New and Improved Modeling Languages in PROC CALIS

To accommodate various modeling backgrounds and philosophies of researchers, more modeling languages are supported in PROC CALIS. Three new modeling languages are provided: LISMOD, MSTRUCT, and PATH.

The LISMOD modeling language is a matrix-based parameter specification method modified from the LISREL model developed by Jöreskog and Sörbom. You can specify parameters as matrix entries by using the LISMOD language. For details, see the LISMOD statement.

The MSTRUCT modeling language is also a matrix-based parameter specification method. You can specify parameters directly in the structured mean and covariance matrices in this language. For details, see the MSTRUCT statement.

The PATH modeling language provides a tool to specify causal relations among variables by using paths (represented by arrows). It is especially suitable for path analysis, although it can also be applied to general structural models. For details, see the PATH statement.

Although the FACTOR modeling language is not new, its syntax has been changed for easier specification. Previously, the FACTOR language was a matrix-based specification methods in PROC CALIS. When you specify parameters in your model, you must use row and column numbers of the model matrices to refer to the variables involved. However, in this version of PROC CALIS, this matrix-based language is replaced by a more intuitive approach. For confirmatory factor analysis in PROC CALIS, you can specify the factors to variables paths (or loadings) by using the factor and variable names directly in the FACTOR statement.

To provide a quick and easy way to specify similar models, the REFMODEL statement is provided in PROC CALIS. Using this statement, you can specify a new model by referring to another well-defined model. Supporting options PARM_PREFIX= and PARM_SUFFIX= and the RENAMEPARM statement enable you to change parameter names efficiently.

Multiple-Group Analysis

You can do multiple-group analysis in PROC CALIS. Groups can also be fitted by multiple models simultaneously. You can use multiple GROUP statements to define independent groups of data. Within the scope of each GROUP statement, you can set group-specific attributes and options for the associated group. See the GROUP statement for details.

You can use multiple MODEL statements to define models and the groups they fit. Within the scope of each MODEL statement, you specify your model by using one of the modeling languages provided by PROC CALIS. You can use different modeling languages for different models. You can also set model-specific analysis and options for the model within the scope of a MODEL statement. See the MODEL statement for details.

Improved Mean Structures Analysis

In PROC CALIS, the mean structures are analyzed by means of augmented uncorrected moment matrices. This approach is an viable option only for maximum likelihood estimation. Often, this approach creates some interpretation problems in standardized results, R-square calculations, and so on. It is also difficult to set the mean parameters by using this approach.

In PROC CALIS, the mean structures are analyzed directly as a term in the objective function being optimized. This method is applicable to all estimation methods and yields more interpretable results. You can use the MEANSTR option in the PROC CALIS or MODEL statements to specify the analysis of mean structures explicitly. Alternatively, when you specify Intercept terms in LINEQS models, parameters in the MEAN statements, or parameters in the intercept or mean vector in the MATRIX statements, the mean structures of the model will be analyzed automatically.

As a result of the improved mean structures analysis, AUG, NOINT, UCOV, and UCORR options are obsolete in PROC CALIS.

General Parametric Function Testing

You can test any differentiable parametric functions separately or simultaneously by using the TESTFUNC and the SIMTESTS statements. A parametric function can be either a parameter in the model or a computed function defined by the SAS Programming statements. PROC CALIS will analytically generate the necessary partial derivatives for computing the test statistics.

Customizable Fit Summary Table

In PROC CALIS, you can customize the display of the fit summary table by selecting a subset of the fit indices to display. See the FITINDEX statement for details. You can also choose a particular type of chi-square correction for model fit chi-square statistics. A new OUTFIT= option enables you to store the fit indices in a SAS data set.

Improved Standardized Results

Standardized parameter estimates with standard errors are provided by default in PROC CALIS. You can turn off the printing of standard error estimates by the NOSE option. To suppress the printing of the entire standardized results, you can use the NOSTAND option.

The standardized results in PROC CALIS are somewhat different from that of PROC CALIS. In particular, in PROC CALIS path coefficients attached to error terms will remain equal to 1 after standardization. The error variances are rescaled appropriately so as to maintain mathematical consistency. In contrast, after standardization PROC CALIS will make all error variances equal to 1 and the path coefficients attached to error terms will not be 1 in general. For interpretation, this is not desirable because error terms, by nature, should be a non-deterministic term added without modification (that is, multiplied by a path coefficient) to the deterministic terms in an equation. In this sense, the standardized method in PROC CALIS is more interpretable.

Improved Effect Analysis

There are several improvements regarding the effects partitioning in PROC CALIS. First, standardized effects are displayed in addition to unstandardized effects. Second, standard error estimates are provided for the standardized and unstandardized effects. Third, you can customize the effects analysis by using the EFFPART statement. This will enable you to display only those effects of interest. See the EFFPART statement statement for details.

