MSTRUCT stands for matrix structures. As opposed to other modeling languages, in which the mean and covariance structures are implied from paths, equations, or complicated model matrix computations, the MSTRUCT language is for direct structured mean and covariance models.
In the MSTRUCT statement, you define the list of variables. You can use MATRIX statements to specify the parameters in the mean and covariance structures:
You use the MATRIX _COV_ statement to specify the covariance and variance parameters in the structured covariance matrix. When applicable, you use the MATRIX _MEAN_ statement to specify the parameters in the structured mean vector. Each of these matrices can be specified no more than once within a model. See the MATRIX statement for details. If you do not use any MATRIX statement for specifying parameters, a saturated model is assumed. This means that all elements in the covariance and mean (if modeled) matrices are free parameters in the model.
The order of variables in the var-list of the MSTRUCT statement is important; it is used to refer to the row and column variables of the _COV_ and the _MEAN_ matrices. The variables specified in the list should be present in the input data set that is intended for the MSTRUCT model. With direct mean and covariance structures on the observed variables, no latent variables are explicitly involved in the MSTRUCT modeling language. However, this does not mean that the MSTRUCT modeling language cannot handle latent variable models. With additional specifications in the PARAMETERS and the SAS programming statements , it is possible to fit certain latent variable models by using the MSTRUCT modeling language. Despite this, the code might get too complicated and error-prone. Hence, using the MSTRUCT modeling language for latent variable modeling is not recommended for novice users. The LINEQS, LISMOD, PATH, or RAM modeling language should be considered first for latent variable modeling. For applications of the MSTRUCT modeling, see Yung, Browne, and Zhang (2014).
It is important to understand the default parameters in the MSTRUCT model. If you know which parameters are default free parameters, you can make your specification more efficient by omitting the specifications of those parameters that can be set by default. For example, you do not need to specify any elements of the _COV_ matrix if all elements are supposed to free parameters. See the section Default Parameters in the MSTRUCT Model for details about the default parameters of the FACTOR model.
This section assumes that you use a REFMODEL statement within the scope of a MODEL statement and that the reference model (or base model) is also an MSTRUCT model. The reference model is called the old model, and the model that refers to the old model is called the new model. If the new model is not intended to be an exact copy of the old model, you can use the following extended MSTRUCT modeling language to make modifications within the scope of the MODEL statement for the new model. The syntax is similar to, but not exactly the same as, the ordinary MSTRUCT modeling language, as described in the section MSTRUCT Statement. The syntax for respecifying or modifying an MSTRUCT model takes the following form:
In the respecification, you should not put any VAR= list in the MSTRUCT statement, as you would do for specifying the original base model. The reason is that parameter respecifications in the new model refer to the variables in the VAR= list of the old model. Therefore, the VAR= list in the new model is implicitly assumed to be exactly the same as that in the old model. This renders the specification of a VAR= list of the MSTRUCT statement of the new model unnecessary. Because the VAR= option is the only possible option in the MSTRUCT statement, it also implies that the entire MSTRUCT statement is optional for the new model.
You can use the MATRIX _COV_ and MATRIX _MEAN_ statements to modify from the old model by using the same syntax as in ordinary MSTRUCT modeling language. In addition, in the respecification syntax, you can use the missing value '.' to drop a parameter location from the old model.
The new model is formed by integrating with the old model in the following ways:
If you do not specify in the new model a parameter location that exists in the old model, the old parameter specification is duplicated in the new model.
If you specify in the new model a parameter location that does not exist in the old model, the new parameter specification is used in the new model.
If you specify in the new model a parameter location that also exists in the old model and the new parameter is denoted by the missing value '.', the old parameter specification is not copied into the new model.
If you specify in the new model a parameter location that also exists in the old model and the new parameter is not denoted by the missing value '.', the new parameter specification replaces the old one in the new model.
For example, consider the following statements for a two-group analysis:
proc calis; group 1 / data=d1; group 2 / data=d2; model 1 / group=1; mstruct var=V1-V6; matrix _COV_ [1,1] = 6*vparm (8.), [2,] = cv21, [3,] = cv31, [4,] = cv41 cv42 cv43, [5,] = cv51 cv52 cv53 cv54, [6,] = cv61 cv62 cv63 cv64 cv65; model 2 / group=2; refmodel 1; matrix _COV_ [2,] = 3., [3,2] = cv32, [4,] = . . . , [5,] = . . . , [6,] = . . . ; run;
In these statements, you specify Model 2 by referring to Model 1 in the REFMODEL
statement. Hence, Model 2 is called the new model that refers to the old model, Model 1. Because they are not respecified
in the new model, all parameters on the diagonal of the covariance matrix are duplicated from the old model for the new model.
Similarly, parameter locations associated with the cv54
, cv64
, and cv65
parameters are also duplicated in the new model.
An added parameter in the new model is cv32
for the covariance between V3
and V2
. This parameter location is not specified in the old model.
In the new model, parameters for the covariances between the variable sets {V1
V2
V3
} and {V4
V5
V6
} are all deleted from the old model. The corresponding parameter locations for these covariances are given missing values
'.' in the new model, indicating that they are no longer free parameters as in the old model. Deleting these parameters amounts
to setting the corresponding covariances to fixed zeros in the new model.
Finally, covariance between V2
and V1
is changed from a free parameter cv21
in the old model to a fixed constant 3 in the new model. This illustrates the replacement rule of the respecification syntax.