PROC TCALIS: PCOV Statement :: SAS/STAT(R) 9.2 User's Guide, Second Edition

The TCALIS Procedure

PCOV Statement

PCOV assignment <, assignment ...> ;

where assignment represents:
variables < $\text{[math]}$ variables2 > = parameter-spec

The PCOV statement defines the covariance or partial covariance parameters in the PATH model. You can use the PCOV statement with the PATH modeling language only. On the left-hand side of each assignment, variables involved are listed in the variables and variables2 lists. In the parameter-spec list, covariance or partial covariance parameters are specified. Names in the parameter-spec represent covariance or partial covariance parameters to estimate. Numbers enclosed in parentheses in the parameter-spec list are initial values for the parameters. Numbers not enclosed in parentheses in the parameter-spec list are fixed values for covariances or partial covariances. The assignments in the PCOV statement must be separated by commas. You can specify only one PCOV statement in each model specification.

The syntax of the PCOV statement is the same as the COV statement. Refer to the COV statement for details about specifying within- and between- list (partial) covariances.

The concept behind the PCOV statement, however, is broader than that of the COV statement. The PCOV statement supports the partial covariance parameter specification in addition to the covariance parameter specification. The COV statement supports only the latter type of parameters. This discrepancy is also reflected from the sets of variables and variables2 you can use in the PCOV statement. In the COV statement, variables on the left-hand side of an assignment must be exogenous. However, in the PCOV statement, both exogenous and endogenous variables can be specified. If both variables are exogenous in a specification of the PCOV statement, you are defining a covariance parameter between the variables. If both variables are endogenous, you are defining a partial covariance parameter between of the variables. This partial covariance is usually interpreted as error covariance between the two endogenous variables. If one variable is exogenous while the other is endogenous, you are defining a covariance parameter between the exogenous variable and the error term for the endogenous variable.

Automatic Covariance Parameters among Exogenous Manifest Variables

In the PATH model, all covariances among exogenous manifest variables are automatically free parameters to estimate unless you specify otherwise in the PCOV statement. The parameter names for these covariances will be generated by PROC TCALIS with the prefix _Add, appended with unique integer for each occurrence. If you want any of these covariances to be fixed values, you must specify them explicitly in the PCOV statement.

By default covariances among exogenous latent variables are fixed zeros unless they are specified otherwise in the PCOV statement. The same applies to any partial covariance among endogenous variables and to any partial covariance between an exogenous latent variable and an exogenous manifest variable.

This is different from the case of partial variance parameters specified in the PVAR statement. Variances of all exogenous variables and partial variances of all endogenous variables are automatically free parameters if they are not specified otherwise in the PVAR statement.

Modifying a Parameter Specification from a Reference Model

If you define a new PATH model by using a reference (or base) model in the REFMODEL statement, in some situations you might want to modify some parameter specifications from the PCOV statement of the reference model before transferring the specifications to the new model. If you want to change a particular PCOV parameter specification from the reference model, you can simply put the corresponding parameter location with a new parameter specification in the new model. If you want to delete a particular parameter location from the reference model, you can put that parameter location with the missing value '.' in the new model. For example, suppose you are defining a new PATH model by using the REFMODEL statement and the covariance between variables F1 and V2 is defined as a fixed or free parameter in the reference model. If you do not want this parameter specification to be copied into your new model, you can use the following specification in the new model:

   PCOV F1 V2 = .;

Note that the missing value syntax is valid only when used with the REFMODEL statement. See the section Modifying a PATH Model from a Reference Model for a more detailed example of PATH model respecification.

In the PATH model, all covariances among exogenous manifest variables are free parameters to estimate unless you specify otherwise in the PCOV statement (see the section Automatic Covariance Parameters among Exogenous Manifest Variables). This is also true for PATH models specified under the REFMODEL statement. In the reference model, covariance parameters generated by PROC TCALIS are named with the _Add prefix and appended with integer suffixes. These parameter specifications in the reference model do not transfer to the new model. Only after the new model is resolved from the reference model, the REFMODEL statement options, the RENAMEPARM statement, and the model respecifications are the additional covariance parameters with the _Add prefix generated for the unspecified covariances among exogenous manifest variables. In this way, the covariance parameters in the new model are not constrained to be the same as the corresponding parameters in the reference model. If you want any of these covariance parameters constrained across the models, you must specify them explicitly in the PCOV statement of the reference model so that the covariance specifications are transferred to the new model.

Note: This procedure is experimental.

Top of Page