterations.

writes periodic notes to the log describing the current status of computations. It is designed for use with analyses requiring extensive CPU resources.

specifies the maximum number of likelihood evaluations in the optimization process. The default is 150.

specifies the maximum number of iterations. The default is 50.

specifies the estimation method for the covariance parameters. The REML specification performs residual (restricted) maximum likelihood, and it is the default method. The ML specification performs maximum likelihood, and the MIVQUE0 specification performs minimum variance quadratic unbiased estimation of the covariance parameters.

The METHOD=TYPE specifications apply only to variance component models with no SUBJECT= effects and no REPEATED statement. An analysis of variance table is included in the output, and the expected mean squares are used to estimate the variance components (see Chapter 39, The GLM Procedure, for further explanation). The resulting method-of-moment variance component estimates are used in subsequent calculations, including standard errors computed from ESTIMATE and LSMEANS statements. For ODS purposes, the new table names are "Type1," "Type2," and "Type3," respectively.

requests that coefficients of the mixed model equations be displayed. These are

assuming that is nonsingular. If is singular, PROC MIXED produces the following coefficients:

See the section Estimating Fixed and Random Effects in the Mixed Model for further information about these equations.

requests that a solution to the mixed model equations be produced, as well as the inverted coefficients matrix. Formulas for these equations are provided in the preceding description of the MMEQ option.

When is singular, and a generalized inverse of the left-hand-side coefficient matrix are transformed by using to produce and , respectively, where is a generalized inverse of the left-hand-side coefficient matrix of the original equations.

specifies the length to which long effect names are shortened. The default and minimum value is 20.

has the same effect as the NOBOUND option in the PARMS statement.

suppresses the display of the "Class Level Information" table if you do not specify number. If you do specify number, only levels with totals that are less than number are listed in the table.

suppresses the display of the "Model Information," "Dimensions," and "Number of Observations" tables.

suppresses the display of the "Iteration History" table.

includes the residual variance as part of the Newton-Raphson iterations. This option applies only to models that have a residual variance parameter. By default, this parameter is profiled out of the likelihood calculations, except when you have specified the HOLD= option in the PARMS statement.

displays ordinates of the relevant distribution in addition to p-values. The ordinate can be viewed as an approximate odds ratio of hypothesis probabilities.

specifies the sorting order for the levels of all CLASS variables. This ordering determines which parameters in the model correspond to each level in the data, so the ORDER= option can be useful when you use CONTRAST or ESTIMATE statements.

The default is ORDER=FORMATTED, and its behavior has been modified for SAS 8. When the default ORDER=FORMATTED is in effect for numeric variables for which you have supplied no explicit format, the levels are ordered by their internal values. In releases previous to SAS 8, numeric class levels with no explicit format were ordered by their BEST12. formatted values. In order to revert to the previous method you can specify this format explicitly for the CLASS variables. The change was implemented because the former default behavior for ORDER=FORMATTED often resulted in levels not being ordered numerically and required you to use an explicit format or ORDER=INTERNAL to get the more natural ordering.

Table 56.4 shows how PROC MIXED interprets values of the ORDER= option.

For FORMATTED and INTERNAL, the sort order is machine dependent.

For more information about sort order, see the chapter on the SORT procedure in the SAS Procedures Guide and the discussion of BY-group processing in SAS Language Reference: Concepts.

requests that the MIXED procedure produce statistical graphics via the Output Delivery System, provided that the ODS GRAPHICS statement has been specified. For general information about ODS Graphics, see Chapter 21, Statistical Graphics Using ODS. For examples of the basic statistical graphics produced by the MIXED procedure and aspects of their computation and interpretation, see the section ODS Graphics.

The global-plot-options apply to all relevant plots generated by the MIXED procedure. The global-plot-options supported by the MIXED procedure follow.

Global Plot Options

Specific Plot Options

The following listing describes the specific plots and their options.

Multiple Plot Request

You can list a plot request one or more times with different options. For example, the following statements request a panel of marginal raw residuals, individual plots generated from a panel of the conditional raw residuals, and a panel of marginal studentized residuals:

   ods graphics on;
   proc mixed plots(only)=(
          ResidualPanel(marginal)
          ResidualPanel(unpack conditional)
          StudentPanel(marginal box));

The inset of residual statistics is replaced in this last panel by a box plot of the studentized residuals. Similarly, if you specify the INFLUENCE option in the MODEL statement, then the following statements request statistical graphics of fixed-effects deletion estimates (in a panel), covariance parameter deletion estimates (unpacked in individual plots), and box plots for the SUBJECT= and fixed classification effects based on residuals and observed values:

   ods graphics on / imagefmt=staticmap;
   proc mixed plots(only)=(
          InfluenceEstPlot(fixed)
          InfluenceEstPlot(random unpack)
          BoxPlot(observed fixed subject);

The STATICMAP image format enables tooltips that show, for example, values of influence diagnostics associated with a particular delete estimate.

This concludes the syntax section for the PLOTS= option in the PROC MIXED statement.

produces the ratio of the covariance parameter estimates to the estimate of the residual variance when the latter exists in the model.

specifies the starting value for the minimum ridge value used in the Newton-Raphson algorithm. The default is 0.3125.

requests that Fisher scoring be used in association with the estimation method up to iteration number, which is 0 by default. When you use the SCORING= option and PROC MIXED converges without stopping the scoring algorithm, PROC MIXED uses the expected Hessian matrix to compute approximate standard errors for the covariance parameters instead of the observed Hessian. The output from the ASYCOV and ASYCORR options is similarly adjusted.

is an alias for the NOPROFILE option.

is an alias for the LOGNOTE option.