|The TCALIS Procedure|
The MEAN statement invokes the fitting of the mean structures of the model. The MEAN statement is one of the subsidiary model specification statements for supplementing modeling specification. You can use the MEAN statements to specify mean parameters in the FACTOR, LINEQS, and PATH modeling languages. You can also use the MEAN statement to specify the intercept parameters in the FACTOR or PATH modeling languages. The syntax of the MEAN statement is essentially the same as that of the STD or PVAR statement.
In each assignment of the MEAN statement, you put the variables on the left-hand side of the equal sign and specify the parameters on the right-hand side parameter-spec. Like elsewhere in the PROC TCALIS syntax, in parameter-spec you can put numbers for fixed values or parameter names for free or constrained parameters. Parameter names are optionally followed by numbers in parentheses for starting values. See the STD statement for examples.
In the FACTOR or PATH model, the variables in each assignment can be exogenous or endogenous. If a variable in the variables list is exogenous, the corresponding parameter is the mean parameter for the variable. Otherwise, the corresponding parameter is the intercept parameter for the variable. In the LINEQS model, however, only non-error type exogenous variables (that is, not E- or D- variables) can be used in the MEAN statement. The parameters are for the means of the exogenous variables. You cannot specify the intercept parameters in the MEAN statement of the LINEQS modeling language. Instead, you should specify intercepts in the equations of the LINEQS statement.
If the names of any exogenous manifest variables in the LINEQS model are not included in the MEAN statement, the means of those exogenous manifest variables are assumed to be parameters to estimate. These parameters will be named automatically with the prefix _Add and appended with integer suffixes. However, all other mean parameters other than those for exogenous manifest variables are fixed zeros by default unless they are specified otherwise in the MEAN statement. In addition, all intercept parameters are assumed to be fixed zeros, unless they are specified otherwise in the LINEQS statement.
If you define a new FACTOR, LINEQS, or 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 MEAN statement of the reference model before transferring the specifications to the new model. If you want to change a particular MEAN 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 LINEQS model by using the REFMODEL statement and the mean of variable F1 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:
mean F1 = .;
Notice 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.
In LINEQS models, all means of exogenous manifest variables are free parameters to estimate unless you specify otherwise in the MEAN statement (see the section Automatic Mean Parameters among Exogenous Variables). This is also true for LINEQS models specified under the REFMODEL statement. In the reference model, mean 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 options, and model respecifications are the additional mean parameters with the _Add prefix generated for the remaining unspecified means of exogenous manifest variables. In this way, the generated mean parameters for the exogenous mainfest variables in the new model are not constrained to be the same as the corresponding means in the reference model. If you want any of these mean parameters to be constrained across the models, you must specify them explicitly in the MEAN statement of the reference model so that the constrained mean specifications are transferred to the new model.
Note: This procedure is experimental.