The CALIS Procedure
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Overview
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Getting Started
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Syntax
Classes of Statements in PROC CALIS Single-Group Analysis Syntax Multiple-Group Multiple-Model Analysis Syntax PROC CALIS Statement BOUNDS Statement BY Statement COSAN Statement COV Statement DETERM Statement EFFPART Statement FACTOR Statement FITINDEX Statement FREQ Statement GROUP Statement LINCON Statement LINEQS Statement LISMOD Statement LMTESTS Statement MATRIX Statement MEAN Statement MODEL Statement MSTRUCT Statement NLINCON Statement NLOPTIONS Statement OUTFILES Statement PARAMETERS Statement PARTIAL Statement PATH Statement PCOV Statement PVAR Statement RAM Statement REFMODEL Statement RENAMEPARM Statement SAS Programming Statements SIMTESTS Statement STD Statement STRUCTEQ Statement TESTFUNC Statement VAR Statement VARIANCE Statement VARNAMES Statement WEIGHT Statement
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Details
Input Data Sets Output Data Sets The COSAN Model The FACTOR Model The LINEQS Model The LISMOD Model and Submodels The MSTRUCT Model The PATH Model The RAM Model Naming Variables and Parameters Setting Constraints on Parameters Automatic Variable Selection Estimation Criteria Relationships among Estimation Criteria Gradient, Hessian, Information Matrix, and Approximate Standard Errors Counting the Degrees of Freedom Assessment of Fit Total, Direct, and Indirect Effects Standardized Solutions Modification Indices Missing Values and the Analysis of Missing Patterns Measures of Multivariate Kurtosis Initial Estimates Use of Optimization Techniques Computational Problems Displayed Output ODS Table Names ODS Graphics
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Examples
Estimating Covariances and Correlations Estimating Covariances and Means Simultaneously Testing Uncorrelatedness of Variables Testing Covariance Patterns Testing Some Standard Covariance Pattern Hypotheses Linear Regression Model Multivariate Regression Models Measurement Error Models Testing Specific Measurement Error Models Measurement Error Models with Multiple Predictors Measurement Error Models Specified As Linear Equations Confirmatory Factor Models Confirmatory Factor Models: Some Variations The Full Information Maximum Likelihood Method Comparing the ML and FIML Estimation Path Analysis: Stability of Alienation Simultaneous Equations with Mean Structures and Reciprocal Paths Fitting Direct Covariance Structures Confirmatory Factor Analysis: Cognitive Abilities Testing Equality of Two Covariance Matrices Using a Multiple-Group Analysis Testing Equality of Covariance and Mean Matrices between Independent Groups Illustrating Various General Modeling Languages Testing Competing Path Models for the Career Aspiration Data Fitting a Latent Growth Curve Model Higher-Order and Hierarchical Factor Models Linear Relations among Factor Loadings Multiple-Group Model for Purchasing Behavior Fitting the RAM and EQS Models by the COSAN Modeling Language Second-Order Confirmatory Factor Analysis Linear Relations among Factor Loadings: COSAN Model Specification Ordinal Relations among Factor Loadings Longitudinal Factor Analysis
- References
| 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:
scaling the covariance matrix
providing better initial values
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:
Change the update formula with the UPDATE= option.
Change the line-search algorithm with the LIS= option.
Specify a more precise line search with the LSPRECISION= option, if you use LIS=2 or LIS=3.
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:
Set the variance parameter values in the model specification manually.
Use the DEMPHAS= option to increase all initial variance parameter values.
Use a slightly different, but more stable, model to obtain preliminary estimates.
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
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is said to be identified in a parameter space 
, if
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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 
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 
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:
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When 
, 
is negative. This might indicate poor model fit or is an inappropriate measure for the model. For the latter case, for example, negative might be due to cyclical (nonrecursive) paths in the model so that the interpretation is not appropriate.