The CALIS Procedure

Output Data Sets

OUTEST= Data Set
OUTMODEL= or OUTRAM= Data Set
OUTSTAT= Data Set
OUTWGT= Data Set
OUTFIT= Data Set

OUTEST= Data Set

The OUTEST= (or OUTVAR=) data set is of TYPE=EST and contains the final parameter estimates, the gradient, the Hessian, and boundary and linear constraints. For METHOD=ML, METHOD=GLS, and METHOD=WLS, the OUTEST= data set also contains the approximate standard errors, the information matrix (crossproduct Jacobian), and the approximate covariance matrix of the parameter estimates ((generalized) inverse of the information matrix). If there are linear or nonlinear equality or active inequality constraints at the solution, the OUTEST= data set also contains Lagrange multipliers, the projected Hessian matrix, and the Hessian matrix of the Lagrange function.

The OUTEST= data set can be used to save the results of an optimization by PROC CALIS for another analysis with either PROC CALIS or another SAS procedure. Saving results to an OUTEST= data set is advised for expensive applications that cannot be repeated without considerable effort.

The OUTEST= data set contains the BY variables, two character variables _TYPE_ and _NAME_, t numeric variables corresponding to the parameters used in the model, a numeric variable _RHS_ (right-hand side) that is used for the right-hand-side value of a linear constraint or for the value of the objective function at the final point $x^{*}$ of the parameter space, and a numeric variable _ITER_ that is set to zero for initial values, set to the iteration number for the OUTITER output, and set to missing for the result output.

The _TYPE_ observations in Table 27.5 are available in the OUTEST= data set, depending on the request.

Table 27.5: _TYPE_ Observations in the OUTEST= Data Set

_TYPE_

Description

ACTBC

If there are active boundary constraints at the solution $x^{*}$ , three observations indicate which of the parameters are actively constrained, as follows:

_NAME_	Description
GE	indicates the active lower bounds
LE	indicates the active upper bounds
EQ	indicates the active masks

COV

Contains the approximate covariance matrix of the parameter estimates; used in computing the approximate standard errors.

COVRANK

contains the rank of the covariance matrix of the parameter estimates.

CRPJ_LF

Contains the Hessian matrix of the Lagrange function (based on CRPJAC).

CRPJAC

Contains the approximate Hessian matrix used in the optimization process. This is the inverse of the information matrix.

If linear constraints are used, this observation contains the ith linear constraint $\sum _ j a_{ij} x_ j = b_ i$ . The parameter variables contain the coefficients $a_{ij}$ , $j=1,\ldots ,n$ , the _RHS_ variable contains , and _NAME_=ACTLC or _NAME_=LDACTLC.

If linear constraints are used, this observation contains the ith linear constraint $\sum _ j a_{ij} x_ j \geq b_ i$ . The parameter variables contain the coefficients $a_{ij}$ , $j=1,\ldots ,n$ , and the _RHS_ variable contains . If the constraint i is active at the solution $x^{*}$ , then _NAME_=ACTLC or _NAME_=LDACTLC.

GRAD

Contains the gradient of the estimates.

GRAD_LF

Contains the gradient of the Lagrange function. The _RHS_ variable contains the value of the Lagrange function.

HESSIAN

Contains the Hessian matrix.

HESS_LF

Contains the Hessian matrix of the Lagrange function (based on HESSIAN).

INFORMAT

Contains the information matrix of the parameter estimates (only for METHOD=ML, METHOD=GLS, or METHOD=WLS).

INITGRAD

Contains the gradient of the starting estimates.

INITIAL

Contains the starting values of the parameter estimates.

JACNLC

Contains the Jacobian of the nonlinear constraints evaluated at the final estimates.

LAGM BC

Contains Lagrange multipliers for masks and active boundary constraints.

`_NAME_`	Description
GE	Indicates the active lower bounds
LE	Indicates the active upper bounds
EQ	Indicates the active masks

LAGM LC

Contains Lagrange multipliers for linear equality and active inequality constraints in pairs of observations containing the constraint number and the value of the Lagrange multiplier.

`_NAME_`	Description
LEC_NUM	Number of the linear equality constraint
LEC_VAL	Corresponding Lagrange multiplier value
LIC_NUM	Number of the linear inequality constraint
LIC_VAL	Corresponding Lagrange multiplier value

LAGM NLC

contains Lagrange multipliers for nonlinear equality and active inequality constraints in pairs of observations that contain the constraint number and the value of the Lagrange multiplier.

