Output Data Sets

The CALIS Procedure

Output Data Sets

OUTEST= SAS-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 b_i of a linear constraint or for the value f=f(x) 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 19.5 are available in the OUTEST= data set, depending on the request.

Table 19.5: _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, ... ,n, the _RHS_ variable contains b_i, 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, ... ,n, and the _RHS_ variable contains b_i. 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).

INITIAL

contains the starting values of the parameter estimates.

JACNLC

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

JACOBIAN

contains the Jacobian matrix (only if the OUTJAC option is used).

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 containing 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, ... ,n, and the _RHS_ variable contains b_i. 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 constr.
NLCACTLD	linear dependent active nonlinear constr.

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_act values of the projected gradient g_Z = Z'g in the variables corresponding to the first n-n_act parameters. The _RHS_ variable contains a missing value, and the _NAME_ variable is blank.

PROJHESS

contains the projected Hessian matrix (based on HESSIAN).

SIGSQ

contains the scalar factor of the covariance matrix of the parameter estimates.

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 TECH= 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 may contain only some of the observations (usually only the PARMS and GRAD observations).

OUTRAM= SAS-data-set

The OUTRAM= data set is of TYPE=RAM and contains the model specification and the computed parameter estimates. This data set is intended to be reused as an INRAM= data set to specify good initial values in a subsequent analysis by PROC CALIS. For a structural equation model, after some alterations, this data set can be used for plotting a path diagram by the NETDRAW procedure, a SAS/OR procedure.

The OUTRAM= data set contains the following variables:

the BY variables, if any
the character variable _TYPE_, which takes the values MODEL, ESTIM, VARNAME, METHOD, and STAT
six additional variables whose meaning depends on the _TYPE_ of the observation

Each observation with _TYPE_ =MODEL defines one matrix in the generalized COSAN model. The additional variables are as follows.

Table 19.6: Additional Variables when _TYPE_=MODEL

Variable	Contents
_NAME_	name of the matrix (character)
_MATNR_	number for the term and matrix in the model (numeric)
_ROW_	matrix row number (numeric)
_COL_	matrix column number (numeric)
_ESTIM_	first matrix type (numeric)
_STDERR_	second matrix type (numeric)

If the generalized COSAN model has only one matrix term, the _MATNR_ variable contains only the number of the matrix in the term. If there is more than one term, then it is the term number multiplied by 10,000 plus the matrix number (assuming that there are no more than 9,999 matrices specified in the COSAN model statement).

Each observation with _TYPE_ =ESTIM defines one element of a matrix in the generalized COSAN model. The variables are used as follows.

Table 19.7: Additional Variables when _TYPE_=ESTIM

Variable	Contents
_NAME_	name of the parameter (character)
_MATNR_	term and matrix location of parameter (numeric)
_ROW_	row location of parameter (numeric)
_COL_	column location of parameter (numeric)
_ESTIM_	parameter estimate or constant value (numeric)
_STDERR_	standard error of estimate (numeric)

For constants rather than estimates, the _STDERR_ variable is 0. The _STDERR_ variable is missing for ULS and DWLS estimates if NOSTDERR is specified or if the approximate standard errors are not computed.

Each observation with _TYPE_ =VARNAME defines a column variable name of a matrix in the generalized COSAN model.

The observations with _TYPE_=METHOD and _TYPE_=STAT are not used to build the model. The _TYPE_=METHOD observation contains the name of the estimation method used to compute the parameter estimates in the _NAME_ variable. If METHOD=NONE is not specified, the _ESTIM_ variable of the _TYPE_=STAT observations contains the information summarized in Table 19.8 (described in the section "Assessment of Fit").

Table 19.8: _ESTIM_ Contents for _TYPE_=STAT

_NAME_	_ESTIM_
N	sample size
NPARM	number of parameters used in the model
DF	degrees of freedom
N_ACT	number of active boundary constraints
	for ML, GLS, and WLS estimation
FIT	fit function
GFI	goodness-of-fit index (GFI)
AGFI	adjusted GFI for degrees of freedom
RMR	root mean square residual
PGFI	parsimonious GFI of Mulaik et al. (1989)
CHISQUAR	overall $\chi^2$
P_CHISQ	probability $\gt \chi^2$
CHISQNUL	null (baseline) model $\chi^2$
RMSEAEST	Steiger & Lind's (1980) RMSEA index estimate
RMSEALOB	lower range of RMSEA confidence interval
RMSEAUPB	upper range of RMSEA confidence interval
P_CLOSFT	Browne & Cudeck's (1993) probability of close fit
ECVI_EST	Browne & Cudeck's (1993) ECV index estimate
ECVI_LOB	lower range of ECVI confidence interval
ECVI_UPB	upper range of ECVI confidence interval
COMPFITI	Bentler's (1989) comparative fit index
ADJCHISQ	adjusted $\chi^2$ for elliptic distribution
P_ACHISQ	probability corresponding adjusted $\chi^2$
RLSCHISQ	reweighted least-squares $\chi^2$ (only ML estimation)
AIC	Akaike's information criterion
CAIC	Bozdogan's consistent information criterion
SBC	Schwarz's Bayesian criterion
CENTRALI	McDonald's centrality criterion
PARSIMON	Parsimonious index of James, Mulaik, and Brett
ZTESTWH	z test of Wilson and Hilferty
BB_NONOR	Bentler-Bonett (1980) nonnormed index $\rho$
BB_NORMD	Bentler-Bonett (1980) normed index $\Delta$
BOL_RHO1	Bollen's (1986) normed index $\rho_1$
BOL_DEL2	Bollen's (1989a) nonnormed index $\Delta_2$
CNHOELT	Hoelter's critical N index

You can edit the OUTRAM= data set to use its contents for initial estimates in a subsequent analysis by PROC CALIS, perhaps with a slightly changed model. But you should be especially careful for _TYPE_=MODEL when changing matrix types. The codes for the two matrix types are listed in Table 19.9.

