|The TCALIS Procedure|
The STD statement defines the variance parameters in the LINEQS models. STD, instead of VAR, is used as the statement name for defining variance parameters because it avoids conflicts with the VAR statement for specifying variables for analysis. You can specify no more than one STD statement with each LINEQS statement.
In each assignment of the STD statement, you specify the variance parameters of the variables. The variables are specified on the left-hand side of the equal sign of each assignment, while the parameter in the parameter-spec list on the right-hand side of the equal sign might be one of the following types:
free or constrained parameters without starting values
Names in the parameter-spec list denote parameters to estimate. They might be free or constrained parameters.
free or constrained parameters with starting values
Names followed by numbers inside a pair of parentheses in the parameter-spec list denote free or constrained parameters with starting values given by the parenthesized numbers.
fixed parameter values
Fixed constants not inside a pair of parentheses in the parameter-spec list denote fixed parameter values.
The assignments in the STD statement must be separated by commas. The variables listed on the left-hand side of the equal sign should contain only names of exogenous variables—that is, variance parameters in the LINEQS model are defined only for exogenous mainfest or latent variables, errors, and disturbances.
If the parameter-spec list is longer than the variables list, the parameter-spec list is shortened to the length of the variables list. If the parameter-spec is shorter than the variables list, the parameter-spec list is filled with repetitions of the last item in the list.
The parameter-spec list can contain prefix names. A prefix name is a short name called "root" followed by two underscores, '__'. A prefix name without a root (that is, as in '__') has its root replaced with parm. Whenever a prefix name is encountered, the TCALIS procedure generates a parameter name by appending a unique integer to the root of the prefix name. The root of the prefix name should have few characters so that the generated parameter name is not longer than 32 characters. To avoid unintentional equality constraints, the prefix names should not coincide with explicitly defined parameter names.
To illustrate various specification in the STD statement, consider the following statement:
std E1-E6 = vp1 GEN__ (1. 2.) GEN__ 4. vp5 ;
You specify the variance of E1 as a free parameter vp1 with a starting value at 1. The variance of E2 is a parameter named GEN1, with a starting value at 2. The variance of E3 is a parameter named GEN2, without a starting value provided. The variance of E4 is fixed at 4. The variance of E5 is parameter vp5, without a starting value given. Finally, the variance of E6 is denoted also by parameter vp5 because the parameter-spec list is shorter than the variables list so that the last member in the parameter-spec list is repeated.
If the names of any exogenous variables (manifest, latent, or errors) in the LINEQS model are not included in the STD statement, the variances of those exogenous variables are assumed to be parameters to estimate. These parameters will be named automatically with the prefix _Add and appended with a unique integer in each name generation.
If you define a new LINEQS 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 STD statement of the reference model before transferring the specifications to the new model. If you want to change a particular STD 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 variance of variable V1 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:
std V1 = .;
Notice that the missing value syntax is valid only when you use the REFMODEL statement. For a more detailed example of the LINEQS model respecification (see the section Modifying a LINEQS Model from a Reference Model).
In the LINEQS model, all variances among exogenous variables are free parameters to estimate unless you specify otherwise in the STD statement (see the section Automatic Variance Parameters among Exogenous Variables). This is also true for LINEQS models specified under the REFMODEL statement. In the reference model, variance 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 the model respecifications are the unspecified variances of exogenous variables generated as free parameters named with the _Add prefix and integer suffixes. In this way, the variance parameters in the new model are not constrained to be the same as the corresponding parameters in the reference model. If you want any of these variance parameters constrained across the models, you must specify them explicitly in the STD statement of the reference model so that the variance specification is transferred to the new model.
Note: This procedure is experimental.