`_NAME_`	Description
NLEC_NUM	Number of the nonlinear equality constraint
NLEC_VAL	Corresponding Lagrange multiplier value
NLIC_NUM	Number of the linear inequality constraint
NLIC_VAL	Corresponding Lagrange multiplier value

If linear constraints are used, this observation contains the ith linear constraint $\sum _ j a_{ij} x_ j \leq b_ i$ . The parameter variables contain the coefficients $a_{ij}$ , $j=1,\ldots ,n$ , and the _RHS_ variable contains . If the constraint i is active at the solution $x^{*}$ , then _NAME_=ACTLC or _NAME_=LDACTLC.

LOWERBD
| LB

If boundary constraints are used, this observation contains the lower bounds. Those parameters not subjected to lower bounds contain missing values. The _RHS_ variable contains a missing value, and the _NAME_ variable is blank.

NACTBC

All parameter variables contain the number $n_{abc}$ of active boundary constraints at the solution $x^{*}$ . The _RHS_ variable contains a missing value, and the _NAME_ variable is blank.

NACTLC

All parameter variables contain the number $n_{alc}$ of active linear constraints at the solution $x^{*}$ that are recognized as linearly independent. The _RHS_ variable contains a missing value, and the _NAME_ variable is blank.

NLC_EQ
NLC_GE
NLC_LE

Contains values and residuals of nonlinear constraints. The _NAME_ variable is described as follows:

`_NAME_`	Description
NLC	Inactive nonlinear constraint
NLCACT	Linear independent active nonlinear constraint
NLCACTLD	Linear dependent active nonlinear constraint

NLDACTBC

Contains the number of active boundary constraints at the solution $x^{*}$ that are recognized as linearly dependent. The _RHS_ variable contains a missing value, and the _NAME_ variable is blank.

NLDACTLC

Contains the number of active linear constraints at the solution $x^{*}$ that are recognized as linearly dependent. The _RHS_ variable contains a missing value, and the _NAME_ variable is blank.

_NOBS_

Contains the number of observations.

PARMS

Contains the final parameter estimates. The _RHS_ variable contains the value of the objective function.

PCRPJ_LF

Contains the projected Hessian matrix of the Lagrange function (based on CRPJAC).

PHESS_LF

Contains the projected Hessian matrix of the Lagrange function (based on HESSIAN).

PROJCRPJ

Contains the projected Hessian matrix (based on CRPJAC).

PROJGRAD

If linear constraints are used in the estimation, this observation contains the $n - n_{\mathit{act}}$ values of the projected gradient $\mb {g}_ z = \bZ ^{\prime }\mb {g}$ in the variables corresponding to the first $n-n_{\mathit{act}}$ parameters. The _RHS_ variable contains a missing value, and the _NAME_ variable is blank.

PROJHESS

Contains the projected Hessian matrix (based on HESSIAN).

STDERR

Contains approximate standard errors (only for METHOD=ML, METHOD=GLS, or METHOD=WLS).

TERMINAT

The _NAME_ variable contains the name of the termination criterion.

UPPERBD
| UB

If boundary constraints are used, this observation contains the upper bounds. Those parameters not subjected to upper bounds contain missing values. The _RHS_ variable contains a missing value, and the _NAME_ variable is blank.

If the technique specified by the OMETHOD= option cannot be performed (for example, no feasible initial values can be computed or the function value or derivatives cannot be evaluated at the starting point), the OUTEST= data set can contain only some of the observations (usually only the PARMS and GRAD observations).

OUTMODEL= or OUTRAM= Data Set

The OUTMODEL= (or OUTRAM=) data set is of TYPE=CALISMDL and contains the model specification, the computed parameter estimates, and the standard error estimates. This data set is intended to be reused as an INMODEL= data set to specify good initial values in a subsequent analysis by PROC CALIS.

The OUTMODEL= data set contains the following variables:

the BY variables, if any
an _MDLNUM_ variable for model numbers, if used
a character variable _TYPE_, which takes various values that indicate the type of model specification
a character variable _NAME_, which indicates the model type, parameter name, or variable name
a character variable _MATNR_, which indicates the matrix number (COSAN models only)
a character variable _VAR1_, which is the name or number of the first variable in the specification
a character variable _VAR2_, which is the name or number of the second variable in the specification
a numerical variable _ESTIM_ for the final estimate of the parameter location
a numerical variable _STDERR_ for the standard error estimate of the parameter location
a numerical variable _SDEST_ for the final standardized estimate of the parameter location
a numerical variable _SDSE_ for the standard error of the standardized estimate of the parameter location

Although the _SDEST_ and _SDSE_ variables are created for COSAN models, the values for these two variables are always missing because there are no rules to carry out the standardization of COSAN models.

