Overview of PROC TCALIS

The section Overview: TCALIS Procedure gives you an overview of the PROC TCALIS procedure and an overall picture of the TCALIS procedure but without the details.

Changes and Enhancement from PROC CALIS

Read the section Changes and Enhancement from PROC CALIS if you have previous experience with PROC CALIS, the predecessor of PROC TCALIS. If you have not used PROC CALIS previously, you may skip this section.

Basic Model Specification

The structural equation example in the section Getting Started: TCALIS Procedure provides the best starting point for learning the basic model specification. You learn how to represent your theory by using a path diagram and then translate the diagram into the PATH model for PROC TCALIS to analyze. Because the PATH modeling language is new, this example is useful whether or not you have previous experience with PROC CALIS. The PATH model is specified in the section PATH Model. The corresponding results are shown and discussed in Example 88.1.

After you learn about the PATH modeling language and an example of its application, you can either continue to learn more modeling languages or skip to the syntax overview. However, you do not need to learn all of the modeling languages in PROC TCALIS. Any one of the modeling languages (LINEQS, LISMOD, PATH, or RAM) is sufficient for specifying a very wide class of structural equation models. PROC TCALIS provides different kinds of modeling languages because different researchers might have previously learned different modeling languages or approaches.

You can go to the next step for an overview of the PROC TCALIS syntax and learn other modeling languages at a later time. See Getting Started: TCALIS Procedure for a brief overview of the various modeling languages. In these examples, model specifications are shown and explained, but no analysis results are discussed. Each subsection discusses the same model but uses a different modeling language. In the subsections LISMOD Model, LINEQS Model, and RAM Model, you learn how to specify a structural equation model equivalently by using the LINEQS, LISMOD, and RAM modeling languages, respectively. In the subsection A Factor Model Example, you learn how to specify a confirmatory factor model by using the FACTOR modeling language. In the subsection Direct Covariance Structures Analysis, you learn how to specify the covariance structures directly on the covariance matrix by using the MSTRUCT modeling language.

After studying the examples in the Getting Started: TCALIS Procedure section, you can strengthen your understanding of the various modeling languages by studying more examples such as those in section Examples: TCALIS Procedure. Unlike the examples in the Getting Started: TCALIS Procedure section, examples in the Examples: TCALIS Procedure section include the analysis results, in addition to the explanations of the model specifications. The following figure provides a guide to studying the examples in the Examples: TCALIS Procedure section.

Example 88.1. Path Analysis: Stability of Alienation

In this example, you learn how to specify a simple PATH model and interpret the basic estimation results. The results are shown in considerable detail. The output and analyses include: a model summary, initial model specification, initial estimation method, optimization history and results, residual analyses, residual graphics, estimation results, squared multiple correlations, and standardized results.

Example 88.2. Simultaneous Equations with Mean Structures and Reciprocal Paths

In this econometric example, you learn how to specify models using the LINEQS modeling language. This example also illustrates the specification of reciprocal effects, the simultaneous analysis of the mean and covariance structures, the setting of bounds for parameters, and the definitions of meta-parameters by using the PARAMETERS and SAS programming statements. You also learn how to shorten your output results by using some global display options such as the PSHORT and NOSTAND options in the PROC TCALIS statement.

Example 88.3. A Direct Covariance Structures Model

In this example, you fit your covariance structures directly on the covariance matrix by using the MSTRUCT modeling language. You also learn how to use the FITINDEX statement to create a customized model fit summary and how to save the fit summary statistics into an external file.

Example 88.4. Confirmatory Factor Analysis: Cognitive Abilities

Confirmatory factor analysis is illustrated in this example by using the FACTOR modeling language. In addition, you use the MODIFICATION option in the PROC TCALIS statement to compute LM test indices for model modifications.

Example 88.5. Testing Equality of Two Covariance Matrices Using A Multiple-Group Analysis

In this example, a simple multiple-group analysis is illustrated by the MSTRUCT modeling language. You also learn how to use the ods select statement to customize your printed output.

Example 88.6. Illustrating Various General Modeling Languages

This example extends Example 88.1, which uses the PATH modeling language, and shows how to use the other general modeling languages: RAM, LINEQS, and LISMOD. These modeling languages enable you to specify the same path model as in Example 88.1 and get equivalent results. This example shows the connections between the general modeling languages supported in PROC TCALIS. A good understanding of Example 88.1 is a prerequisite for this example.

Example 88.7. Fitting a Latent Growth Curve Model

This is an advanced example that illustrates the use of structural equation modeling techniques for fitting latent growth curve models. In this example, you learn how to specify random intercepts and random slopes by using the LINEQS modeling language. In addition to the modeling of the covariance structures, you also learn how to specify the mean structure parameters.

Example 88.8. Higher-Order and Hierarchical Factor Models

This is an advanced example for confirmatory factor analysis. It involves the specifications of higher-order and hierarchical factor models. Because higher-order factor models cannot be specified by the FACTOR modeling language, you need to use the LINEQS model specification instead. A second-order factor model and a bifactor model are fit. Linear constraints on parameters are illustrated by using the PARAMETERS and the SAS programming statements. Relationships between the second-order factor model and the bifactor model are numerically illustrated.

Example 88.9. Linear Relations Among Factor Loadings

This is an advanced example of a first-order confirmatory factor analysis by using the FACTOR modeling language. In this example, you learn how to use the PARAMETERS and the SAS programming statements to set up dependent parameters in your model. You also learn how to specify the correlation structures for a specific confirmatory factor model.

Example 88.10. A Multiple-group Model for Purchasing Behavior

This is a sophisticated example of analyzing a path model. The PATH modeling language is used. In this example, a two-group analysis of mean and covariance structures is conducted. You learn how to use a SAS macro to organize your model specification, the REFMODEL statement to reference properly defined models, and the SIMTEST statement to test a priori simultaneous hypotheses.

Once you are familiar with various modeling languages, you might wonder which modeling language should be used in a given situation. The section Which Modeling Language? provides some guidelines and suggestions.