The MIXED Procedure 
PROC MIXED Statement 
The PROC MIXED statement invokes the procedure. Table 56.2 summarizes important options in the PROC MIXED statement by function. These and other options in the PROC MIXED statement are then described fully in alphabetical order.
Option 
Description 

Basic Options 

specifies input data set 

specifies the estimation method 

includes scale parameter in optimization 

determines the sort order of CLASS variables 

Displayed Output 

displays asymptotic correlation matrix of covariance parameter estimates 

displays asymptotic covariance matrix of covariance parameter estimates 

requests confidence limits for covariance parameter estimates 

displays asymptotic standard errors and Wald tests for covariance parameters 

displays a table of information criteria 

displays estimates and gradients added to "Iteration History" 

writes periodic status notes to the log 

displays mixed model equations 

displays the solution to the mixed model equations 

suppresses "Class Level Information" completely or in parts 

suppresses "Iteration History" table 

produces ODS statistical graphics 

produces ratio of covariance parameter estimates with residual variance 

Optimization Options 

specifies the maximum number of likelihood evaluations 

specifies the maximum number of iterations 

Computational Options 

requests and tunes the relative function convergence criterion 

requests and tunes the relative gradient convergence criterion 

requests and tunes the relative Hessian convergence criterion 

selects betweenwithin degree of freedom method 

computes empirical ("sandwich") estimators 

unbounds covariance parameter estimates 

specifies starting value for minimum ridge value 

applies Fisher scoring where applicable 
You can specify the following options.
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 GreenhouseGeiser 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 variancecovariance matrix of the fixedeffects 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 fixedeffects 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 KenwardRoger 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 smallerisbetter form, and are described in Table 56.3.
Criterion 
Formula 
Reference 

AIC 

Akaike (1974) 
AICC 

Hurvich and Tsai (1989) 
Burnham and Anderson (1998) 

HQIC 

Hannan and Quinn (1979) 
BIC 

Schwarz (1978) 
CAIC 

Bozdogan (1987) 
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 finitesample 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 NewtonRaphson 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 methodofmoment 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 lefthandside coefficient matrix are transformed by using to produce and , respectively, where is a generalized inverse of the lefthandside 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.
includes the residual variance as part of the NewtonRaphson 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 pvalues. 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.
Value of ORDER= 
Levels Sorted By 

