The COVTEST statement provides a mechanism to obtain statistical inferences for the covariance parameters. Significance tests are based on the ratio of (residual) likelihoods or pseudolikelihoods. Confidence limits and bounds are computed as Wald or likelihood ratio limits. You can specify multiple COVTEST statements.
The likelihood ratio test is obtained by fitting the model subject to the constraints imposed by the testspecification. The test statistic is formed as twice the difference of the (possibly restricted) log (pseudo) likelihoods of the full and the reduced models. Note that fitting the null model does not necessarily require fewer computer resources compared to fitting the full model. The optimization settings for refitting the model are the same as for the full model and can be controlled with the NLOPTIONS statement.
Common questions in mixed modeling are whether variance components are zero, whether random effects are independent, and whether
rows (columns) can be added or removed from an unstructured covariance matrix. When the parameters under the null hypothesis
fall on the boundary of the parameter space, the distribution of the likelihood ratio statistic can be a complicated mixture
of distributions. In certain situations it is known to be a relatively straightforward mixture of central chisquare distributions. When the GLIMMIX procedure recognizes the model and hypothesis as a case for
which the mixture is readily available, the pvalue of the likelihood ratio test is determined accordingly as a linear combination of central chisquare probabilities.
The Note
column in the "Likelihood Ratio Tests for Covariance Parameters" table along with the table’s footnotes informs you about
when mixture distributions are used in the calculation of pvalues. You can find important statistical and computational details about likelihood ratio testing of covariance parameters
with the GLIMMIX procedure in the section Statistical Inference for Covariance Parameters.
In generalized linear mixed models that depend on pseudodata, the GLIMMIX procedure fits the null model for a test of covariance parameters to the final pseudodata of the converged optimization.
Table 44.6 summarizes the options available in the COVTEST statement.
Table 44.6: COVTEST Statement Options
Option 
Description 

Test specification 

Reads in covariance parameter values from a SAS data set 

Provides a general facility to test linear combinations of covariance parameters 

Covariance Test Options 

Requests confidence limits for the covariance parameter estimates 

Computes the likelihood ratio test pvalue using the classical method 

Specifies the degrees of freedom 

Displays the estimates of the covariance parameters under the null hypothesis 

Limits the number of iterations 

Displays the values of the covariance parameters under the null hypothesis 

Specifies that starting values for the covariance parameters 

Sets the tolerance level of the parameter space boundary 

Produces Wald Z tests 

Supplies weights for the computation of pvalues 
The testspecification in the COVTEST statement draws on keywords that represent a particular null hypothesis, lists or data sets of parameter values, or general contrast specifications. Valid keywords are as follows:
tests the model against a null model of complete independence. All Gside covariance parameters are eliminated and the Rside covariance structure is reduced to a diagonal structure.
tests for a diagonal G matrix by constraining offdiagonal elements in G to zero. The Rside structure is not modified.
tests for conditional independence by reducing the Rside covariance structure to diagonal form. The Gside structure is not modified.
tests homogeneity of covariance parameters across groups by imposing equality constraints. For example, the following statements fit a oneway model with heterogeneous variances and test whether the model could be reduced to a oneway analysis with the same variance across groups:
proc glimmix; class A; model y = a; random _residual_ / group=A; covtest 'common variance' homogeneity; run;
See Example 44.9 for an application with groups and unstructured covariance matrices.
compares the final estimates to the starting values of the covariance parameter estimates. This option is useful, for example, if you supply starting values in the PARMS statement and want to test whether the optimization produced significantly better values. In GLMMs based on pseudodata, the likelihoods that use the starting and the final values are based on the final pseudodata.
tests whether the G matrix can be reduced to a zero matrix. This eliminates all Gside random effects from the model.
Only a single keyword is permitted in the COVTEST statement. To test more complicated hypotheses, you can formulate tests with the following specifications.