Each observation (record) of the OUTMODEL= data set contains a piece of information regarding the model specification. Depending on the type of the specification indicated by the value of the _TYPE_ variable, the meanings of _NAME_, _VAR1_, and _VAR2_ differ. The following tables summarize the meanings of the _NAME_, _MATNR_ (COSAN models only), _VAR1_, and _VAR2_ variables for each value of the _TYPE_ variable, given the type of the model.

COSAN Models

`_TYPE_`=	Description	`_NAME_`	`_MATNR_`	`_VAR1_`	`_VAR2_`
MDLTYPE	Model type	COSAN
VAR	Variable	Variable name	Matrix number	Column location
MATRIX	Matrix	Matrix name	Matrix number	Number of rows	Number of columns
MODEL	Model formula	COV or MEAN	Matrix number	Term number	Location in term
ESTIM	Parameters	Parameter name	Matrix number	Row number	Column number

The value of the _NAME_ variable is COSAN for the _TYPE_=MDLTYPE observation.

The _TYPE_=VAR observations store the information about the column variables in matrices. The _NAME_ variable stores the variable names. The value of _VAR1_ indicates the column location of the variable in the matrix with the matrix number stored in _MATNR_.

The _TYPE_=MATRIX observations store the information about the model matrices. The _NAME_ variable stores the matrix names. The value of _MATNR_ indicates the corresponding matrix number. The values of_VAR1_ and _VAR2_ indicates the numbers of rows and columns, respectively, of the matrix.

The _TYPE_=MODEL observations store the covariance and mean structure formulas. The _NAME_ variable indicates whether the mean (MEAN) or covariance (COV) structure information is stored. The value of _MATNR_ indicates the matrix number in the mean or covariance structure formula. The _VAR1_ variable indicates the term number, and the _VAR2_ variable indicates the location of the matrix in the term.

The _TYPE_=ESTIM observations store the information about the parameters and their estimates. The _NAME_ variable stores the parameter names. The value of _MATNR_ indicates the matrix number. The values of _VAR1_ and _VAR2_ indicate the associated row and column numbers, respectively, of the parameter.

FACTOR Models

`_TYPE_`=	Description	`_NAME_`	`_VAR1_`	`_VAR2_`
MDLTYPE	Model type	Model type
FACTVAR	Variable	Variable name	Variable number	Variable type
LOADING	Factor loading	Parameter name	Manifest variable	Factor variable
COV	Covariance	Parameter name	First variable	Second variable
PVAR	(Partial) variance	Parameter name	Variable
MEAN	Mean or intercept	Parameter name	Variable
ADDCOV	Added covariance	Parameter name	First variable	Second variable
ADDPVAR	Added (partial) variance	Parameter name	Variable
ADDMEAN	Added mean or intercept	Parameter name	Variable

For factor models, the value of the _NAME_ variable is either EFACTOR (exploratory factor model) or CFACTOR (confirmatory factor model) for the _TYPE_=MDLTYPE observation.

The _TYPE_=FACTVAR observations store the information about the variables in the model. The _NAME_ variable stores the variable names. The value of _VAR1_ indicates the variable number. The value of _VAR2_ indicates the type of the variable: either DEPV for dependent observed variables or INDF for latent factors.

Other observations specify the parameters and their estimates in the model. The _NAME_ values for these observations are the parameter names. Observation with _TYPE_=LOADING, _TYPE_=COV, or _TYPE_=ADDCOV are for parameters that are associated with two variables. The _VAR1_ and _VAR2_ values of these two types of observations indicate the variables involved.

Observations with _TYPE_=PVAR, _TYPE_=MEAN, _TYPE_=ADDPVAR, or _TYPE_=ADDMEAN are for parameters that are associated with a single variable. The value of _VAR1_ indicates the variable involved.

LINEQS Models

`_TYPE_`=	Description	`_NAME_`	`_VAR1_`	`_VAR2_`
MDLTYPE	Model type	LINEQS
EQSVAR	Variable	Variable name	Variable number	Variable type
EQUATION	Path coefficient	Parameter	Outcome variable	Predictor variable
COV	Covariance	Parameter	First variable	Second variable
VARIANCE	Variance	Parameter	Variable
MEAN	Mean	Parameter	Variable
ADDCOV	Added covariance	Parameter	First variable	Second variable
ADDVARIA	Added variance	Parameter	Variable
ADDINTE	Added intercept	Parameter	Variable
ADDMEAN	Added mean	Parameter	Variable

The value of the _NAME_ variable is LINEQS for the _TYPE_=MDLTYPE observation.

