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
| LMTESTS Statement |
- LMTESTS | LMTEST option <option ...> ;
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.
The LM Tests Display Options
The following are the display-options for the LM tests:
- DEFAULT
conducts the default sets of LM tests for freeing fixed parameters in the model. This option is used when you need to reset the default sets of LM tests in the local model. For example, you might have turned off the default LM tests by using the NODEFAULT option in the LMTESTS statement within the scope of PROC CALIS statement. However, for the model under the scope of a particular MODEL statement, you can use this DEFAULT option in the local LMTESTS statement to turn on the default LM tests again.
- MAXRANK
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sets the maximum number of rankings within a set of LM tests. The actual number of test rankings might be smaller because the number of possible LM tests within a set might be smaller than the maximum number requested.
- NODEFAULT
turns off the default sets of LM tests for freeing fixed parameters in the model. As a result, only the customized LM tests defined in the test-sets of the LMTESTS statement are conducted and displayed. Note that the LM tests for equality and active boundary constraints are not turned off by this option. If you specify this option in the LMTESTS statement within the scope of the PROC CALIS statement, it will propagate to all models.
- NORANK
turns off the ranking of the LM tests. Ranking of the LM tests is done automatically when the model modification indices are requested. The NORANK option is ignored if you also set the MAXRANK option.
- LMMAT
prints the sets of LM tests in matrix form, in addition to the normal LM test results.
The Customized Sets of LM Tests: Syntax of the Test-sets
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 LM Test Regions for COSAN Models
- ALLMAT
specifies all parameter locations in all matrices.
- CENTRAL
specifies all parameter locations in the central covariance matrices in all terms.
- MATRIX | MAT | MATSET = [set-of-matrices] | {set-of-matrices}
specifies the parameter locations in the matrices specified in set-of-matrices.
- MEANVEC
specifies all parameter locations in the central mean vectors in all terms.
- OUTER
specifies all parameter locations in all matrices except for the central covariance matrices and central mean vectors in all terms.
The LM Test Regions for FACTOR Models
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.
Keywords for Matrix-Based Regions
- _FACTERRV_ | FACTERRV
specifies the error variances.
- _FACTFCOV_ | FACTFCOV
specifies the covariances among factors.
- _FACTINTE_ | FACTINTE
specifies the intercepts.
- _FACTLOAD_ | FACTLOAD
specifies the factor loadings.
- _FACTMEAN_ | FACTMEAN
specifies the factor means.
Keywords for Non-Matrix-Based Regions
- ALL
specifies all parameter locations.
- COV
specifies the covariances among factors.
- COVERR
specifies the covariances among errors.
- COVFACT | COVLV
specifies the covariances among factors.
- FIRSTMOMENTS
specifies the means of factors and the intercepts.
- INTERCEPTS
specifies the intercepts.
- LOADINGS
specifies the factor loadings.
- MEANS | MEAN
specifies the means of factors.
The LM Test Regions for LINEQS Models
Keywords for Matrix-Based Regions
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.
- _EQSALPHA_ | EQSALPHA
specifies the intercepts of dependent variables.
- _EQSBETA_ | EQSBETA
specifies effects of dependent variables on dependent variables.
- _EQSGAMMA_ | _EQSGAMMA_SUB_ | EQSGAMMA | EQSGAMMASUB
specifies the effects of independent variables (excluding errors) on dependent variables. Because effects of errors on dependent variables are restricted to ones in the LINEQS model, LM tests on _EQSGAMMA_ and _EQSGAMMA_SUB_ (submatrix of _EQSGAMMA_) are the same.
- _EQSNU_ | _EQSNU_SUB_ | EQSNU | EQSNUSUB
specifies the means of independent variables (excluding errors). Because means of errors are restricted to zero in the LINEQS model, LM tests on _EQSNU_ and _EQSNU_SUB_ (submatrix of _EQSNU_) are the same.
- _EQSPHI_ | EQSPHI
specifies variances and covariances among all independent variables, including errors.
- _EQSPHI11_ | EQSPHI11
specifies variances and covariances among independent variables, excluding errors.
