specifies which parameter values be constrained to equal the specified values. For example, the following statement constrains the first and third semivariance parameters to equal 0.5 and 12, respectively. The fourth parameter is fixed to the default initial value that is assigned to it by PROC VARIOGRAM.

parms (0.5) (3) (12) (.) / hold=1,3,4;

The HOLD= option accepts only nonmissing values in its list. If you specify more than the available parameters in the HOLD= option list, then the ones in excess are ignored. If the HOLD= option list has integer values that do not correspond to variables in the PARMS list, then they are also ignored. Noninteger values are rounded to the closest integer and evaluated accordingly.

When you specify more than one set of parameter initial values, the HOLD= option list applies to the set that gives the lowest objective function value before this set is sent to the optimizer for the fitting.

specifies lower boundary constraints on the semivariance parameters. The value-list specification is a list of numbers or missing values (.) separated by commas. You must list the numbers in the order that PROC VARIOGRAM uses for the semivariance parameters, and each number corresponds to the lower boundary constraint. A missing value instructs PROC VARIOGRAM to use its default constraint.

If you do not specify lower bounds for all of the semivariance parameters, then PROC VARIOGRAM assumes that the remaining parameters are not bounded. If you specify more lower bounds in the value-list than the available parameters, then the numbers in excess are ignored. If you specify lower bounds for parameters with missing initial values, then the VARIOGRAM procedure enforces the specified bounds in the fitting process. By default, the lower bound for all parameters is zero.

When you specify the HOLD= option together with the LOWERB= option, the lower bounds in the LOWERB= option value-list that correspond to fixed parameters are ignored. When you specify the NOBOUND option together with the LOWERB= option, the LOWERB= option is ignored.

specifies a positive upper threshold for the fitted semivariogram sill. This option imposes a linear constraint on the optimization of the nonfixed semivariogram scale and nugget parameters so that the sum of all scale and nugget parameters does not exceed the specified MAXSCALE= value. The MAXSCALE= constraint is ignored if all the semivariogram scale and nugget parameters are fixed.

requests the removal of boundary constraints on semivariance parameters. For example, semivariance parameters have a default zero lower boundary constraint since they have a physical meaning only for positive values. The NOBOUND option enables the fitting process to derive negative estimates; hence, you need to be cautious with the outcome when you specify this option.

The NOBOUND option has no effect on the power model exponent parameter. The exponent must range within [0,2) so that the model is a valid semivariance function. Also, the options LOWERB= and UPPERB= are ignored if either of them is specified together with the NOBOUND option in the PARMS statement.

specifies that semivariance parameters values be read from a SAS data set. The data set should contain the values in the sequence required by the PARMS statement in either of the following two ways:

• Specify one single column under the variable Estimate (or Est) that contains all the parameter values.

• Use one column for each parameter, and place the n columns under the Parm1–Parmn variables.

For example, the following two data sets are valid and equivalent ways to specify initial values for the nugget effect and the parameters of the Matérn and exponential structures that have been used in the previous examples in the PARMS statement section:

data parData1;
   input Estimate @@;
   datalines;
   . 3 20 4.5 . 15
   ;
run;

data parData2;
   input Parm1 Parm2 Parm3 Parm4 Parm5 Parm6;
   datalines;
   . 3 20 4.5 . 15
   ;
run;

If you have the parData1 data set, then you can import this information into the PARMS statement as follows:

proc variogram data=FirstData;
   < other VARIOGRAM statements >
   model form=(mat,exp);
   parms / pdata=parData1 hold=(2 to 4,6);
run;

You can specify more than one set of initial values in the PDATA= data set by following the preceding guidelines. PROC VARIOGRAM seeks among the specified sets for the one that gives the lowest objective function value. Then, the procedure uses the initial values in the selected set for the fitting optimization.

You can explicitly specify initial parameter values in the PARMS statement or use the PDATA= option, but you cannot use both at the same time.

specifies upper boundary constraints on the semivariance parameters. The value-list specification is a list of numbers or missing values (.) separated by commas. You must list the numbers in the order that PROC VARIOGRAM uses for the semivariance parameters, and each number corresponds to the upper boundary constraint. A missing value instructs PROC VARIOGRAM to use its default constraint.

If you do not specify upper bounds for all of the semivariance parameters, then PROC VARIOGRAM assumes that the remaining parameters are not bounded. If you specify more upper bounds in the value-list than the available parameters, then the numbers in excess are ignored. If you specify upper bounds for parameters with missing initial values, then the VARIOGRAM procedure enforces the specified bounds in the fitting process. By default, the scale, range, nugget, and Matérn smoothness parameters have no upper bounds, whereas the power model exponent parameter is lower than two.

When you specify the HOLD= option together with the UPPERB= option, the upper bounds in the UPPERB= option value-list that correspond to fixed parameters are ignored. When you specify the NOBOUND option together with the UPPERB= option, the UPPERB= option is ignored.