LMTESTS  LMTEST
option <option …> ;
where option represents one of the following: displayoption testsetand testset represents one of the following: setname = [ regions ] setname = regions where setname 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 displayoptions or to customize the testsets 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 displayoptions 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 testsets 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 Testsets
In addition to the displayoptions, you can define customized sets of LM tests as testsets in the LMTESTS statement. You can define as many testsets as you like. Ranking of the LM tests will be done individually for each testset. For example, the following LMTESTS statement requests that the default sets of LM tests not be conducted by the NODEFAULT
option. Instead, two customized testsets 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: matrixbased or nonmatrixbased.
The matrixbased regions can be used if you are familiar with the matrix representations of various types of models. Note that defining testsets by using matrixbased 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 testsets for LM test ranking. For matrix output of LM tests, use the LMMAT option in the LMTESTS statement.
Nonmatrixbased regions do not assume the knowledge of the model matrices. They are easier to use in most situations. In addition, nonmatrixbased
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 matrixbased regions are limited. For example, you cannot use any matrixbased 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 nonmatrix 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 = [setofmatrices]  {setofmatrices}

specifies the parameter locations in the matrices specified in setofmatrices.

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 matrixbased 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 MatrixBased 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 NonMatrixBased 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 MatrixBased Regions
The keywords for the matrixbased 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 NonMatrixBased 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 matrixbased 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 MatrixBased 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 NonMatrixBased 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  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 matrixbased 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 MatrixBased Regions

_MSTRUCTCOV_  _COV_  MSTRUCTCOV

specifies the _MSTRUCTCOV_ or _COV_ matrix.

_MSTRUCTMEAN_  _MEAN_  MSTRUCTMEAN

specifies the _MSTRUCTMEAN_ or _MEAN_ vector.
Keywords for NonMatrixBased 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 matrixbased 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 MatrixBased 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 NonMatrixBased 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).