- _EQSPHI21_ | EQSPHI21
specifies covariances between errors and disturbances with other independent variables.
- _EQSPHI22_ | EQSPHI22
specifies variances and covariances among errors and disturbances.
Keywords for Non-Matrix-Based Regions
- ALL
specifies all possible parameter locations.
- COV
specifies all covariances among independent variables, including errors and disturbances.
- COVERR
specifies covariances among errors or disturbances.
- COVEXOG
specifies covariances among independent variables, excluding errors and disturbances.
- COVEXOGERR
specifies covariances of errors and disturbances with other independent variables.
- COVLV | COVFACT
specifies covariances among latent variables (excluding errors and disturbances).
- COVMV | COVOV
specifies covariance among independent manifest variables.
- EQUATION | EQUATIONS
specifies all possible linear relationships among variables.
- FIRSTMOMENTS
specifies means and intercepts.
- INTERCEPTS | INTERCEPT
specifies intercepts of dependent variables.
- LV–>LV
specifies all possible effects of latent factors on latent factors.
- LV–>MV | MV<–LV
specifies all possible effects of latent factors on manifest variables.
- LV<–MV | MV–>LV
specifies all possible effects of manifest variables on latent factors.
- MEANS | MEAN
specifies the means of independent factors.
- MV–>MV
specifies all possible effects of manifest variables on manifest variables.
- NEWDEP | NEWENDO
specifies effects of other variables on the independent variables in the original model.
- PATHS | PATH
specifies all possible linear relationships among variables.
The LM Test Regions for LISMOD Models
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.
Keywords for Matrix-Based Regions
- _ALPHA_ | ALPHA
specifies the _ALPHA_ matrix.
- _BETA_ | BETA
specifies the _BETA_ matrix.
- _GAMMA_ | GAMMA
specifies the _GAMMA_ matrix.
- _KAPPA_ | KAPPA
specifies the _KAPPA_ matrix.
- _LAMBDA_ | LAMBDA
specifies the _LAMBDAX_ and _LAMBDAY_ matrices.
- _LAMBDAX_ | LAMBDAX
specifies the _LAMBDAX_ matrix.
- _LAMBDAY_ | LAMBDAY
specifies the _LAMBDAY_ matrix.
- _NU_ | NU
specifies the _NUX_ and _NUY_ matrices.
- _NUX_ | NUX
specifies the _NUX_ matrix.
- _NUY_ | NUY
specifies the _NUY_ matrix.
- _PHI_ | PHI
specifies the _PHI_ matrix.
- _PSI_ | PSI
specifies the _PSI_ matrix.
- _THETA_ | THETA
specifies the _THETAX_ and _THETAY_ matrices.
- _THETAX_ | THETAX
specifies the _THETAX_ matrix.
- _THETAY_ | THETAY
specifies the _THETAY_ matrix.
Keywords for Non-Matrix-Based Regions
- ALL
specifies all model matrices.
- COV
specifies all covariance parameters in _THETAY_, _THETAX_, _PHI_, and _PSI_.
- COVERR
specifies all covariances for errors or disturbances in _THETAY_, _THETAX_, and _PSI_.
- COVFACT | COVLV
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
specifies all intercepts and means in _NUY_, _NUX_, _ALPHA_, and _KAPPA_.
- INTERCEPTS | INTERCEPT
specifies all intercepts in _NUY_, _NUX_, and _ALPHA_.
- LOADING | LOADINGS
specifies the coefficients in _LAMBDAY_ and _LAMBDAX_.
- LV–>LV
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 | MV<–LV
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
specifies the mean parameters. Depending on the type of LISMOD model, the _ALPHA_ and _KAPPA_ matrices might be involved.
- MV–>MV
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
specifies all path coefficients. Depending on the type of LISMOD model, the _LAMBDAY_, _LAMBDAX_, _BETA_, and _GAMMA_ matrices might be involved.
The LM Test Regions for MSTRUCT Models
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.
Keywords for Matrix-Based Regions
- _MSTRUCTCOV_ | _COV_ | MSTRUCTCOV
specifies the _MSTRUCTCOV_ or _COV_ matrix.