The _TYPE_=EQSVAR observations store the information about the variables in the model. The _NAME_ variable stores the variable names. The value of _VAR1_ indicates the variable number. The value of _VAR2_ indicates the type of the variable. There are six types of variables in the LINEQS model:

DEPV for dependent observed variables
INDV for independent observed variables
DEPF for dependent latent factors
INDF for independent latent factors
INDD for independent error terms
INDE for independent disturbance terms

Other observations specify the parameters and their estimates in the model. The _NAME_ values for these observations are the parameter names. Observation with _TYPE_=EQUATION, _TYPE_=COV, or _TYPE_=ADDCOV are for parameters that are associated with two variables. The _VAR1_ and _VAR2_ values of these two types of observations indicate the variables involved.

Observations with _TYPE_=VARIANCE, _TYPE_=MEAN, _TYPE_=ADDVARIA, _TYPE_=ADDINTE, or _TYPE_=ADDMEAN are for parameters associated with a single variable. The value of _VAR1_ indicates the variable involved.

LISMOD Models

`_TYPE_`=	Description	`_NAME_`	`_VAR1_`	`_VAR2_`
MDLTYPE	model type	LISMOD
XVAR	$\mb {x}$ -variable	Variable	Variable number
YVAR	$\mb {y}$ -variable	Variable	Variable number
ETAVAR	$\bm {\eta }$ -variable	Variable	Variable number
XIVAR	$\bxi$ -variable	Variable	Variable number
ALPHA	_ALPHA_ entry	Parameter	Row number
BETA	_BETA_ entry	Parameter	Row number	Column number
GAMMA	_BETA_ entry	Parameter	Row number	Column number
KAPPA	_KAPPA_ entry	Parameter	Row number
LAMBDAX	_LAMBDAX_ entry	Parameter	Row number	Column number
LAMBDAY	_LAMBDAY_ entry	Parameter	Row number	Column number
NUX	_NUX_ entry	Parameter	Row number
NUY	_NUY_ entry	Parameter	Row number
PHI	_PHI_ entry	Parameter	Row number	Column number
PSI	_PSI_ entry	Parameter	Row number	Column number
THETAX	_THETAX_ entry	Parameter	Row number	Column number
THETAY	_THETAY_ entry	Parameter	Row number	Column number
ADDALPHA	Added _ALPHA_ entry	Parameter	Row number
ADDKAPPA	Added _KAPPA_ entry	Parameter	Row number
ADDNUX	Added _NUX_ entry	Parameter	Row number
ADDNUY	Added _NUY_ entry	Parameter	Row number
ADDPHI	Added _PHI_ entry	Parameter	Row number	Column number
ADDPSI	Added _PSI_ entry	Parameter	Row number	Column number
ADTHETAX	Added _THETAX_ entry	Parameter	Row number	Column number
ADTHETAY	Added _THETAY_ entry	Parameter	Row number	Column number

The value of the _NAME_ variable is LISMOD for the _TYPE_=MDLTYPE observation. Other observations specify either the variables or the parameters in the model.

Observations with _TYPE_ values equal to XVAR, YVAR, ETAVAR, and XIVAR indicate the variables in the respective lists in the model. The _NAME_ variable of these observations stores the names of the variables, and the _VAR1_ variable stores the variable numbers in the respective list. The variable numbers in this data set are not arbitrary—that is, they define the variable orders in the rows and columns of the LISMOD model matrices. The _VAR2_ variable of these observations is not used.

All other observations in this data set specify the parameters in the model. The _NAME_ values of these observations are the parameter names. The corresponding _VAR1_ and _VAR2_ values of these observations indicate the row and column locations of the parameters in the LISMOD model matrices that are specified in the _TYPE_ variable. For example, when the value of _TYPE_ is ADDPHI or PHI, the parameter specified is located in the _PHI_ matrix, with its row and column numbers indicated by the _VAR1_ and _VAR2_ values, respectively. Some observations for specifying parameters do not have values in the _VAR2_ variable. This means that the associated LISMOD matrices are vectors so that the column numbers are always 1 for these observations.

MSTRUCT Models

`_TYPE_`=	Description	`_NAME_`	`_VAR1_`	`_VAR2_`
MDLTYPE	Model type	MSTRUCT
VAR	Variable	Variable	Variable number
COVMAT	Covariance	Parameter	Row number	Column number
MEANVEC	Mean	Parameter	Row number
ADCOVMAT	Added covariance	Parameter	Row number	Column number
AMEANVEC	Added mean	Parameter	Row number

The value of the _NAME_ variable is MSTRUCT for the _TYPE_=MDLTYPE observation. Other observations specify either the variables or the parameters in the model.

