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
Example 26.2 Estimating Covariances and Means Simultaneously
This example uses the same data set that is used in Example 26.1 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 26.2.1 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 26.1.
| Saturated Means and Covariance Structures Using MSTRUCT |
| Modeling Information | |
|---|---|
| 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 26.2.2 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.
| Fit Summary | |
|---|---|
| Chi-Square | 0.0000 |
| Chi-Square DF | 0 |
| Pr > Chi-Square | . |
Output 26.2.3 shows the estimates of the means, together with the standard error estimates and the 
values. These estimated means are exactly the same as the sample means, which are not shown here.
| 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 26.2.4 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 26.1.5 of Example 26.1, where only the covariance structures are analyzed.
| 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 26.1 and Example 26.2 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 26.3 and Example 26.4 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.