The CALIS Procedure

You specify the “causal” paths or linear functional relationships among variables in the PATH statement. For example, if there is a path from v2 to v1 in your model and the effect parameter is named parm1 with a starting value at 0.5, you can use either of these specifications:

path     v1 <===  v2    = parm1(0.5);

path     v2 ===>  v1    = parm1(0.5);

If you have more than one path in your model, path specifications should be separated by commas, as shown in the following PATH statement:

path
   v1 <===  v2   = parm1(0.5),
   v2 <===  v3   = parm2(0.3);

Because the PATH statement can be used only once in each model specification, all paths in the model must be specified together in a single PATH statement. See the PATH statement for more details about the syntax.

If v2 is an exogenous variable in the PATH model and you want to specify its variance as a parameter named parm2 with a starting value at 10, you can use the following PVAR statement specification:

pvar     v2  = parm2(10.);

If v1 is an endogenous variable in the PATH model and you want to specify its partial variance or error variance as a parameter named parm3 with a starting value at 5.0, you can also use the following PVAR statement specification:

pvar     v1 = parm3(5.0);

Therefore, the PVAR statement can be used for both exogenous and endogenous variables. When a variable in the statement is exogenous (which can be automatically determined by PROC CALIS), you are specifying the variance parameter of the variable. Otherwise, you are specifying the partial or error variance for an endogenous variable.

You do not need to supply the parameter names for the variances or partial variances if these parameters are not constrained. For example, the following statement specifies the unnamed free parameters for variances or partial variances of v1 and v2:

pvar     v1 v2;

If you have more than one variance or partial variance parameter to specify in your model, you can put a variable list on the left-hand side of the equal sign, and a parameter list on the right-hand side, as shown in the following PVAR statement specification:

pvar
   v1 v2 v3 = parm1(0.5) parm2 parm3;

In the specification, variance or partial variance parameters for variables v1–v3 are parm1, parm2, and parm3, respectively. Only parm1 is given an initial value at 0.5. The initial values for other parameters are generated by PROC CALIS.

You can also separate the specifications into several entries in the PVAR statement. Entries should be separated by commas. For example, the preceding specification is equivalent to the following specification:

pvar
   v1 = parm1 (0.5),
   v2 = parm2,
   v3 = parm3;

Because the PVAR statement can be used only once in each model specification, all variance and partial variance parameters in the model must be specified together in a single PVAR statement. See the PVAR statement for more details about the syntax.

If you want to specify the (partial) covariance between two variables v3 and v4 as a parameter named parm4 with a starting value at 3, you can use the following PCOV statement specification:

pcov  v3  v4 = parm4 (5.);

Whether parm4 is a covariance or partial covariance parameter depends on the variable types of v3 and v4. If both v3 and v4 are exogenous variables (manifest or latent), parm4 is a covariance parameter between v3 and v4. If both v3 and v4 are endogenous variables (manifest or latent), parm4 is a parameter for the covariance between the errors for v3 and v4. In other words, it is a partial covariance or error covariance parameter for v3 and v4.

A less common case is when one of the variables is exogenous and the other is endogenous. In this case, parm4 is a parameter for the partial covariance between the endogenous variable and the exogenous variable, or the covariance between the error for the endogenous variable and the exogenous variable. Fortunately, such covariances are relatively uncommon in statistical modeling. Their uses confuse the roles of systematic and unsystematic sources in the model and lead to difficulties in interpretations. Therefore, you should almost always avoid this kind of partial covariance.

Like the syntax of the PVAR statement, you can specify a list of (partial) covariance parameters in the PCOV statement. For example, consider the following statement:

pcov
   v1 v2 = parm4,
   v1 v3 = parm5,
   v2 v3 = parm6;

In the specification, three (partial) covariance parameters parm4, parm5, and parm6 are specified, respectively, for the variable pairs (v1,v2), (v1,v3), and (v2,v3). Entries for (partial) covariance specification are separated by commas.

Again, if all these covariances are not constrained, you can omit the names for the parameters. For example, the preceding specification can be specified as the following statement when the three covariances are free parameters in the model:

pcov
   v1 v2,
   v1 v3,
   v2 v3;

Or, you can simply use the following within-list covariance specification:

pcov
   v1 v2 v3;

Three covariance parameters are generated by this specification.

Because the PCOV statement can be used only once in each model specification, all covariance and partial covariance parameters in the model must be specified together in a single PCOV statement. See the PCOV statement for more details about the syntax.

Means and intercepts are specified when the mean structures of the model are of interest. You can specify mean and intercept parameters in the MEAN statement. For example, consider the following statement:

mean     V5 = parm5(11.);

If V5 is an exogenous variable (which is determined by PROC CALIS automatically), you are specifying parm5 as the mean parameter of V5. If V5 is an endogenous variable, you are specifying parm5 as the intercept parameter for V5.

Because each named variable in the PATH model is either exogenous or endogenous (exclusively), each variable in the PATH model would have either a mean or an intercept parameter (but not both) to specify in the MEAN statement. Like the syntax of the PVAR statement, you can specify a list of mean or intercept parameters in the MEAN statement. For example, in the following statement you specify a list of mean or intercept parameters for variables v1–v4:

mean
   v1-v4 = parm6-parm9;

This specification is equivalent to the following specification with four entries of parameter specifications:

mean
   v1 = parm6,
   v2 = parm7,
   v3 = parm8,
   v4 = parm9;

Again, entries in the MEAN statement must be separated by commas, as shown in the preceding statement.

Because the MEAN statement can be used only once in each model specification, all mean and intercept parameters in the model must be specified together in a single MEAN statement. See the MEAN statement for more details about the syntax.

If you do not have any knowledge about the initial value for a parameter, you can omit the initial value specification and let PROC CALIS compute it. For example, you can provide just the parameter locations and parameter names as in the following specification:

path    v1 <=== v2   = parm1;
   pvar v2 = parm2,
        v1 = parm3;

If you want to specify a fixed parameter value, you do not need to provide a parameter name. Instead, you provide the fixed value (without parentheses) in the specification.

For example, in the following statement the path coefficient for the path is fixed at 1.0 and the (partial) variance of F1 is also fixed at 1.0:

path    v1 <=== F1  = 1.;
   pvar
        F1 = 1.;

The following specification shows a more complete PATH model specification:

path     v1 <===  v2 ,
         v1 <===  v3 ;
   pvar  v1,
         v2 = parm3,
         v3 = parm3;
   pcov  v3 v2 =  parm5(5.);

The two paths specified in the PATH statement have unnamed free effect parameters. These parameters are named by PROC CALIS with the _Parm prefix and unique integer suffixes. The error variance of v1 is an unnamed parameter, while the variances of v2 and v3 are constrained by using the same parameter parm3. The covariance between v2 and v3 is a free parameter named parm5, with a starting value of 5.0.