DATA 
order of appearance in the input data set 
FORMATTED 
external formatted value, except for numeric variables with no explicit format, which are sorted by their unformatted (internal) value 
FREQ 
descending frequency count; levels with the most observations come first in the order 
INTERNAL 
unformatted value 
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 BYgroup 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 globalplotoptions apply to all relevant plots generated by the MIXED procedure. The globalplotoptions supported by the MIXED procedure follow.
Global Plot Options
uses the data set observation number to identify observations in tooltips, provided that the observation number can be determined. Otherwise, the number displayed in tooltips is the index of the observation as it is used in the analysis within the BY group.
suppresses the default plots. Only the plots specifically requested are produced.
breaks a graphic that is otherwise paneled into individual component plots.
Specific Plot Options
The following listing describes the specific plots and their options.
requests that all plots appropriate for the particular analysis be produced.
requests box plots for the effects in your model that consist of classification effects only. Note that these effects can involve more than one classification variable (interaction and nested effects), but they cannot contain any continuous variables. By default, the BOXPLOT request produces box plots based on (conditional) raw residuals for the qualifying effects in the MODEL, RANDOM, and REPEATED statements. See the discussion of the boxplotoptions in a later section for information about how to tune your box plot request.
requests a plot of the likelihood or restricted likelihood distance. When influence diagnostics are requested with set selection according to an effect, the USEINDEX option enables you to replace the formatted tick values on the horizontal axis with integer indices of the effect levels in order to reduce the space taken up by the horizontal plot axis.
requests panels of the deletiob estimates in an influence analysis, provided that the INFLUENCE option is specified in the MODEL statement. No plots are produced for fixedeffects parameters associated with singular columns in the matrix or for covariance parameters associated with singularities in the ASYCOV matrix. By default, separate panels are produced for the fixedeffects and covariance parameters delete estimates. The FIXED and RANDOM options enable you to select these specific panels. The UNPACK option produces separate plots for each of the parameter estimates. The USEINDEX option replaces formatted tick values for the horizontal axis with integer indices.
requests panels of influence statistics. For iterative influence analysis (see the INFLUENCE option in the MODEL statement), the panel shows the Cook’s and CovRatio statistics for fixedeffects and covariance parameters, enabling you to gauge impact on estimates and precision for both types of estimates. In noniterative analysis, only statistics for the fixed effects are plotted. The UNPACK option produces separate plots from the elements in the panel. The USEINDEX option replaces formatted tick values for the horizontal axis with integer indices.
requests a panel of raw residuals. By default, the conditional residuals are produced. See the discussion of residualplotoptions in a later section for information about how to tune this panel.
requests a panel of studentized residuals. By default, the conditional residuals are produced. See the discussion of residualplotoptions in a later section for information about how to tune this panel.
requests a panel of Pearson residuals. By default, the conditional residuals are produced. See the discussion of residualplotoptions in a later section for information about how to tune this panel.
requests a plot of PRESS residuals or PRESS statistics. These are based on "leaveoneout" or "leavesetout" prediction of the marginal mean. When influence diagnostics are requested with set selection according to an effect, the USEINDEX option enables you to replace the formatted tick values on the horizontal axis with integer indices of the effect levels in order to reduce the space taken up by the horizontal plot axis.
requests a panel of residual graphics based on the scaled residuals. See the VCIRY option in the MODEL statement for details about these scaled residuals. Only the UNPACK and BOX options of the residualplotoptions are available for this type of residual panel.
suppresses all plots.
Residual Plot Options
The residualplotoptions determine both the composition of the panels and the type of residuals being plotted.
replaces the inset of summary statistics in the lowerright corner of the panel with a box plot of the residual (the "PROC GLIMMIX look").
constructs plots from conditional residuals.
constructs plots from marginal residuals.
produces separate plots from the elements of the panel. The inset statistics are not part of the unpack operation.
Box Plot Options
The boxplotoptions determine whether box plots are produced for residuals or for residuals and observed values, and for which model effects the box plots are constructed. The available boxplotoptions are as follows.
constructs box plots from conditional residuals—that is, residuals using the estimated BLUPs of random effects.
produces box plots for all fixed effects (MODEL statement) consisting entirely of classification variables
produces box plots for all GROUP= effects (RANDOM and REPEATED statement) consisting entirely of classification variables
constructs box plots from marginal residuals.
provides the ability to break a box plot into multiple graphics. If number is negative, no balancing of the number of boxes takes place and number is the maximum number of boxes per graphic. If number is positive, the number of boxes per graphic is balanced. For example, suppose variable A has 125 levels, and consider the following statements:
ods graphics on; proc mixed plots=boxplot(npanel=20); class A; model y = A; run;
The box balancing results in six plots with 18 boxes each and one plot with 17 boxes. If number is zero, and this is the default, all levels of the effect are displayed in a single plot.
adds box plots of the observed data for the selected effects.
produces box plots for all random effects (RANDOM statement) consisting entirely of classification variables. This does not include effects specified in the GROUP= or SUBJECT= options of the RANDOM statement.
produces box plots for the repeated effects (REPEATED statement). This does not include effects specified in the GROUP= or SUBJECT= options of the REPEATED statement.
constructs box plots from studentized residuals rather than from raw residuals.
produces box plots for all SUBJECT= effects (RANDOM and REPEATED statement) consisting entirely of classification variables.
uses as the horizontal axis label the index of the effect level rather than the formatted value(s). For classification variables with many levels or model effects that involve multiple classification variables, the formatted values identifying the effect levels can take up too much space as axis tick values, leading to extensive thinning. The USEINDEX option replaces tick values constructed from formatted values with the internal level number.
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 fixedeffects 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 NewtonRaphson 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.
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