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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Example 27.2 Estimating Covariances and Means Simultaneously
This example uses the same data set that is used in Example 27.1 and estimates the means and covariances. Use the MSTRUCT model specification as shown in the following statements:
proc calis data=sales meanstr nostand; mstruct var=q1-q4; run;
In the PROC CALIS statement, specify the MEANSTR option to request the mean structure analysis in addition to the default covariance structure analysis. If you are not interested in the standardized solution, specify the NOSTAND option in the PROC CALIS statement to suppress computation of the standardized estimates. Without further model specification (such as the MATRIX statement), PROC CALIS assumes a saturated structural model with all means, variances, and covariances as model parameters.
Output 27.2.1 shows the modeling information. With the MEANSTR option specified in the PROC CALIS statement, the current analysis type is Means and Covariances, instead of the default Covariances in Example 27.1.
Output 27.2.1: Modeling Information of the Saturated Mean and Covariance Structure Model for the Sales Data
| Saturated Means and Covariance Structures Using MSTRUCT |
| Modeling Information | |
|---|---|
| Maximum Likelihood Estimation | |
| Data Set | WORK.SALES |
| N Records Read | 14 |
| N Records Used | 14 |
| N Obs | 14 |
| Model Type | MSTRUCT |
| Analysis | Means and Covariances |
| Variables in the Model |
|---|
| q1 q2 q3 q4 |
| Number of Variables = 4 |
Output 27.2.2 shows the fit summary of the current model. Again, this is a perfect model fit with 0 chi-square value and 0 degrees of freedom.
Output 27.2.2: Fit Summary of the Saturated Mean and Covariance Structure Model for the Sales Data
| Fit Summary | |
|---|---|
| Chi-Square | 0.0000 |
| Chi-Square DF | 0 |
| Pr > Chi-Square | . |
Output 27.2.3 shows the estimates of the means, together with the standard error estimates and the t values. These estimated means are exactly the same as the sample means, which are not shown here.
Output 27.2.3: Mean Estimates for the Sales Data
| MSTRUCT _Mean_ Vector | |||
|---|---|---|---|
| Variable | Estimate | Standard Error |
t Value |
| q1 | 1.36714 | 0.16132 | 8.47491 |
| q2 | 2.07429 | 0.13146 | 15.77902 |
| q3 | 2.20286 | 0.21596 | 10.20008 |
| q4 | 3.65500 | 0.45281 | 8.07176 |
Output 27.2.4 shows the variance and covariance estimates. These estimates are exactly the same as the elements in the sample covariance matrix. In addition, these estimates match the estimates in Output 27.1.5 of Example 27.1, where only the covariance structures are analyzed.
Output 27.2.4: Variance and Covariance Estimates for the Sales Data
| MSTRUCT _COV_ Matrix: Estimate/StdErr/t-value | ||||||||||||||||
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These estimates are essentially the same as the sample means, variances, and covariances. This kind of analysis is much easier using PROC CORR with the NOMISS option. However, the main purpose of Example 27.1 and Example 27.2 is to introduce the MSTRUCT modeling language and some basic but important options in PROC CALIS. You can apply the MSTRUCT modeling language to more sophisticated situations that are beyond the saturated mean and covariance structure models. Example 27.3 and Example 27.4 fit some patterned covariance models that are nonsaturated. Also, options such as NOSE, NOSTAND, and MEANSTR are useful for all modeling languages in PROC CALIS.