The CALIS Procedure
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Overview
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Getting Started
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SyntaxClasses of Statements in PROC CALISSingle-Group Analysis SyntaxMultiple-Group Multiple-Model Analysis SyntaxPROC CALIS StatementBOUNDS StatementBY StatementCOSAN StatementCOV StatementDETERM StatementEFFPART StatementFACTOR StatementFITINDEX StatementFREQ StatementGROUP StatementLINCON StatementLINEQS StatementLISMOD StatementLMTESTS StatementMATRIX StatementMEAN StatementMODEL StatementMSTRUCT StatementNLINCON StatementNLOPTIONS StatementOUTFILES StatementPARAMETERS StatementPARTIAL StatementPATH StatementPCOV StatementPVAR StatementRAM StatementREFMODEL StatementRENAMEPARM StatementSAS Programming StatementsSIMTESTS StatementSTD StatementSTRUCTEQ StatementTESTFUNC StatementVAR StatementVARIANCE StatementVARNAMES StatementWEIGHT Statement
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DetailsInput Data SetsOutput Data SetsDefault Analysis Type and Default ParameterizationThe COSAN ModelThe FACTOR ModelThe LINEQS ModelThe LISMOD Model and SubmodelsThe MSTRUCT ModelThe PATH ModelThe RAM ModelNaming Variables and ParametersSetting Constraints on ParametersAutomatic Variable SelectionEstimation CriteriaRelationships among Estimation CriteriaGradient, Hessian, Information Matrix, and Approximate Standard ErrorsCounting the Degrees of FreedomAssessment of FitCase-Level Residuals, Outliers, Leverage Observations, and Residual DiagnosticsTotal, Direct, and Indirect EffectsStandardized SolutionsModification IndicesMissing Values and the Analysis of Missing PatternsMeasures of Multivariate KurtosisInitial EstimatesUse of Optimization TechniquesComputational ProblemsDisplayed OutputODS Table NamesODS Graphics
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ExamplesEstimating Covariances and CorrelationsEstimating Covariances and Means SimultaneouslyTesting Uncorrelatedness of VariablesTesting Covariance PatternsTesting Some Standard Covariance Pattern HypothesesLinear Regression ModelMultivariate Regression ModelsMeasurement Error ModelsTesting Specific Measurement Error ModelsMeasurement Error Models with Multiple PredictorsMeasurement Error Models Specified As Linear EquationsConfirmatory Factor ModelsConfirmatory Factor Models: Some VariationsResidual Diagnostics and Robust EstimationThe Full Information Maximum Likelihood MethodComparing the ML and FIML EstimationPath Analysis: Stability of AlienationSimultaneous Equations with Mean Structures and Reciprocal PathsFitting Direct Covariance StructuresConfirmatory Factor Analysis: Cognitive AbilitiesTesting Equality of Two Covariance Matrices Using a Multiple-Group AnalysisTesting Equality of Covariance and Mean Matrices between Independent GroupsIllustrating Various General Modeling LanguagesTesting Competing Path Models for the Career Aspiration DataFitting a Latent Growth Curve ModelHigher-Order and Hierarchical Factor ModelsLinear Relations among Factor LoadingsMultiple-Group Model for Purchasing BehaviorFitting the RAM and EQS Models by the COSAN Modeling LanguageSecond-Order Confirmatory Factor AnalysisLinear Relations among Factor Loadings: COSAN Model SpecificationOrdinal Relations among Factor LoadingsLongitudinal Factor Analysis
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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:
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Moment Structures Analyzed |
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Covariance structures |
Covariance structures are analyzed by default (COVARIANCE option). |
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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. |
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Default Parameterization |
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Variance parameters |
Free variance parameters for independent latent factors, observed variables, and errors. |
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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. |
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Mean parameters |
Free mean parameters for all exogenous observed variables. Fixed zero means for all exogenous latent factors and error terms. |
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Intercept parameters |
Free intercept parameters for all endogenous observed variables; Fixed zero intercepts for all endogenous latent factors. |
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Role of the VAR Statement in Model Specification |
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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. |
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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.