The CALIS Procedure

You can continue to learn more modeling languages in the section Getting Started: CALIS Procedure.

You can skip to the section Syntax Overview for an overview of the PROC CALIS syntax and learn other modeling languages at a later time.

LINEQS: Section LINEQS Model

RAM: Section RAM Model

LISMOD: Section LISMOD Model

FACTOR: Section A Factor Model Example

MSTRUCT: Section Direct Covariance Structures Analysis

MSTRUCT model examples The basic MSTRUCT model examples demonstrate the testing of covariance structures directly on the covariance matrices. Although the MSTRUCT model is not the most common structural equation models in applications, these MSTRUCT examples can help you understand the basic form of covariance structures and the corresponding specifications in PROC CALIS.

PATH model examples The basic PATH model examples demonstrate how you can represent your model by path diagrams and by the PATH modeling language. These examples show the most common applications of structural equation modeling.

Example 29.1, Estimating Covariances and Correlations shows how you can estimate the covariances and correlations with standard error estimates for the variables in your model. The model you fit is a saturated covariance structure model.

Example 29.2, Estimating Covariances and Means Simultaneously extends Example 29.1 to include the mean structures in the model. The model you fit is a saturated mean and covariance structure model.

Example 29.3, Testing Uncorrelatedness of Variables shows a very basic covariance structure model, in which the covariance structures can be specified directly. The variables in this model are uncorrelated. You learn how to specify the covariance pattern directly.

Example 29.4, Testing Covariance Patterns extends Example 29.3 to include other covariance structures that you can specify directly.

Example 29.5, Testing Some Standard Covariance Pattern Hypotheses illustrates the use of built-in covariance patterns supported by PROC CALIS.

Example 29.6, Linear Regression Model shows how you can fit a linear regression model with the PATH modeling language of PROC CALIS. This example also introduces the path diagram representation of "causal" models. You compare results obtained from PROC CALIS and from the REG procedure, which is designed specifically for regression analysis.

Example 29.7, Multivariate Regression Models extends Example 29.6 in several different ways. You fit covariance structure models with more than one predictor, with direct and indirect effects. This example also discusses how you can choose the "best" model for your data.

Example 29.8, Measurement Error Models explores the case where the predictor in simple linear regression is measured with error. The concept of latent true score variable is introduced. You use PROC CALIS to fit a simple measurement error model.

Example 29.9, Testing Specific Measurement Error Models extends Example 29.8 to test special measurement error models with constraints. By using PROC CALIS, you can constrain your measurement error models in many different ways. For example, you can constrain the error variances or the intercepts to test specific hypotheses.

Example 29.10, Measurement Error Models with Multiple Predictors extends Example 29.8 to include more predictors in the measurement error models. The measurement errors in the predictors can be correlated in the model.

Example 29.17, Path Analysis: Stability of Alienation shows you 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, an initial model specification, an initial estimation method, an optimization history and results, residual analyses, residual graphics, estimation results, squared multiple correlations, and standardized results.

Example 29.19, Fitting Direct Covariance Structures shows you how to 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 29.21, Testing Equality of Two Covariance Matrices Using a Multiple-Group Analysis uses the MSTRUCT modeling language to illustrate a simple multiple-group analysis. You also learn how to use the ODS SELECT statement to customize your printed output.

Example 29.22, Testing Equality of Covariance and Mean Matrices between Independent Groups uses the COVPATTERN= and MEANPATTERN= options to show some tests of equality of covariance and mean matrices between independent groups. It also illustrates how you can improve your model fit by the exploratory use of the Lagrange multiplier statistics for releasing equality constraints.

Example 29.24, Testing Competing Path Models for the Career Aspiration Data illustrates how you can fit competing models by using the OUTMODEL= and INMODEL= data sets for transferring and modifying model information from one analysis to another. This example also demonstrates how you can choose the best model among several competing models for the same data.

Example 29.11, Measurement Error Models Specified As Linear Equations explores another way to specify measurement error models in PROC CALIS. The LINEQS modeling language is introduced. You learn how to specify linear equations of the measurement error model by using the LINEQS statement. Unlike the PATH modeling language, in the LINEQS modeling language, you need to specify the error terms explicitly in the model specification.

Example 29.12, Confirmatory Factor Models introduces a basic confirmatory factor model for test items. You use the FACTOR modeling language to specify the factor-variable relationships.

Example 29.13, Confirmatory Factor Models: Some Variations extends Example 29.12 to include some variants of the confirmatory factor model. With the flexibility of the FACTOR modeling language, this example shows how you fit models with parallel items, tau-equivalent items, or partially parallel items.

Example 29.14, Residual Diagnostics and Robust Estimation illustrates the use of several graphical residual plots to detect model outliers and leverage observations, to study the departures from the theoretical case-level residual distribution, and to examine the linearity and homoscedasticity of variance. In addition, this example illustrates the use of robust estimation technique to downweight the outliers and to estimate the model parameters.

