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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Computational Problems
First Iteration Overflows
Analyzing a covariance matrix that includes high variances in the diagonal and using bad initial estimates for the parameters can easily lead to arithmetic overflows in the first iterations of the minimization algorithm. The line-search algorithms that work with cubic extrapolation are especially sensitive to arithmetic overflows. If this occurs with quasi-Newton or conjugate gradient minimization, you can specify the INSTEP= option to reduce the length of the first step. If an arithmetic overflow occurs in the first iteration of the Levenberg-Marquardt algorithm, you can specify the INSTEP= option to reduce the trust region radius of the first iteration. You also can change the minimization technique or the line-search method. If none of these help, you can consider doing the following:
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scaling the covariance matrix
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providing better initial values
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changing the model
No Convergence of Minimization Process
If convergence does not occur during the minimization process, perform the following tasks:
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If there are negative variance estimates, you can do either of the following:
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Change the estimation method to obtain a better set of initial estimates. For example, if you use METHOD=ML, you can do either of the following:
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Change the optimization technique. For example, if you use the default OMETHOD=LEVMAR, you can do either of the following:
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Change or modify the update technique or the line-search algorithm or both when using OMETHOD=QUANEW or OMETHOD=CONGRA. For example, if you use the default update formula and the default line-search algorithm, you can do any or all of the following:
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Change the update formula with the UPDATE= option.
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Change the line-search algorithm with the LIS= option.
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Specify a more precise line search with the LSPRECISION= option, if you use LIS=2 or LIS=3.
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Add more iterations and function calls by using the MAXIT= and MAXFU= options.
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Change the initial values. For many categories of model specifications, PROC CALIS computes an appropriate set of initial values automatically. However, for some of the model specifications (for example, structural equations with latent variables on the left-hand side and manifest variables on the right-hand side), PROC CALIS might generate very obscure initial values. In these cases, you have to set the initial values yourself.
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Increase the initial values of the variance parameters by one of the following ways:
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Set the variance parameter values in the model specification manually.
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Use the DEMPHAS= option to increase all initial variance parameter values.
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Use a slightly different, but more stable, model to obtain preliminary estimates.
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Use additional information to specify initial values, for example, by using other SAS software like the FACTOR, REG, SYSLIN, and MODEL (SYSNLIN) procedures for the modified, unrestricted model case.
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Unidentified Model
The parameter vector 
in the structural model
![\[ \bSigma = \bSigma (\bTheta ) \]](images/statug_calis0920.png){kind=small} |
is said to be identified in a parameter space G, if
![\[ \bSigma (\bTheta ) = \bSigma (\tilde{\bTheta }), \quad \tilde{\bTheta } \in G \quad \]](images/statug_calis0921.png){kind=small} |
implies 
. The parameter estimates that result from an unidentified model can be very far from the parameter estimates of a very similar
but identified model. They are usually machine dependent. Do not use parameter estimates of an unidentified model as initial
values for another run of PROC CALIS.
Singular Predicted Covariance Model Matrix
Sometimes you might inadvertently specify models with singular predicted covariance model matrices (for example, by fixing diagonal elements to zero). In such cases, you cannot compute maximum likelihood estimates (the ML function value F is not defined). Since singular predicted covariance model matrices can also occur temporarily in the minimization process, PROC CALIS tries in such cases to change the parameter estimates so that the predicted covariance model matrix becomes positive definite. This process does not always work well, especially if there are fixed instead of free diagonal elements in the predicted covariance model matrices. A famous example where you cannot compute ML estimates is a component analysis with fewer components than given manifest variables. See the section FACTOR Statement for more details. If you continue to obtain a singular predicted covariance model matrix after changing initial values and optimization techniques, then your model might be specified so that ML estimates cannot be computed.
Saving Computing Time
For large models, the most computing time is needed to compute the modification indices. If you do not really need the Lagrange multipliers or multiple Wald test indices (the univariate Wald test indices are the same as the t values), using the NOMOD option can save a considerable amount of computing time.
Predicted Covariance Matrices with Negative Eigenvalues
A covariance matrix cannot have negative eigenvalues, since a negative eigenvalue means that some linear combination of the
variables has negative variance. PROC CALIS displays a warning if the predicted covariance matrix has negative eigenvalues
but does not actually compute the eigenvalues. Sometimes this warning can be triggered by 0 or very small positive eigenvalues
that appear negative because of numerical error. If you want to be sure that the predicted covariance matrix you are fitting
can be considered to be a variance-covariance matrix, you can use the SAS/IML command VAL=EIGVAL(U) to compute the vector VAL of eigenvalues of matrix 
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Negative 
Values
The estimated squared multiple correlations 
of the endogenous variables are computed using the estimated error variances:
![\[ R^2_ i = 1 - \frac{\widehat{\mathit{var}(\zeta _ i)}}{\widehat{\mathit{var}(\eta _ i)} } \]](images/statug_calis0925.png){kind=small} |
When 
, 
is negative. This might indicate poor model fit or R square is an inappropriate measure for the model. For the latter case,
for example, negative R square might be due to cyclical (nonrecursive) paths in the model so that the R square interpretation
is not appropriate.