where assignment represents: var-list < = parameter-spec>
The MEAN statement specifies the mean or intercept parameters in connection with the FACTOR, LINEQS, and PATH modeling languages. With the MEAN statement specification, PROC CALIS analyzes the mean structures in addition to the covariance structures.
In each assignment of the MEAN statement, you list the var-list that you want to specify for their means or intercepts. Optionally, you can provide a list of parameter specifications in a parameter-spec after an equal sign for each var-list. The syntax of the MEAN statement is exactly the same as that of the VARIANCE statement. See the VARIANCE statement for details about the syntax.
For the confirmatory FACTOR or PATH model, the variables in a var-list can be exogenous or endogenous. You specify the mean of a variable if the variable is exogenous. You specify the intercept of a variable if the variable is endogenous. However, for the LINEQS model, you can specify only the means of exogenous variables whose type is not error (that is, not the E- or D- variables) in the MEAN statement. You cannot specify the intercept parameters in the MEAN statement for the LINEQS model. Instead, you must specify the intercepts in the equations of the LINEQS statement. For the exploratory FACTOR model, the MEAN statement is used merely to include the mean structures into analysis. In this case, the parameter specification by the assignment syntax is not interpreted. Instead, the intercept parameters for the exploratory factor model are automatically generated by PROC CALIS.
You can specify the following five types of the parameters for the means or intercepts in the MEAN 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 MEAN statement illustrates the five types of specifications in five assignments:
mean x1 , x2 = (3.0), x3 = 1.5, y4 = intercept1, y5 = intercept2(0.6);
In this statement, the mean of x1
is specified as an unnamed free parameter. For this mean, PROC CALIS generates a parameter name with the _Parm
prefix and appended with a unique integer (for example, _Parm1
). The mean of x2
is an unnamed free parameter with an initial value of 3.0. PROC CALIS also generates a parameter name for this mean. The
mean of x3
is a fixed value of 1.5. This value stays the same during the estimation. The intercept of endogenous variable y4
is a free parameter named intercept1
. The intercept of endogenous variable y5
is a free parameter named intercept2
with an initial value of 0.6.
The syntax of the MEAN statement is the same as the syntax of the VARIANCE statement. See the VARIANCE statement for more illustrations about the usage.
If the mean structures are analyzed, either the means or intercepts of the manifest variables in the FACTOR, LINEQS, or PATH model are free parameters by default. If a manifest variable is exogenous, then
its mean is a free parameter by default. If a manifest variable is endogenous, then its intercept is a free parameter by default.
Except for the exploratory FACTOR model, PROC CALIS generates parameter names for these default free mean or intercept parameters
that include the _Add
prefix and are appended with unique integer suffixes. The default intercepts of the exploratory FACTOR model use the _a
prefix instead. For the confirmatory FACTOR model and the PATH model, you can use the MEAN statement to override these default
mean or intercept parameters in situations where you want to set parameter constraints, provide initial or fixed values, or
make parameter references. However, you cannot override any default intercept parameters for the exploratory FACTOR model.
For the LINEQS model, you can use the MEAN statement specification to override only the default mean parameters. The intercept
parameters of the LINEQS model must be specified in the equations of the LINEQS
statement.
Fixed zero is another type of default mean or intercept parameters for the FACTOR, LINEQS, or PATH model. All the intercepts and means of the latent variables in these models are fixed zeros by default. For the confirmatory FACTOR and PATH models, you can override these default fixed zeros by using the MEAN statement specifications. However, you cannot override the fixed zero factor means for the exploratory FACTOR model, For the LINEQS model, you can override only the default fixed zeros of latent variables whose type is not error. That is, you can use the MEAN statement to override the default zero mean for the exogenous latent factors (excluding the error or disturbance variables) or use the LINEQS statement to override the default zero intercept for the endogenous latent factors. The fixed zero means for the error or disturbance variables in the LINEQS model reflects model restrictionsâ€”there is no way you can override these default zero means.
If you define a new FACTOR (confirmatory factor model only), LINEQS, or PATH model by using a reference (old) model in the REFMODEL statement, you might want to modify some parameter specifications from the MEAN statement of the reference model before transferring the specifications to the new model. To change a particular mean or intercept specification from the reference model, you can simply respecify the same mean or intercept with the desired parameter specification in the MEAN statement of the new model. To delete a particular mean or intercept parameter from the reference model, you can specify the desired mean or intercept with a missing value specification in the MEAN statement of the new model.
For example, suppose that the mean of F1
is specified in the reference model, but you do not want this mean specification be transferred to the new model. You can
use the following MEAN statement specification in the new model:
mean F1 = .;
Note that the missing value syntax is valid only when you use with 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 LINEQS Model from a Reference Model for a more detailed example of LINEQS model respecification. See the section Modifying a PATH Model from a Reference Model for a more detailed example of PATH model respecification.
As discussed in a preceding section, PROC CALIS generates default free mean or intercept parameters for manifest variables in the FACTOR, LINEQS, or PATH model if you do not specify them explicitly in the MEAN statement (and the LINEQS statement for the LINEQS model). When you use the REFMODEL statement for defining a reference model, these default free mean or intercept parameters in the old (reference) model are not transferred to the new model. Instead, the new model generates its own set of default free mean or intercept parameters after the new model is resolved from the reference model, the REFMODEL statement options, the RENAMEPARM statement, and the MEAN statement (and the LINEQS statement for the LINEQS model) specifications in the new model. This also implies that if you want any of the mean or intercept parameters to be constrained across the models by means of the REFMODEL specification, you must specify them explicitly in the MEAN statement (or the LINEQS statement for the LINEQS model) of the reference model so that the same mean or intercept specification is transferred to the new model.