Customizable Lagrange Multiplier Tests

In PROC CALIS, you can set your own regions of the parameter space for the Lagrange multiplier (LM) tests. In the LMTESTS statement, you define sets of parameter regions. In each set, you include the regions of interest. In the output, LM statistics ranked within sets are displayed. The parameter that improves the model fit the most appears first. You can also set other display options in the LMTESTS statement.

More Rotation Options in Exploratory Factor Analysis

PROC CALIS provides more orthogonal and oblique rotation options for exploratory factor analytic solutions. See the ROTATE= option in the FACTOR statement for details.

Input Order Respecting

When you use the LINEQS statement, PROC CALIS displays equations in the order you specify in the input. The terms within each equation are also ordered the same way you specify them. Unfortunately, previous versions of PROC CALIS does not have these properties—it might display equations and terms in a certain order that is not consistent with the input.

PROC CALIS also respects the order of parameter specification in the following statements:

• COV

• MEAN

• PATH

• PCOV

• PVAR

• RAM

• VARIANCE

If you want to order the specification by parameter types, you can use the ORDERSPEC option.

PROC CALIS also respects order when displaying model and group results. By default, the output results for models or groups follow the order of your input. By using the ORDERMODELS and ORDERGROUPS options, the output results for models or groups are ordered by the model or group numbers provided in the specification. The ORDERALL option combines all these ordering options.

Improved OUTRAM= (OUTMODEL=) Data Set Format

The OUTRAM= data sets in PROC CALIS stores the model specifications in terms of the RAM model matrix entries, even if the original model is specified by the LINEQS or FACTOR modeling language. The problem is that the modeler who did not write the original code in the RAM modeling language might not understand the contents of the OUTRAM= data set. This inconsistency is eliminated in PROC CALIS by means of the new OUTMODEL= option (although you can still use the OUTRAM= option for the same purpose). In the OUTMODEL= data sets, different types of models would have different types of observations. The types of observations resemble closely the original modeling language used. See the OUTMODEL= option and the section OUTMODEL= SAS-data-set for more details.

Covariance and Mean Structure Analysis with the COSAN Model

PROC CALIS now supports covariance and mean structure analysis in the COSAN model. You can specify the central mean vector in each term of the mean structure formula. See the COSAN statement and the section The COSAN Model for details.

Improved RAM Model Specification

You can now specify the variable list explicitly in the VAR= option of the RAM statement. This variable list is useful to make immediate references of the variables (manifest or latent) in the model. The mean structure specification of the RAM model is also supported. Note that the RAM statement syntax in PROC TCALIS (SAS/STAT 9.2) is not supported. See the RAM statement and the section The RAM Model for details.

Extended PATH Modeling Language

You can specify variances, covariances, means, and intercepts as paths in the PATH statement. The syntax enables you to map all the parameters in the path diagram to the PATH statement specification. See the section Extended Path Modeling Language of the PATH statement for details. If you specify variances, covariances, means, or intercepts in the PVAR, PCOV, and MEAN statements, you can display these parameter estimates as paths in the table for the ordinary path effect (coefficient) estimates by using the EXTENDPATH option.

Full Information Maximum Likelihood Method

PROC CALIS implements the full information maximum likelihood method (FIML) for treating data with random missing values. The FIML method uses all the available information from the data set, including observations with missing values, so that it is statistically more efficient than the ML (maximum likelihood) method (as implemented in PROC CALIS). You can use METHOD=FIML to invoke the FIML method. Exploratory factor analysis and model modification indices and are not available with METHOD=FIML in this version of PROC CALIS.

Unnamed Free Parameter Specification

You can specify free parameters in all models without using explicit parameter names (that is, unnamed free parameters). This makes your model specification more efficient. For example, in the PATH statement, you can specify only the paths without using the parameter names for the path effects (coefficients). PROC CALIS generates the parameter names automatically. However, you can also input the parameter names whenever it is necessary (for example, for setting parameter constraints). Unnamed free parameters specification is supported in all modeling languages. For details, see the syntax of the following statements: COV, FACTOR, LINEQS, MATRIX, MEAN, PATH, PCOV, PVAR, RAM, and VARIANCE.

Default Parameterization

To make model specification more efficient, PROC CALIS uses some rules for setting default free or fixed parameters in the models. Note that these rules for default parameters might have changed from previous versions of PROC CALIS or PROC TCALIS. In addition, different model types might use different rules for default parameters. Fortunately, PROC CALIS employs rules that are compatible with conventional uses. For details, see the descriptions of the default parameters in the syntax section of the following statements: COSAN, COV, FACTOR, LINEQS, LISMOD, MEAN, MSTRUCT, PATH, PCOV, PVAR, RAM, and VARIANCE.

The following sections for different types of models are also useful:

• Default Parameters in the COSAN Model

• Default Parameters in the FACTOR Model

• Default Parameters in the LINEQS Model

• Default Parameters in the LISMOD Model

• Default Parameters in the MSTRUCT Model

• Default Parameters in the PATH Model

• Default Parameters in the RAM Model