Observations with _TYPE_ values equal to VAR indicate the variables in the model. The _NAME_ variable of these observations stores the names of the variables, and the _VAR1_ variable stores the variable numbers in the variable list. The variable numbers in this data set are not arbitrary—that is, they define the variable orders in the rows and columns of the mean and covariance matrices. The _VAR2_ variable of these observations is not used.

All other observations in this data set specify the parameters in the model. The _NAME_ values of these observations are the parameter names. The corresponding _VAR1_ and _VAR2_ values of these observations indicate the row and column locations of the parameters in the mean or covariance matrix, as specified in the _TYPE_ model. For example, when _TYPE_=COVMAT, the parameter specified is located in the covariance matrix, with its row and column numbers indicated by the _VAR1_ and _VAR2_ values, respectively. For observations with _TYPE_=MEANVEC, the _VAR2_ variable is not used because the column numbers are always 1 for parameters in the mean vector.

PATH Models

`_TYPE_`=	Description	`_NAME_`	`_VAR1_`	`_VAR2_`
MDLTYPE	Model type	PATH
PATHVAR	Variable	Variable name	Variable number	Variable type
LEFT	Path coefficient	Parameter	Outcome variable	Predictor variable
RIGHT	Path coefficient	Parameter	Predictor variable	Outcome variable
PCOV	(Partial) covariance	Parameter	First variable	Second variable
PCOVPATH	(Partial) covariance path	Parameter	First variable	Second variable
PVAR	(Partial) variance	Parameter	Variable
PVARPATH	(Partial) variance path	Parameter	Variable	Variable
MEAN	Mean or intercept	Parameter	Variable
ONEPATH	Mean or intercept path	Parameter	_ONE_	Variable
ADDPCOV	Added (partial) covariance	Parameter	First variable	Second variable
ADDPVAR	Added (partial) variance	Parameter	Variable
ADDMEAN	Added mean	Parameter	Variable

The value of the _NAME_ variable is PATH for the _TYPE_=MDLTYPE observation.

The _TYPE_=PATHVAR observations store the information about the variables in the model. The _NAME_ variable stores the variable names. The value of _VAR1_ indicates the variable number. The value of _VAR2_ indicates the type of the variable. There are four types of variables in the PATH model:

DEPV for dependent observed variables
INDV for independent observed variables
DEPF for dependent latent factors
INDF for independent latent factors

Other observations specify the parameters in the model. The _NAME_ values for these observations are the parameter names. Observation with _TYPE_=LEFT, _TYPE_=RIGHT, _TYPE_=PCOV, or _TYPE_=ADDPCOV are for parameters that are associated with two variables. The _VAR1_ and _VAR2_ values of these two types of observations indicate the variables involved.

RAM Models

`_TYPE_`=	Description	`_NAME_`	`_VAR1_`	`_VAR2_`
MDLTYPE	Model type	RAM
RAMVAR	Variable name	Variable	Variable number	Variable type
_A_	`_A_` entry	Parameter	Row number	Column number
_P_	`_P_` entry	Parameter	Row number	Column number
_W_	`_W_` entry	Parameter	Row number	Column number
ADD_P_	Added `_P_` entry	Parameter	Row number	Column number
ADD_W_	Added `_W_` entry	Parameter	Row number	Column number

The value of the _NAME_ variable is RAM for the _TYPE_=MDLTYPE observation.

For the _TYPE_=RAMVAR observations, the _NAME_ variable stores the variable names, the _VAR1_ variable stores the variable number, and the _VAR2_ variable stores the variable type. There are four types of variables in the PATH model:

DEPV for dependent observed variables
INDV for independent observed variables
DEPF for dependent latent factors
INDF for independent latent factors

Other observations specify the parameters in the model. The _NAME_ variable stores the parameter name. The _TYPE_ variable indicates the associated matrix with the row number indicated in _VAR1_ and column number indicated in _VAR2_.

Reading an OUTMODEL= Data Set As an INMODEL= Data Set in Subsequent Analyses

When the OUTMODEL= data set is treated as an INMODEL= data set in subsequent analyses, you need to pay attention to observations with _TYPE_ values prefixed by “ADD”, “AD”, or “A” (for example, ADDCOV, ADTHETAY, or AMEANVEC). These observations represent default parameter locations that are generated by PROC CALIS in a previous run. Because the context of the new analyses might be different, these observations for added parameter locations might no longer be suitable in the new runs. Hence, these observations are not read as input model information. Fortunately, after reading the INMODEL= specification in the new analyses, CALIS analyzes the new model specification again. It then adds an appropriate set of parameters in the new context when necessary. If you are certain that the added parameter locations in the INMODEL= data set are applicable, you can force the input of these observations by using the READADDPARM option in the PROC CALIS statement. However, you must be very careful about using the READADDPARM option. The added parameters from the INMODEL= data set might have the same parameter names as those for the generated parameters in the new run. This might lead to unnecessary constraints in the model.

