# The MIXED Procedure

### ODS Graphics

Subsections:

Statistical procedures use ODS Graphics to create graphs as part of their output. ODS Graphics is described in detail in Chapter 21: Statistical Graphics Using ODS.

Before you create graphs, ODS Graphics must be enabled (for example, by specifying the ODS GRAPHICS ON statement). For more information about enabling and disabling ODS Graphics, see the section Enabling and Disabling ODS Graphics in Chapter 21: Statistical Graphics Using ODS.

The overall appearance of graphs is controlled by ODS styles. Styles and other aspects of using ODS Graphics are discussed in the section A Primer on ODS Statistical Graphics in Chapter 21: Statistical Graphics Using ODS.

Some graphs are produced by default; other graphs are produced by using statements and options.

#### ODS Graph Names

You can reference every graph produced through ODS Graphics with a name. The names of the graphs that PROC MIXED generates are listed in Table 65.28, along with the required statements and options.

Table 65.28: Graphs Produced by PROC MIXED

ODS Graph Name

Plot Description

Statement or Option

Box plots

PLOTS= BOXPLOT

CovRatioPlot

CovRatio statistics for fixed effects or covariance parameters

PLOTS= INFLUENCESTATPANEL(UNPACK)
and MODEL / INFLUENCE

CooksDPlot

Cook’s D for fixed effects or covariance parameters

PLOTS= INFLUENCESTATPANEL(UNPACK)
and MODEL / INFLUENCE

Likelihood or restricted likelihood distance

Panel of deletion estimates

MODEL / INFLUENCE (EST )
or PLOTS= INFLUENCEESTPLOT and
MODEL / INFLUENCE

InfluenceEstPlot

Parameter estimates after removing observation or sets of observations

PLOTS= INFLUENCEESTPLOT(UNPACK)
and MODEL / INFLUENCE

Panel of influence statistics

PearsonBoxPlot

Box plot of Pearson residuals

PLOTS= PEARSONPANEL(UNPACK BOX)

PearsonByPredicted

Pearson residuals vs. predicted

PLOTS= PEARSONPANEL(UNPACK)

PearsonHistogram

Histogram of Pearson residuals

PLOTS= PEARSONPANEL(UNPACK)

PearsonPanel

Panel of Pearson residuals

PearsonQQplot

Q-Q plot of Pearson residuals

PLOTS= PEARSONPANEL(UNPACK)

PressPlot

Plot of PRESS residuals or PRESS statistic

PLOTS= PRESS and MODEL / INFLUENCE

ResidualBoxplot

Box plot of (raw) residuals

PLOTS= RESIDUALPANEL(UNPACK BOX)

ResidualByPredicted

Residuals vs. predicted

PLOTS= RESIDUALPANEL(UNPACK)

ResidualHistogram

Histogram of raw residuals

PLOTS= RESIDUALPANEL(UNPACK)

ResidualPanel

Panel of (raw) residuals

ResidualQQplot

Q-Q plot of raw residuals

PLOTS= RESIDUALPANEL(UNPACK)

ScaledBoxplot

Box plot of scaled residuals

PLOTS= VCIRYPANEL(UNPACK BOX)

ScaledByPredicted

Scaled residuals vs. predicted

PLOTS= VCIRYPANEL(UNPACK)

ScaledHistogram

Histogram of scaled residuals

PLOTS= VCIRYPANEL(UNPACK)

ScaledQQplot

Q-Q plot of scaled residuals

PLOTS= VCIRYPANEL(UNPACK)

StudentBoxplot

Box plot of studentized residuals

PLOTS= STUDENTPANEL(UNPACK BOX)

StudentByPredicted

Studentized residuals vs. predicted

PLOTS= STUDENTPANEL(UNPACK)

StudentHistogram

Histogram of studentized residuals

PLOTS= STUDENTPANEL(UNPACK)

Panel of studentized residuals

StudentQQplot

Q-Q plot of studentized residuals

PLOTS= STUDENTPANEL(UNPACK)

VCIRYPanel

Panel of scaled residuals

When ODS Graphics is enabled, the LSMESTIMATE and SLICE statements can produce plots that are associated with their analyses. For information about these plots, see the sections LSMESTIMATE Statement and SLICE Statement in Chapter 19: Shared Concepts and Topics.

#### Residual Plots

The MIXED procedure can generate panels of residual diagnostics. Each panel consists of a plot of residuals versus predicted values, a histogram with normal density overlaid, a Q-Q plot, and summary residual and fit statistics (Figure 65.15). The plots are produced even if the OUTP= and OUTPM= options in the MODEL statement are not specified. Residual panels can be generated for marginal and conditional raw, studentized, and Pearson residuals as well as for scaled residuals (see the section Residual Diagnostics).

Recall the example in the section Getting Started: MIXED Procedure. The following statements generate several panels of residual graphs:

ods graphics on;
proc mixed data=heights plots=studentpanel(marginal conditional);
class Family Gender;
model Height = Gender / residual;
random Family Family*Gender;
run;
ods graphics off;


The graphs are created when ODS Graphics is enabled. The panel of the studentized marginal residuals is shown in Figure 65.15, and the panel of the studentized conditional residuals is shown in Figure 65.16.

Figure 65.15: Panel of the Studentized (Marginal) Residuals

Since the fixed-effects part of the model comprises only an intercept and the gender effect, the marginal mean takes on only two values, one for each gender. The "Residual Statistics" inset in the lower-right corner provides descriptive statistics for the set of residuals that is displayed. Note that residuals in a mixed model do not necessarily sum to zero, even if the model contains an intercept.

Figure 65.16: Panel of the Conditional Studentized Residuals

#### Influence Plots

The graphical features of the MIXED procedure enable you to generate plots of influence diagnostics and of deletion estimates. The type and number of plots produced depend on your modifiers of the INFLUENCE option in the MODEL statement and on the PLOTS= option in the PROC MIXED statement. Plots related to covariance parameters are produced only when diagnostics are computed by iterative methods (ITER= ). The estimates of the fixed effects—and covariance parameters when updates are iterative—are plotted when you specify the ESTIMATES modifier or when you request PLOTS= INFLUENCEESTPLOT.

Two basic types of influence panels are shown in Figure 65.17 and Figure 65.18. The diagnostics panel shows Cook’s D and CovRatio statistics for the fixed effects and the covariance parameters. For the SAS statements that produce these influence panels, see Example 65.8. In this example, the impact of subjects (Person) on the analysis is assessed. The Cook’s D statistic measures a subject’s impact on the estimates, and the CovRatio statistic measures a subject’s impact on the precision of the estimates. Separate statistics are computed for the fixed effects and the covariance parameters. The CovRatio statistic has a threshold of 1.0. Values larger than 1.0 indicate that precision of the estimates is lost by exclusion of the observations in question. Values smaller than 1.0 indicate that precision is gained by exclusion of the observations from the analysis. For example, it is evident from Figure 65.17 that person 20 has considerable impact on the covariance parameter estimates and moderate influence on the fixed-effects estimates. Furthermore, exclusion of this subject from the analysis increases the precision of the covariance parameters, whereas the effect on the precision of the fixed effects is minor.

Figure 65.18 shows another type of influence plot, a panel of the deletion estimates. Each plot within the panel corresponds to one of the model parameters. A reference line is drawn at the estimate based on the full data.

Figure 65.17: Influence Diagnostics

Figure 65.18: Deletion Estimates