MEAN Statement |
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.
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, all the means and intercepts of the manifest variables in the confirmatory FACTOR, LINEQS, or PATH model are free parameters by default. For these default free mean or intercept parameters, PROC CALIS generate the parameter names with the _Add prefix and appended with unique integer suffixes. For the FACTOR and PATH model, you can use the MEAN statement specification 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. 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 FACTOR and PATH models, you can override these default fixed zeros by using the MEAN statement specifications. However, for the LINEQS model, you can override only the default fixed zeros of the 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 the model restrictions. There is no way you can override these default zero means.
If you define a new FACTOR, 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.