OUTSTAT= Data Set

The OUTSTAT= data set is similar to the TYPE=COV, TYPE=UCOV, TYPE=CORR, or TYPE=UCORR data set produced by the CORR procedure. The OUTSTAT= data set contains the following variables:

the BY variables, if any
the _GPNUM_ variable for groups numbers, if used in the analysis
two character variables, _TYPE_ and _NAME_
the manifest and the latent variables analyzed

The OUTSTAT= data set contains the following information (when available) in the observations:

the mean and standard deviation
the skewness and kurtosis (if the DATA= data set is a raw data set and the KURTOSIS option is specified)
the number of observations
if the WEIGHT statement is used, sum of the weights
the correlation or covariance matrix to be analyzed
the robust covariances, standard deviations, and means for robust estimation
the predicted correlation or covariance matrix
the standardized or normalized residual correlation or covariance matrix
if the model contains latent variables, the predicted covariances between latent and manifest variables and the latent variable (or factor) score regression coefficients (see the PLATCOV option )

In addition, for FACTOR models the OUTSTAT= data set contains:

the unrotated factor loadings, the error variances, and the matrix of factor correlations
the standardized factor loadings and factor correlations
the rotation matrix, rotated factor loadings, and factor correlations
standardized rotated factor loadings and factor correlations

If effects are analyzed, the OUTSTAT= data set also contains:

direct, indirect, and total effects and their standard error estimates
standardized direct, indirect, and total effects and their standard error estimates

Each observation in the OUTSTAT= data set contains some type of statistic as indicated by the _TYPE_ variable. The values of the _TYPE_ variable are shown in the following tables:

Basic Descriptive Statistics

Value of `_TYPE_`	Contents
ADJCOV	Adjusted covariances
ADJSTD	Adjusted standard deviations
CORR	Correlations
COV	Covariances
KURTOSIS	Univariate kurtosis
MEAN	Means
N	Sample size
NPARTIAL	Number of partial variables
PARTCOV	Covariances after partialling
PARTCORR	Correlations after partialling
PARTMEAN	Means after partialling
PARTSTD	Standard deviations after partialling
ROBCOV	Robust covariances
ROBMEAN	Robust means
ROBSTD	Robust standard deviations
SKEWNESS	Univariate skewness
STD	Standard deviations
SUMWGT	Sum of weights (if the WEIGHT statement is used)
VARDIV	Variance divisor
VARDIVAJ	Variance divisor adjustment

For the _TYPE_=CORR or COV observations, the _NAME_ variable contains the name of the manifest variable that corresponds to each row for the covariance or correlation. For other observations, _NAME_ is blank.

Predicted Moments and Residuals

value of `_TYPE_`	Contents
METHOD=DWLS
DWLSPRED	DWLS predicted moments
DWLSRES	DWLS raw residuals
DWLSSRES	DWLS variance standardized residuals
METHOD=GLS
GLSASRES	GLS asymptotically standardized residuals
GLSNRES	GLS normalized residuals
GLSPRED	GLS predicted moments
GLSRES	GLS raw residuals
GLSSRES	GLS variance standardized residuals
METHOD=ML or FIML
MAXASRES	ML asymptotically standardized residuals
MAXNRES	ML normalized residuals
MAXPRED	ML predicted moments
MAXRES	ML raw residuals
MAXSRES	ML variance standardized residuals
METHOD=ULS
ULSPRED	ULS predicted moments
ULSRES	ULS raw residuals
ULSSRES	ULS variance standardized residuals
METHOD=WLS
WLSASRES	WLS asymptotically standardized residuals
WLSNRES	WLS normalized residuals
WLSPRED	WLS predicted moments
WLSRES	WLS raw residuals
WLSSRES	WLS variance standardized residuals

For residuals or predicted moments of means, the _NAME_ variable is a fixed value denoted by _Mean_. For residuals or predicted moments for covariances or correlations, the _NAME_ variable is used for names of variables.

Effects and Latent Variable Scores Regression Coefficients

Value of `_TYPE_`	Contents
Unstandardized Effects
DEFFECT	Direct effects
DEFF_SE	Standard error estimates for direct effects
IEFFECT	Indirect effects
IEFF_SE	Standard error estimates for indirect effects
TEFFECT	Total effects
TEFF_SE	Standard error estimates for total effects
Standardized Effects
SDEFF	Standardized direct effects
SDEFF_SE	Standard error estimates for standardized direct effects
SIEFF	Standardized indirect effects
SIEFF_SE	Standard error estimates for standardized indirect effects
STEFF	Standardized total effects
STEFF_SE	Standard error estimates for standardized total effects
Latent Variable Scores Coefficients
LSSCORE	Latent variable (or factor) scores regression coefficients for ULS method
SCORE	Latent variable (or factor) scores regression coefficients other than ULS method

For latent variable or factor scores coefficients, the _NAME_ variable contains factor or latent variables in the observations. For other observations, the _NAME_ variable contains manifest or latent variable names.

