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The CALIS Procedure |
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.
| ||||||||||||
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. | ||||||||||||
EQ | If linear constraints are used, this observation contains the ith linear constraint . The parameter variables contain the coefficients a_{ij}, j = 1, ... ,n, the _RHS_ variable contains b_{i}, and _NAME_=ACTLC or _NAME_=LDACTLC. | ||||||||||||
GE | If linear constraints are used, this observation contains the ith linear constraint . 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.
| ||||||||||||
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.
| ||||||||||||
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.
| ||||||||||||
LE | If linear constraints are used, this observation contains the ith linear constraint . 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.
| ||||||||||||
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. |
The OUTRAM= data set contains the following variables:
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_=ESTIMVariable | 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 |
P_CHISQ | probability |
CHISQNUL | null (baseline) model |
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 for elliptic distribution |
P_ACHISQ | probability corresponding adjusted |
RLSCHISQ | reweighted least-squares (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 |
BB_NORMD | Bentler-Bonett (1980) normed index |
BOL_RHO1 | Bollen's (1986) normed index |
BOL_DEL2 | Bollen's (1989a) nonnormed index |
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 CodesCode | 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 () in LINEQS model statement | |
14: | third matrix () 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 |
The OUTSTAT= data set contains the following information (when available):
In addition, if the FACTOR model statement is used, the OUTSTAT= data set contains:
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.
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 EstimationVariable | Contents |
_TYPE_ | WEIGHT (character) |
_NAME_ | name of variable varnam_{i} (character) |
varnam_{1} | weight w_{i1} for variable varnam_{1} (numeric) |
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 EstimationVariable | 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) |
varnam_{1} | weight w_{ij,k1} for variable varnam_{1} (numeric) |
varnam_{n} | weight w_{ij,kn} for variable varnam_{n} (numeric) |
Symmetric redundant elements are set to missing values.
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