- _MSTRUCTMEAN_ | _MEAN_ | MSTRUCTMEAN
specifies the _MSTRUCTMEAN_ or _MEAN_vector.
Keywords for Non-Matrix-Based Regions
- ALL
specifies the _MSTRUCTCOV_ (or _COV_) and _MSTRUCTMEAN_ (or _MEAN_) matrices.
- COV
specifies the _MSTRUCTCOV_ or _COV_ matrix.
- MEANS | MEAN
specifies the _MSTRUCTMEAN_ or _MEAN_ matrix.
The LM Test Regions for PATH and RAM Models
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.
Keywords for Matrix-Based Regions
- _RAMA_ | _A_ | RAMA
specifies the _RAMA_ matrix.
- _RAMA_LEFT_ | _A_LEFT_ | RAMALEFT
specifies the left portion of the _RAMA_ matrix.
- _RAMA_LL_ | _A_LL_ | RAMALL
specifies the lower left portion of the _RAMA_ matrix.
- _RAMA_LR_ | _A_LR_ | RAMALR
specifies the lower right portion of the _RAMA_ matrix.
- _RAMA_LOWER_ | _A_LOWER_ | RAMALOWER
specifies the lower portion of the _RAMA_ matrix. This is equivalent to the region specified by the NEWENDO keyword.
- _RAMA_RIGHT_ | _A_RIGHT_ | RAMARIGHT
specifies the right portion of the _RAMA_ matrix.
- _RAMA_UPPER_ | _A_UPPER_ | RAMAUPPER
specifies the upper portion of the _RAMA_ matrix.
- _RAMALPHA_ | RAMALPHA
specifies the _RAMALPHA_ matrix.
- _RAMBETA_ | RAMBETA
specifies the _RAMBETA_ matrix.
- _RAMGAMMA_ | RAMGAMMA
specifies the _RAMGAMMA_ matrix.
- _RAMNU_ | RAMNU
specifies the _RAMNU_ matrix.
- _RAMP_ | _P_ | RAMP
specifies the _RAMP_ matrix.
- _RAMP11_ | RAMP11
specifies the _RAMP11_ matrix.
- _RAMP21_ | RAMP21
specifies the _RAMP21_ matrix.
- _RAMP22_ | RAMP22
specifies the _RAMP22_ matrix.
- _RAMW_ | _W_ | RAMW
specifies the _RAMW_ vector.
Keywords for Non-Matrix-Based Regions
- ALL
specifies all possible parameter locations.
- ARROWS | ARROW
specifies all possible paths (that is, the entries in the _RAMA_ matrix).
- COV
specifies all covariances and partial covariances (that is, the entries in the _RAMP_ matrix).
- COVERR
specifies partial covariances among endogenous variables (that is, the entries in the _RAMP11_ matrix).
- COVEXOG
specifies covariances among exogenous variables (that is, the entries in the _RAMP22_ matrix).
- COVEXOGERR
specifies partial covariances of endogenous variables with exogenous variables (that is, the entries in the _RAM21_ matrix).
- COVLV | COVFACT
specifies covariance among latent factors (that is, entries in _RAMP11_ pertaining to latent variables).
- COVMV | COVOV
specifies covariance among manifest variables (that is, entries in _RAMP11_ pertaining to manifest variables).
- FIRSTMOMENTS
specifies means or intercepts (that is, entries in _RAMW_ vector).
- INTERCEPTS | INTERCEPT
specifies intercepts for endogenous variables (that is, entries in _RAMALPHA_ vector).
- LV–>LV
specifies effects of latent variables on latent variables.
- LV–>MV | MV<–LV
specifies effects of latent variables on manifest variables.
- LV<–MV | MV–>LV
specifies effects of manifest variables on latent variables.
- MEANS | MEAN
specifies the means of exogenous variables (that is, entries in the _RAMNU_ vector).
- MV–>MV
specifies effects of manifest variables on manifest variables.
- NEWENDO
specifies new paths to the exogenous variables in the original model.
- PATHS | PATH
specifies all possible paths (that is, the entries in the _RAMA_ matrix).