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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LINCON Statement
LINCON constraint <, constraint …> ;
where constraint represents one of the following: 
number operator linear-term linear-term operator number and linear-term is <+|-> <coefficient *> parameter <<+|-> <coefficient *> parameter …>
The LINCON statement specifies a set of linear equality or inequality constraints of the following form:
![\[ \sum _{j=1}^ n a_{ij} x_ j \le b_ i , \quad i=1,\ldots ,m \]](images/statug_calis0161.png){kind=small} |
The constraints must be separated by commas. Each linear constraint i in the statement consists of a linear combination 
of a subset of the n parameters 
and a constant value 
separated by a comparison operator. Valid operators are <=, <, >=, >, and = or, equivalently, LE, LT, GE, GT, and EQ. PROC
CALIS cannot enforce the strict inequalities < or >. Note that the coefficients 
in the linear combination must be constant numbers and must be followed by an asterisk and the name of a parameter (that
is, listed in the PARMS, main, or subsidiary model specification statements). The following is an example of the LINCON statement that sets a linear constraint on parameters
x1 and x2:
lincon x1 + 3 * x2 <= 1;
Although you can express boundary constraints of individual parameters in LINCON statements, it is much more convenient to specify these boundary constraints with the BOUNDS statement. For example, the following LINCON statement essentially specifies boundary constraints on four parameters:
lincon x1 <= 1,
x2 <= 1,
v1 > 0,
v2 > 0;
Instead of using the LINCON statement, you can specify the following BOUNDS statement:
bounds x1 x2 <= 1,
v1 v2 > 0;
Another advantage of using the BOUNDS statement for setting bounds for individual parameters is that when a boundary constraint becomes active in the solution (that is, when the final estimate is on the boundary), a Lagrange multiplier test on releasing the boundary constraint would be conducted when you also specify the MOD option. However, no Lagrange multiplier test would be conducted if you specified the boundary constraint with the LINCON statement.