New Modeling Languages in PROC TCALIS

To accommodate various modeling backgrounds and philosophies of researchers, more modeling languages are supported in PROC TCALIS. 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 and RAM modeling languages are not new, their syntax has been changed for easier specifications. The FACTOR and RAM modeling languages are both 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 PROC TCALIS these matrix-based languages are replaced by the more intuitive approach. For confirmatory factor analysis in PROC TCALIS, you can specify the factors to variables paths (or loadings) by using the factor and variable names directly in the FACTOR statement. For the RAM specification in PROC TCALIS, you no longer need to implicitly assume a certain order for the variables and factors in matrices, as you do in PROC CALIS. Also, you no longer need to use the matrix numbers to refer to the types of parameter specifications. In each parameter specification of the RAM statement in PROC TCALIS, the variables and the parameter type involved are specified directly by using the variable names or meaningful keywords for parameter types.

To provide a quick and easy way to specify similar models, the REFMODEL statement is provided in PROC TCALIS. 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 TCALIS. 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 TCALIS. 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 TCALIS, 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 TCALIS 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 TCALIS.

General Parametric Function Testing

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

Customizable Fit Summary Table

In PROC TCALIS, 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 an external data set.

Improved Standardized Results

Standardized parameter estimates with standard errors are provided by default in PROC TCALIS. 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 TCALIS are somewhat different from that of PROC CALIS. In particular, in PROC TCALIS 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 TCALIS is more interpretable.

Improved Effect Analysis

There are several improvements regarding the effects partitioning in PROC TCALIS. 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 TCALIS, 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 TCALIS 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 TCALIS will display equations in the order you specify in the input. The terms within each equation are also ordered the same way you specify them. Unfortunately, PROC CALIS does not have these properties. PROC CALIS might display equations and terms in a certain order that is not consistent with the input.

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

• COV

• MEAN

• PATH

• PCOV

• PVAR

• RAM

• STD

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

PROC TCALIS 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= 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 TCALIS 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.