Table 19.9: Matrix Type Codes

Code	First Matrix Type	Description
1:	IDE	identity matrix
2:	ZID	zero:identity matrix
3:	DIA	diagonal matrix
4:	ZDI	zero:diagonal matrix
5:	LOW	lower triangular matrix
6:	UPP	upper triangular matrix
7:		temporarily not used
8:	SYM	symmetric matrix
9:	GEN	general-type matrix
10:	BET	identity minus general-type matrix
11:	PER	selection matrix
12:		first matrix (J) in LINEQS model statement
13:		second matrix ( ${\beta}$ ) in LINEQS model statement
14:		third matrix ( ${\gamma}$ ) in LINEQS model statement
Code	Second Matrix Type	Description
0:		noninverse model matrix
1:	INV	inverse model matrix
2:	IMI	'identity minus inverse' model matrix

OUTSTAT= SAS-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
two character variables, _TYPE_ and _NAME_
the variables analyzed, that is, those in the VAR statement, or if there is no VAR statement, all numeric variables not listed in any other statement but used in the analysis. (Caution: Using the LINEQS or RAM model statements selects variables automatically.)

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

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 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 display option)

In addition, if the FACTOR model statement is used, the OUTSTAT= data set contains:

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

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 given in Table 19.10.

Table 19.10: _TYPE_ Observations in the OUTSTAT= data set

_TYPE_	Contents
MEAN	means
STD	standard deviations
USTD	uncorrected standard deviations
SKEWNESS	univariate skewness
KURTOSIS	univariate kurtosis
N	sample size
SUMWGT	sum of weights (if WEIGHT statement is used)
COV	covariances analyzed
CORR	correlations analyzed
UCOV	uncorrected covariances analyzed
UCORR	uncorrected correlations analyzed
ULSPRED	ULS predicted model values
GLSPRED	GLS predicted model values
MAXPRED	ML predicted model values
WLSPRED	WLS predicted model values
DWLSPRED	DWLS predicted model values
ULSNRES	ULS normalized residuals
GLSNRES	GLS normalized residuals
MAXNRES	ML normalized residuals
WLSNRES	WLS normalized residuals
DWLSNRES	DWLS normalized residuals
ULSSRES	ULS variance standardized residuals
GLSSRES	GLS variance standardized residuals
MAXSRES	ML variance standardized residuals
WLSSRES	WLS variance standardized residuals
DWLSSRES	DWLS variance standardized residuals
ULSASRES	ULS asymptotically standardized residuals
GLSASRES	GLS asymptotically standardized residuals
MAXASRES	ML asymptotically standardized residuals
WLSASRES	WLS asymptotically standardized residuals
DWLSASRS	DWLS asymptotically standardized residuals
UNROTATE	unrotated factor loadings
FCORR	matrix of factor correlations
UNIQUE_V	unique variances
TRANSFOR	transformation matrix of rotation
LOADINGS	rotated factor loadings
STD_LOAD	standardized factor loadings
LSSCORE	latent variable (or factor) score regression coefficients for ULS method
SCORE	latent variable (or factor) score regression coefficients other than ULS method

The _NAME_ variable contains the name of the manifest variable corresponding to each row for the covariance, correlation, predicted, and residual matrices and contains the name of the latent variable in case of factor regression scores. For other observations, _NAME_ is blank.

The unique variances and rotated loadings can be used as starting values in more difficult and constrained analyses.

If the model contains latent variables, the OUTSTAT= data set also contains the latent variable score regression coefficients and the predicted covariances between latent and manifest variables.

You can use the latent variable score regression coefficients with PROC SCORE to compute factor scores. If the analyzed matrix is a (corrected or uncorrected) covariance rather than a correlation matrix, the _TYPE_=STD or _TYPE_=USTD 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 or _TYPE_=USTD observation prevents PROC SCORE from standardizing the observations before computing the factor scores.

OUTWGT= SAS-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 inverse of the weight matrix is used in the corresponding fit function. The OUTWGT= data set contains the weight matrix on which the WRIDGE= and the WPENALTY= options are applied. For unweighted least-squares or maximum likelihood estimation, no OUTWGT= data set can be written. The last weight matrix used in maximum likelihood estimation is the predicted model matrix (observations with _TYPE_ =MAXPRED) that is included in the OUTSTAT= data set.

For generalized and diagonally weighted least-squares estimation, the weight matrices 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 varnam_i be the name of the ith variable in the analysis. In this case, the OUTWGT= data set contains n observations with variables as displayed in the following table.

Table 19.11: Contents of OUTWGT= data set for GLS and DWLS Estimation

Variable	Contents
_TYPE_	WEIGHT (character)
_NAME_	name of variable varnam_i (character)
varnam₁	weight w_i1 for variable varnam₁ (numeric)
$\vdots$	$\vdots$
varnam_n	weight w_in for variable varnam_n (numeric)

For weighted least-squares estimation, the weight matrix W of the OUTWGT= data set contains only the nonredundant elements w_ij,kl. In this case, the OUTWGT= data set contains n(n+1)(2n+1)/6 observations with variables as follows.

Table 19.12: Contents of OUTWGT= data set for WLS Estimation

Variable	Contents
_TYPE_	WEIGHT (character)
_NAME_	name of variable varnam_i (character)
_NAM2_	name of variable varnam_j (character)
_NAM3_	name of variable varnam_k (character)
varnam₁	weight w_ij,k1 for variable varnam₁ (numeric)
$\vdots$	$\vdots$
varnam_n	weight w_ij,kn for variable varnam_n (numeric)

Symmetric redundant elements are set to missing values.

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