Example 29.15, The Full Information Maximum Likelihood Method shows how you can use the full information maximum likelihood (FIML) method to estimate your model when your data contain missing values. It illustrates the analysis of the data coverage of the sample variances, covariances, and means and the analysis of missing patterns and the mean profile. It also shows that the full information maximum likelihood method makes the maximum use of the available information from the data, as compared with the default ML (maximum likelihood) methods.

Example 29.16, Comparing the ML and FIML Estimation discusses the similarities and differences between the ML and FIML estimation methods as implemented in PROC CALIS. It uses an empirical example to show how ML and FIML obtain the same estimation results when the data do not contain missing values.

Example 29.18, Simultaneous Equations with Mean Structures and Reciprocal Paths is an econometric example that shows you 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 metaparameters by using the PARAMETERS statement 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 CALIS statement.

Example 29.20, Confirmatory Factor Analysis: Cognitive Abilities uses the FACTOR modeling language to illustrate confirmatory factor analysis. In addition, you use the MODIFICATION option in the PROC CALIS statement to compute LM test indices for model modifications.

Example 29.25, Fitting a Latent Growth Curve Model is an advanced example that illustrates the use of structural equation modeling techniques for fitting latent growth curve models. 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 29.23, Illustrating Various General Modeling Languages extends Example 29.17, 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 29.17 and get equivalent results. This example shows the connections between the general modeling languages supported in PROC CALIS. A good understanding of Example 29.17 is a prerequisite for this example.

Data Set Options

Model and Estimation Options

Options for Fit Statistics

Options for Statistical Analysis

Global Display Options

Optimization Options

Assessment of fit The section Assessment of Fit presents the fit indices used in PROC CALIS. However, the more important topics covered in this section are about how model fit indices are organized and used, how residuals can be used to gauge the fitting of individual parts of the model, and how the coefficients of determination are defined for equations. To customize your fit summary table, you can use the options on the FITINDEX statement.

Case-level residual diagnostics The section Case-Level Residuals, Outliers, Leverage Observations, and Residual Diagnostics describes details about how the residual diagnostics at the individual data level are accomplished in general structural equation modeling, and how they lead to the graphical techniques for detecting outliers and leverage observations, studying residual distributions, and examining linear relationships and heteroscedasticity of error variances.

Control and customization of path diagrams The section Path Diagrams: Layout Algorithms, Default Settings, and Customization discusses the path diagram layout algorithms that the CALIS procedure uses. It also illustrates useful options that control and customize path diagrams.

Effect partitioning The section Total, Direct, and Indirect Effects discusses the total, direct, and indirect effects and their computations. The stability coefficient of reciprocal causation is also defined. To customize the effect analysis, you can use the EFFPART statement.

Counting and adjusting degrees of freedom The section Counting the Degrees of Freedom describes how PROC CALIS computes model fit degrees of freedom and how you can use some options on the PROC CALIS statement to make degrees-of-freedom adjustments. To adjust the model fit degrees of freedom, you can use the DFREDUCE= and NOADJDF options in the PROC CALIS statement.

Standardized solutions Standardization schemes used in PROC CALIS are described and discussed in the section Standardized Solutions. Standardized solutions are displayed by default. You can turn them off by using the NOSTAND option of the PROC CALIS statement.

Model modifications In the section Modification Indices, modification indices such as Lagrange multiplier test indices and Wald statistics are defined and discussed. These indices can be used either to enhance your model fit or to make your model more precise. To limit the modification process only to those parameters of interest, you can use the LMTESTS statement to customize the sets of LM tests conducted on potential parameters.

A Priori Parametric Function Testing You can use the TESTFUNC statement to test a priori hypotheses individually. You can use the SIMTESTS statement to test a priori hypotheses simultaneously.

Global output control tools in PROC CALIS You can control output displays in PROC CALIS either by the global display options or by the individual output printing options. Each global display option typically controls more than one output display, while each individual output display controls only one output display. The global display options can both enable and suppress output displays, and they can also alter the format of the output. See the ALL , PRINT , PSHORT , PSUMMARY , and NOPRINT options for ways to control the appearances of the output. See the section Global Display Options for details about the global display options and their relationships with the individual output display options. Also see the ORDERALL , ORDERGROUPS , ORDERMODELS , ORDERSPEC , PARMNAME , PRIMAT , NOORDERSPEC , NOPARMNAME , NOSTAND , and NOSE options which control the output formats.

Customized analysis tools in PROC CALIS Many individual output displays in PROC CALIS can be customized via specific options or statements. If you do not use these customization tools, the default output will usually contain a large number of displays or displays with very large dimensions. These customized analysis tools are as follows:

Output selection and destinations by the ODS system This kind of output control is used not only for PROC CALIS, but is used for all procedures that support the ODS system. The most common uses include output selection and output destinations assignment. You use the ODS SELECT statement together with the ODS table names or graph names to select particular output displays. See the section ODS Table Names for these names in PROC CALIS. The default output destination of PROC CALIS is the listing destination. You can add or change the destinations by using statements such as ods html (for html output), ods rtf (for rich text output), and so on. For details, see Chapter 20: Using the Output Delivery System.