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 StatementPATHDIAGRAM 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 SelectionPath Diagrams: Layout Algorithms, Default Settings, and CustomizationEstimation 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
- References
- The LM Tests Display Options
- The Customized Sets of LM Tests: Syntax of the Test-sets
- The LM Test Regions for COSAN Models
- The LM Test Regions for FACTOR Models
- The LM Test Regions for LINEQS Models
- The LM Test Regions for LISMOD Models
- The LM Test Regions for MSTRUCT Models
- The LM Test Regions for PATH and RAM Models
where option represents one of the following: 
display-option test-setand test-set represents one of the following: set-name = [ regions ] set-name = 
regions 
where set-name is the name of the set of Lagrange multiplier (LM) tests defined by the regions that follow after the equal sign and regions are keywords denoting specific sets of parameters in the model.
You can use the LMTESTS statement to set display-options or to customize the test-sets for the LM tests. The LMTESTS statement is one of the model analysis statements . It can be used within the scope of the CALIS statement so that the options will apply to all models. It can also be used within the scope of each MODEL statement so that the options will apply only locally. Therefore, different models within a CALIS run can have very different LMTESTS options.
In addition to the display-options, you can define customized sets of LM tests as test-sets in the LMTESTS statement. You can define as many test-sets as you like. Ranking of the LM tests will be done individually for each test-set. For example, the following LMTESTS statement requests that the default sets of LM tests not be conducted by the NODEFAULT option. Instead, two customized test-sets are defined.
lmtests nodefault MyFirstSet=[ALL] MySecondSet=[COVEXOG COVERR];
The first customized set MyFirstSet pulls all possible parameter locations together for the LM test ranking (ALL keyword). The second customized set MySecondSet pulls only the covariances among exogenous variables (COVEXOG keyword) and among errors (COVERR keyword) together for the
LM test ranking.
Two different kinds of regions for LM tests are supported in PROC CALIS: matrix-based or non-matrix-based.
The matrix-based regions can be used if you are familiar with the matrix representations of various types of models. Note that defining test-sets by using matrix-based regions does not mean that LM tests are printed in matrix format. It means only that the parameter locations within the specified matrices are included into the specific test-sets for LM test ranking. For matrix output of LM tests, use the LMMAT option in the LMTESTS statement.
Non-matrix-based regions do not assume the knowledge of the model matrices. They are easier to use in most situations. In addition, non-matrix-based
regions can cover special subsets of parameter locations that cannot be defined by model matrices and submatrices. For example, because
of the compartmentalization according to independent and dependent variables in the LINEQS model matrices, the sets of LM
tests defined by the LINEQS matrix-based regions are limited. For example, you cannot use any matrix-based regions to request LM tests for new paths to existing independent variables in the LINEQS model. Such a matrix does not exist in
the original specification. However, you can use the non-matrix based region NEWENDO to refer to these new paths.
The regions for parameter locations are specified by keywords in the LMTESTS statement. Because the regions are specific to the types of models, they are described separately for each model type in the following.
The keywords for the matrix-based regions are associated with the FACTOR model matrices. See the section Summary of Matrices in the FACTOR Model for the definitions and properties of these matrices.
The keywords for the matrix-based regions are associated with the LINEQS model matrices. See the section Matrix Representation of the LINEQS Model for definitions of these model matrices and see the section Summary of Matrices and Submatrices in the LINEQS Model for the names and properties and the model matrices and submatrices.
The keywords for the matrix-based regions are associated with the LISMOD model matrices. See the section Model Matrices in the LISMOD Model for the definitions and properties of these matrices.
- ALL
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specifies all model matrices.
- COV
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specifies all covariance parameters in _THETAY_, _THETAX_, _PHI_, and _PSI_.
- COVERR
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specifies all covariances for errors or disturbances in _THETAY_, _THETAX_, and _PSI_.
- COVFACT | COVLV
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specifies all covariances among latent factors in _PHI_ when the
-variables exist, and in _PSI_ when the 
-variables exist without the presence of the -variables.
- FIRSTMOMENTS
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specifies all intercepts and means in _NUY_, _NUX_, _ALPHA_, and _KAPPA_.
- INTERCEPTS | INTERCEPT
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specifies all intercepts in _NUY_, _NUX_, and _ALPHA_.
- LOADING | LOADINGS
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specifies the coefficients in _LAMBDAY_ and _LAMBDAX_.
- LV==>LV | LV–>LV
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specifies the effects of latent variables on latent variables. Depending on the type of LISMOD model, the _BETA_ and _GAMMA_ might be involved.
- LV==>MV | LV–>MV | MV<==LV | MV<–LV
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specifies the effects of latent variables on manifest variables. Depending on the type of LISMOD model, the _LAMBDAY_, _LAMBDAX_, and _GAMMA_ matrices might be involved.
- MEANS | MEAN
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specifies the mean parameters. Depending on the type of LISMOD model, the _ALPHA_ and _KAPPA_ matrices might be involved.
- MV==>MV | MV–>MV
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specifies effects of manifest variables on manifest variables. Depending on the type of LISMOD model, the _BETA_ and _GAMMA_ matrices might be involved.
- PATHS | PATH
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specifies all path coefficients. Depending on the type of LISMOD model, the _LAMBDAY_, _LAMBDAX_, _BETA_, and _GAMMA_ matrices might be involved.
The keywords for the matrix-based regions are associated with the MSTRUCT model matrices. See the section Model Matrices in the MSTRUCT Model for the definitions and properties of these matrices.
The keywords for the matrix-based regions are associated with the submatrices of the RAM model matrices. See the section Partitions of the RAM Model Matrices and Some Restrictions for the definitions of these submatrices and the section Summary of Matrices and Submatrices in the RAM Model for the summary of the names and properties of these submatrices.