The LMIXED Procedure

holds the values of the covariance parameters whose order is specified in the order-list to the initial values that are specified in the value-list in the RANDOM statement.

For example, the following statement constrains the first and third covariance parameters to equal 5 and 2, respectively:

parms (5) (3) (2) (3) / hold=1,3;

If you specify ALL or you do not specify order-list, then all covariance parameters are held to their initial values. When not all parameters are held to their initial values, this is referred to as partial holding.

Specifying the HOLD= option implies the specification of NOPROFILE option in the PROC LMIXED statement.

The partial holding cannot retain the values exactly for the TYPE=UN covariance structure. This is because the underlining structure is TYPE=CHOL in the optimization for covariance parameter estimation.

specifies the lower boundary constraints on the covariance parameters, where value-list is a list of numbers or missing values (.) separated by commas. You must list the numbers in the order that the LMIXED procedure uses for the covariance parameters, and each number corresponds to a lower boundary constraint. A missing value instructs the LMIXED procedure to use its default constraint. If you do not specify numbers for all the covariance parameters, the LMIXED procedure assumes that the remaining ones are missing.

This option is useful when you want to constrain the matrix to be positive definite in order to avoid the more computationally intensive algorithms that would be required when becomes singular. The corresponding statements for a random coefficients model are as follows:

proc lmixed;
   class person;
   model y = time;
   random int time / type=fa0(2) sub=person;
   parms / lowerb=1e-4,.,1e-4;
run;

The TYPE=FA0(2) structure specifies a Cholesky root parameterization for the unstructured blocks in . This parameterization ensures that the matrix is nonnegative definite, and the PARMS statement then ensures that it is positive definite by constraining the two diagonal terms to be greater than or equal to 1E–4.

requests that no optimization iterations be performed and that the LMIXED procedure use the best value from the grid search to perform inferences.

reads in covariance parameter values from a data table. CAS-libref.data-table is a two-level name, where CAS-libref refers to the caslib and session identifier, and data-table specifies the name of the input data table. For more information about this two-level name, see the DATA= option and the section Using CAS Sessions and CAS Engine Librefs.

The data table should contain either the numerical variables Estimate and RowId or the numerical variables Covp1–Covpq, where q denotes the number of covariance parameters.

If the data table contains the numerical variables Covp1–Covpq and it contains multiple sets of values for covariance parameters, then the LMIXED procedure evaluates the initial objective function for each set of values and commences the optimization step by using the set that has the lowest functional value as the starting values. For example, the following statements request that the objective function be evaluated for three sets of initial values:

data mycas.data_covp;
   input covp1-covp4;
   datalines;
180 200 170 1000
170 190 160  900
160 180 150  800
;
proc lmixed;
   class A B C rep;
   model yield = A;
   random rep B C;
   parms / pdata=mycas.data_covp;
run;

Another way of specifying the initial values for the covariance parameters is to use the numerical variables Estimate and RowId in the data table. The values in RowId variable indicate the order of the covariance parameters in the "Covariance Parameter Estimates" table.

data mycas.covparm;
   input rowid estimate;
   datalines;
1  180
2  200
3  170
4  1000
;

A BY variable is not supported in the PARMSDATA= data table. The data table is processed in its entirety for every BY group and a message is written to the log. The same set of starting values is used by all BY groups.

data mycas.data_covp;
   input covp1-covp4;
   datalines;
180 200 170 1000
;
proc lmixed;
   class A B C rep;
   model yield = A;
   random rep B C;
   parms / pdata=mycas.data_covp;
   by year;
run;

specifies upper boundary constraints on the covariance parameters, where the value-list specification is a list of numbers or missing values (.) separated by commas. You must list the numbers in the order that the LMIXED procedure uses for the covariance parameters, and each number corresponds to the upper boundary constraint. A missing value instructs the LMIXED procedure to use its default constraint. If you do not specify numbers for all of the covariance parameters, the LMIXED procedure assumes that the remaining ones are missing.