You can use the latent variable score regression coefficients with PROC SCORE to compute factor scores. If the analyzed matrix is a covariance rather than a correlation matrix, the _TYPE_=STD observation is not included in the OUTSTAT= data set. In this case, the standard deviations can be obtained from the diagonal elements of the covariance matrix. Dropping the _TYPE_=STD observation prevents PROC SCORE from standardizing the observations before computing the factor scores.

Factor Analysis Results

Value of `_TYPE_`	Contents
ERRVAR	Error variances
FCOV	Factor correlations or covariances
LOADINGS	Unrotated factor loadings
RFCOV	Rotated factor correlations or covariances
RLOADING	Rotated factor loadings
ROTMAT	Rotation matrix
STDFCOV	Standardized factor correlations
STDLOAD	Standardized factor loadings
STDRFCOV	Standardized rotated factor correlations or covariances
STDRLOAD	Standardized rotated factor loadings

For the _TYPE_=ERRVAR observation, the _NAME_ variable is blank. For all other observations, the _NAME_ variable contains factor names.

OUTWGT= Data Set

You can create an OUTWGT= data set that is of TYPE=WEIGHT and contains the weight matrix used in generalized, weighted, or diagonally weighted least squares estimation. The OUTWGT= data set contains the weight matrix on which the WRIDGE= and the WPENALTY= options are applied. However, if you input the inverse of the weight matrix with the INWGT= and INWGTINV options (or the INWGT(INV)= option alone) in the same analysis, the OUTWGT= data set contains the same elements of the inverse of the weight matrix. For unweighted least squares or maximum likelihood estimation, no OUTWGT= data set can be written. The weight matrix used in maximum likelihood estimation is dynamically updated during optimization. When the ML solution converges, the final weight matrix is the same as the predicted covariance or correlation matrix, which is included in the OUTSTAT= data set (observations with _TYPE_ =MAXPRED).

For generalized and diagonally weighted least squares estimation, the weight matrices $\mb {W}$ of the OUTWGT= data set contain all elements $w_{ij}$ , where the indices i and j correspond to all manifest variables used in the analysis. Let $\mathit{varnam}_ i$ be the name of the ith variable in the analysis. In this case, the OUTWGT= data set contains n observations with the variables shown in the following table:

Variable	Contents
`_TYPE_`	WEIGHT (character)
`_NAME_`	Name of variable $\mathit{varnam}_ i$ (character)
$\mathit{varnam}_1$	Weight $w_{i1}$ for variable $\mathit{varnam}_1$ (numeric)
$\vdots$	$\vdots$
$\mathit{varnam}_ n$	Weight $w_{in}$ for variable $\mathit{varnam}_ n$ (numeric)

For weighted least squares estimation, the weight matrix $\mb {W}$ of the OUTWGT= data set contains only the nonredundant elements $w_{ij,kl}$ . In this case, the OUTWGT= data set contains observations with the variables shown in the following table:

Variable	Contents
`_TYPE_`	WEIGHT (character)
`_NAME_`	Name of variable $\mathit{varnam}_ i$ (character)
`_NAM2_`	Name of variable $\mathit{varnam}_ j$ (character)
`_NAM3_`	Name of variable $\mathit{varnam}_ k$ (character)
$\mathit{varnam}_1$	Weight $w_{ij,k1}$ for variable $\mathit{varnam}_1$ (numeric)
$\vdots$	$\vdots$
$\mathit{varnam}_ n$	Weight $w_{ij,kn}$ for variable $\mathit{varnam}_ n$ (numeric)

Symmetric redundant elements are set to missing values.

OUTFIT= Data Set

You can create an OUTFIT= data set that is of TYPE=CALISFIT and that contains the values of the fit indices of your analysis. If you use two estimation methods such as LSML or LSWLS, the fit indices are for the second analysis. An OUTFIT=data set contains the following variables:

a character variable _TYPE_ for the types of fit indices
a numerical variable IndexCode for the codes of the fit indices
a character variable FitIndex for the names of the fit indices
a numerical variable FitValue for the numerical values of the fit indices
a character variable PrintChar for the character-formatted fit index values.

