### PVAR Statement

`PVAR` assignment <, assignment …> ;

where assignment represents: var-list <= parameter-spec>

The PVAR statement specifies the variance or error (partial) variance parameters in connection with the confirmatory FACTOR and PATH models.

In each assignment of the PVAR statement, you list the var-list that you want to specify for their variances or error (partial) variances. Optionally, you can provide a list of parameter specifications (parameter-spec) after an equal sign for each var-list list. The syntax of the PVAR statement is exactly the same as that of the VARIANCE statement. See the for details about the syntax.

The concept behind the PVAR statement is broader than that of the VARIANCE statement. The PVAR statement supports the partial variance parameter specification in addition to the variance parameter specification, which is the only type of parameters that the VARIANCE statement supports. This difference is reflected from the set of var-list you can use in the PVAR statement. You can specify both exogenous variables and endogenous variables in the var-list list of the PVAR statement, but you can specify only exogenous variables in the var-list list of the VARIANCE statement. This conceptualization of the PVAR statement is needed in the FACTOR and PATH modeling languages because error variables are not explicitly defined in these models. You specify the variance of a variable if the variable in the var-list list of the PVAR statement is an exogenous (independent) variable in the FACTOR or PATH model. You specify the error (partial) variance of a variable if the variable in the var-list list of the PVAR statement is an endogenous (dependent) variable in the FACTOR or PATH model.

You can specify the following five types of the parameters for the partial variances in the PVAR statement:

• an unnamed free parameter

• an initial value

• a fixed value

• a free parameter with a name provided

• a free parameter with a name and initial value provided

For example, consider a PATH model with exogenous variables `x1`, `x2`, and `x3` and endogenous variables `y4` and `y5`. The following PVAR statement illustrates the five types of specifications in five assignments:

```pvar x1 ,
x2 = (2.0),
x3 = 1.0,
y4 = psi1,
y5 = psi2(0.6);
```

In this statement, the variance of `x1` is specified as an unnamed free parameter. For this variance, PROC CALIS generates a parameter name with the `_Parm` prefix and appended with a unique integer (for example, `_Parm1`). The variance of `x2` is an unnamed free parameter with an initial value of 2.0. PROC CALIS also generates a parameter name for this variance. The variance of `x3` is a fixed value of 1.0. This value stays the same during the estimation. The error variance of endogenous variable `y4` is a free parameter named `psi1`. The error variance of endogenous variable `y5` is a free parameter named `psi2` with an initial value of 0.6.

The syntax of the PVAR statement is the same as the syntax of the VARIANCE statement. See the VARIANCE statement for more illustrations about the usage.

#### Default Partial Variance Parameters

By default, all variances of the exogenous manifest and latent variables and all error (partial) variances of the endogenous manifest and latent variables are free parameters in the FACTOR or PATH model. For these default free variance parameters, PROC CALIS generates the parameter names with the `_Add` prefix and appended with unique integer suffixes. You can also use the PVAR statement specification to override these default variance parameters in situations where you want to specify parameter constraints, provide initial or fixed values, or make parameter references.

In the FACTOR or PATH model, a variable can either be exogenous or endogenous. Therefore, the default free parameters covers all the possible variance or partial variance parameters in the model. There are no default fixed zeros for any variances or partial variances in the model.

#### Modifying a Variance or Partial Variance Parameter Specification from a Reference Model

If you define a new FACTOR or PATH model by using a reference (old) model in the REFMODEL statement, you might want to modify some parameter specifications from the PVAR statement of the reference model before transferring the specifications to the new model. To change a particular variance or partial variance specification from the reference model, you can simply respecify the same variance or partial variance with the desired parameter specification in the PVAR statement of the new model. To delete a particular variance parameter from the reference model, you can specify the desired variance or partial variance with a missing value specification in the PVAR statement of the new model.

For example, suppose that the variance of `V1` is specified in the reference PATH model but you do not want this variance specification to be transferred to the new model. You can use the following PVAR statement specification in the new model:

```pvar
v2 = .;
```

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

As discussed the section Default Partial Variance Parameters, PROC CALIS generates default free variance parameters for the exogenous variables and default free error variance parameters for the endogenous variables in the confirmatory FACTOR or PATH model. When you use the REFMODEL statement for defining a reference model, these default free variance parameters in the old (reference) model are not transferred to the new model. Instead, the new model generates its own set of default free variance parameters after the new model is resolved from the reference model, the REFMODEL statement options, the RENAMEPARM statement, and the PVAR statement specifications in the new model. If you want any of the variance or error (partial) variance parameters to be constrained across the models by means of the REFMODEL specification, you must specify them explicitly in the PVAR statement of the reference model so that the same variance or error (partial) variance specification is transferred to the new model.