Default Analysis Type and Default Parameterization

This section describes the default analysis type and default parameterization of PROC CALIS. Because various types of models supported by PROC CALIS have their own specific features, the following table outlines only those major default settings of PROC CALIS in SAS/STAT 9.22 or later:

Moment Structures Analyzed

Covariance structures

Covariance structures are analyzed by default (COVARIANCE option).

Mean structures

Not analyzed by default. Use the MEANSTR option, the 'Intercept' variable in the LINEQS statement, the MEAN statement, or specific MATRIX statements to specify mean or intercept parameters.

Default Parameterization

Variance parameters

Free variance parameters for independent latent factors, observed variables, and errors.

Covariance parameters

Free covariance parameters for all pairs of independent latent factors and observed variables (except for the latent factors in exploratory factor models). Fixed zero covariances for all pairs of error variables, all pairs between errors and other exogenous variables, and all pairs of latent factors in exploratory factor models.

Mean parameters

Free mean parameters for all exogenous observed variables. Fixed zero means for all exogenous latent factors and error terms.

Intercept parameters

Free intercept parameters for all endogenous observed variables; Fixed zero intercepts for all endogenous latent factors.

Role of the VAR Statement in Model Specification

Inclusion of Variables

If the VAR statement is used, observed variables that are listed in the VAR statement but not mentioned in corresponding model specification are included as exogenous variables in the model. Default variance, covariance, and mean parameterization apply to these exogenous variables.

Exclusion of Variables

If the VAR statement is used, observed variables that are not listed in the VAR statement are not recognized as observed variables in model specification. They might be treated as latent variables instead.

In general, the default settings of PROC CALIS in SAS/STAT 9.22 and later are more consistent with conventional practice of structural equation modeling. For example, because statistical theory of structural equation modeling is based mainly on the analysis of covariance structures, the default analysis type of PROC CALIS in SAS/STAT 9.22 or later is for covariance structures. This means that the CORR option must be specified if you want to analyze correlation matrices. Mean structures in PROC CALIS have also been parameterized more naturally since SAS/STAT 9.22 so that users can make statistical inferences directly on the mean and intercept estimates. Default variance and covariance parameters for all independent factors and observed variables have been implemented since SAS/STAT 9.22 to reflect the common belief that no exogenous variables are absolutely uncorrelated (except for the unrotated factors in the initial solution of exploratory FACTOR models).

For comparisons of these and other default settings before and after SAS/STAT 9.22, see the section Compatibility with the CALIS Procedure in SAS/STAT 9.2 or Earlier.

For details about the default parameters in specific types of model, see the FACTOR, LINEQS, LISMOD, PATH, and RAM statements. Because there are no explicit latent variables and the exogenous/endogenous variable distinction is not used in the COSAN and MSTRUCT modeling languages, the default parameterization outlined in the preceding table does not apply to these two types of models. See the COSAN and the MSTRUCT statements for details. See the following sections for details about model parameterization in various types of models:

By default, PROC CALIS in SAS/STAT 9.22 or later treats observed variables specified in the VAR statement as exogenous variables in the FACTOR, PATH, LINEQS, and RAM models. This minimizes the routine specifications in the COVARIANCE, MEAN, PCOV, PVAR, or VARIANCE for those standalone exogenous observed variables— observed variables that are not functionally related to any other variables in the model. Including these standalone exogenous observed variables into the model is useful during the model modification process (by the MODIFICATION option) where you can do Lagrange multiplier tests to see whether relating these variables to other variables can improve the model fit.

Notice that the use of the VAR statement specification is optional in PROC CALIS. If you have specified all the observed variables that you want in the model specification statements, it is not necessary to use the VAR statement specifications for the purpose of specifying the set of observed variable for analysis.