The possible values of _TYPE_ are:

ModelInfo:: basic modeling statistics and information
Absolute:: stand-alone fit indices
Parsimony:: fit indices that take model parsimony into account
Incremental:: fit indices that are based on comparison with a baseline model

Possible Values of `FitIndex` When `_TYPE_`=`ModelInfo`

Value of `FitIndex`	Description
Number of Observations	Number of observations used in the analysis
Number of Complete Observations	Number of complete observations (METHOD=FIML)
Number of Incomplete Observations	Number of incomplete observations (METHOD=FIML)
Number of Variables	Number of variables
Number of Moments	Number of mean or covariance elements
Number of Parameters	Number of parameters
Number of Active Constraints	Number of active constraints in the solution
Saturated Model Estimation	Estimation status of the saturated model (METHOD=FIML)
Saturated Model Function Value	Saturated model function value (METHOD=FIML)
Saturated Model -2 Log-Likelihood	Saturated model –2 log-likelihood function value (METHOD=FIML)
Baseline Model Estimation	Estimation status of the baseline model (METHOD=FIML)
Baseline Model Function Value	Baseline model function value
Baseline Model -2 Log-Likelihood	Baseline model –2 log-likelihood function value (METHOD=FIML)
Baseline Model Chi-Square	Baseline model chi-square value
Baseline Model Chi-Square DF	Baseline model chi-square degrees of freedom
Baseline Model DF	Baseline model degrees of freedom (METHOD=ULS or METHOD=DWLS)
Pr > Baseline Model Chi-Square	p value of the baseline model chi-square

Possible Values of `FitIndex` When `_TYPE_`=`Absolute`

Value of `FitIndex`	Description
Fit Function	Fit function value
-2 Log-Likelihood	–2 log-likelihood function value for the model (METHOD=FIML)
Chi-Square	Model chi-square value
Chi-Square DF	Degrees of freedom for the model chi-square test
Model DF	Degrees of freedom for model (METHOD=ULS or METHOD=DWLS)
Pr > Chi-Square	Probability of obtaining a larger chi-square than the observed value
Percent Contribution to Chi-Square	Percentage contribution to the chi-square value
Percent Contribution to Likelihood	Percentage contribution to the –2 log-likelihood function value (METHOD=FIML)
Elliptic Corrected Chi-Square	Elliptic-corrected chi-square value
Pr > Elliptic Corr. Chi-Square	Probability of obtaining a larger elliptic-corrected chi-square value
Z-test of Wilson and Hilferty	Z-test of Wilson and Hilferty
Hoelter Critical N	N value that makes a significant chi-square when multiplied to the fit function value
Root Mean Square Residual (RMR)	Root mean square residual
Standardized RMR (SRMR)	Standardized root mean square residual
Goodness of Fit Index (GFI)	Jöreskog and Sörbom goodness-of-fit index

Possible Values of `FitIndex` When `_TYPE_`=`Parsimony`

Value of `FitIndex`	Description
Adjusted GFI (AGFI)	Goodness-of-fit index adjusted for the degrees of freedom of the model
Parsimonious GFI	Mulaik et al. (1989) modification of the GFI
RMSEA Estimate	Steiger and Lind (1980) root mean square error approximation
RMSEA Lower r% Confidence Limit	Lower r% confidence limit for RMSEA
RMSEA Upper r% Confidence Limit	Upper r% confidence limit for RMSEA
Probability of Close Fit	Browne and Cudeck (1993) test of close fit
ECVI Estimate	Expected cross-validation index
ECVI Lower r% Confidence Limit	Lower r% confidence limit for ECVI
ECVI Upper r% Confidence Limit	Upper r% confidence limit for ECVI
Akaike Information Criterion	Akaike information criterion
Bozdogan CAIC	Bozdogan (1987) consistent AIC
Schwarz Bayesian Criterion	Schwarz (1978) Bayesian criterion
McDonald Centrality	McDonald and Marsh (1988) measure of centrality

1. The value of r is one minus the ALPHARMS= value. By default, r=90. 2. The value of r is one minus the ALPHAECV= value. By default, r=90.

Possible Values of `FitIndex` When `_TYPE_`=`Incremental`

Value of `FitIndex`	Description
Bentler Comparative Fit Index	Bentler (1985) comparative fit index
Bentler-Bonett NFI	Bentler and Bonett (1980) normed fit index
Bentler-Bonett Non-normed Index	Bentler and Bonett (1980) nonnormed fit index
Bollen Normed Index Rho1	Bollen normed $\rho _1$
Bollen Non-normed Index Delta2	Bollen nonnormed $\delta _2$
James et al. Parsimonious NFI	James, Mulaik, and Brett (1982) parsimonious normed fit index