The CALIS Procedure

LMTESTS Statement

The LM Tests Display Options
The Customized Sets of LM Tests: Syntax of the Test-sets
The LM Test Regions for COSAN Models
The LM Test Regions for FACTOR Models
The LM Test Regions for LINEQS Models
The LM Test Regions for LISMOD Models
The LM Test Regions for MSTRUCT Models
The LM Test Regions for PATH and RAM Models

LMTESTS | LMTEST option <option …> ;

where option represents one of the following: $\bullet$ display-option $\bullet$ test-setand test-set represents one of the following: $\bullet$ set-name = [ regions ] $\bullet$ 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: 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 | LV–>LV: specifies all possible effects of latent factors on latent factors.
LV==>MV | LV–>MV | MV<==LV | MV<–LV: specifies all possible effects of latent factors on manifest variables.
LV<==MV | LV<–MV | MV==>LV | MV–>LV: specifies all possible effects of manifest variables on latent factors.
MEANS | MEAN: specifies the means of independent factors.
MV==>MV | 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 $\bxi$ -variables exist, and in _PSI_ when the $\bm {\eta }$ -variables exist without the presence of the $\bxi$ -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 | 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 | LV–>MV | MV<==LV | 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 | 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 | LV–>LV: specifies effects of latent variables on latent variables.
LV==>MV | LV–>MV | MV<==LV | MV<–LV: specifies effects of latent variables on manifest variables.
LV<==MV | LV<–MV | MV==>LV | 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 | 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).