FIT Statement

The MODEL Procedure

FIT Statement

FIT [ equations ] [ PARMS=( parameter [values] ... ) ]

               [ START=( parameter values ... ) ]
               [ DROP=( parameter ... ) ]
               [ INITIAL=( variable = [ parameter | constant ] ... )
               [ / options ] ; The FIT statement estimates model parameters by fitting the model equations to input data and optionally selects the equations to be fit. If the list of equations is omitted, all model equations containing parameters are fit.

The following options can be used in the FIT statement:

DROP= ( parameters ... ): specifies that the named parameters not be estimated. All the parameters in the equations fit are estimated except those listed in the DROP= option. The dropped parameters retain their previous values and are not changed by the estimation.
INITIAL= ( variable = [parameter | constant ] ... ): associates a variable with an initial value as a parameter or a constant .
NOOLS
NO2SLS: specify bipassing OLS or 2SLS to get initial parameter estimates for GMM, ITGMM, or FIML. This is important for certian models that are poorly defined in OLS or 2SLS or if good initial parameter values are already provided. Note that for GMM, the V matrix is created using the initial values specified and this may not be consistently estimated.
PARMS= ( parameters [values] ... ): selects a subset of the parameters for estimation. When the PARMS= option is used, only the named parameters are estimated. Any parameters not specified in the PARMS= list retain their previous values and are not changed by the estimation.
START= ( parameter values ... ): supplies starting values for the parameter estimates. If the START= option specifies more than one starting value for one or more parameters, a grid search is performed over all combinations of the values, and the best combination is used to start the iterations. For more information, see the STARTITER= option.

Options to Control the Estimation Method Used

COVBEST=GLS | CROSS | FDA: specifies the variance-covariance estimator used for FIML. COVBEST=GLS selects the generalized least-squares estimator. COVBEST=CROSS selects the crossproducts estimator. COVBEST=FDA selects the inverse of the finite difference approximation to the Hessian. The default is COVBEST=CROSS.
FIML: specifies full information maximum likelihood estimation.
GMM: specifies generalized method of moments estimation.
ITGMM: specifies iterated generalized method of moments estimation.
ITOLS: specifies iterated ordinary least-squares estimation. This is the same as OLS unless there are cross-equation parameter restrictions.
ITSUR: specifies iterated seemingly unrelated regression estimation
IT2SLS: specifies iterated two-stage least-squares estimation. This is the same as 2SLS unless there are cross-equation parameter restrictions.
IT3SLS: specifies iterated three-stage least-squares estimation.
KERNEL=(PARZEN | BART | QS, [c], [e] )
KERNEL=PARZEN | BART | QS: specifies the kernel to be used for GMM and ITGMM. PARZEN selects the Parzen kernel, BART selects the Bartlett kernel, and QS selects the Quadratic Spectral kernel. e >= 0 and c >= 0 are used to compute the bandwidth parameter. The default is KERNEL=(PARZEN, 1, 0.2). See the "Estimation Methods" section for more details.
N2SLS | 2SLS: specifies nonlinear two-stage least-squares estimation. This is the default when an INSTRUMENTS statement is used.
N3SLS | 3SLS: specifies nonlinear three-stage least-squares estimation.
OLS: specifies ordinary least-squares estimation. This is the default when no INSTRUMENTS statement is used.
SUR: specifies seemingly unrelated regression estimation.
VARDEF=N | WGT | DF | WDF: specifies the denominator to be used in computing variances and covariances. VARDEF=N specifies that the number of nonmissing observations be used. VARDEF=WGT specifies that the sum of the weights be used. VARDEF=DF specifies that the number of nonmissing observations minus the model degrees of freedom (number of parameters) be used. VARDEF=WDF specifies that the sum of the weights minus the model degrees of freedom be used. The default is VARDEF=DF. VARDEF=N is used for FIML estimation.

Data Set Options

DATA= SAS-data-set: specifies the input data set. Values for the variables in the program are read from this data set. If the DATA= option is not specified on the FIT statement, the data set specified by the DATA= option on the PROC MODEL statement is used.
ESTDATA= SAS-data-set: specifies a data set whose first observation provides initial values for some or all of the parameters.
MISSING= PAIRWISE | DELETE: The option MISSING=PAIRWISE specifies that missing values are tracked on an equation-by-equation basis. The MISSING=DELETE option specifies that the entire observation is omitted from the analysis when any equation has a missing predicted or actual value for the equation. The default is MISSING=DELETE.
OUT= SAS-data-set: names the SAS data set to contain the residuals, predicted values, or actual values from each estimation. Only the residuals are output by default.
OUTACTUAL: writes the actual values of the endogenous variables of the estimation to the OUT= data set. This option is applicable only if the OUT= option is specified.
OUTALL: selects the OUTACTUAL, OUTERRORS, OUTLAGS, OUTPREDICT, and OUTRESID options.
OUTCOV
COVOUT: writes the covariance matrix of the estimates to the OUTEST= data set in addition to the parameter estimates. The OUTCOV option is applicable only if the OUTEST= option is also specified.
OUTEST= SAS-data-set: names the SAS data set to contain the parameter estimates and optionally the covariance of the estimates.
OUTLAGS: writes the observations used to start the lags to the OUT= data set. This option is applicable only if the OUT= option is specified.
OUTPREDICT: writes the predicted values to the OUT= data set. This option is applicable only if OUT= is specified.
OUTRESID: writes the residual values computed from the parameter estimates to the OUT= data set. The OUTRESID option is the default if neither OUTPREDICT nor OUTACTUAL is specified. This option is applicable only if the OUT= option is specified.
OUTS= SAS-data-set: names the SAS data set to contain the estimated covariance matrix of the equation errors. This is the covariance of the residuals computed from the parameter estimates.
OUTSUSED= SAS-data-set: names the SAS data set to contain the S matrix used in the objective function definition. The OUTSUSED= data set is the same as the OUTS= data set for the methods that iterate the S matrix.
OUTV= SAS-data-set: names the SAS data set to contain the estimate of the variance matrix for GMM and ITGMM.
SDATA= SAS-data-set: specifies a data set that provides the covariance matrix of the equation errors. The matrix read from the SDATA= data set is used for the equation covariance matrix (S matrix) in the estimation. (The SDATA= S matrix is used to provide only the initial estimate of S for the methods that iterate the S matrix.)
TIME= name: specifies the name of the time variable. This variable must be in the data set.
TYPE= name: specifies the estimation type to read from the SDATA= and ESTDATA= data sets. The name specified in the TYPE= option is compared to the _TYPE_ variable in the ESTDATA= and SDATA= data sets to select observations to use in constructing the covariance matrices. When the TYPE= option is omitted, the last estimation type in the data set is used. Valid values are the estimation methods used in PROC MODEL.
VDATA= SAS-data-set: specifies a data set containing a variance matrix for GMM and ITGMM estimation.

Printing Options for FIT Tasks

BREUSCH= ( variable-list ): specifies the modified Breusch-Pagan test, where variable-list is a list of variables used to model the error variance.
COLLIN: prints collinearity diagnostics for the Jacobian crossproducts matrix (XPX) after the parameters have converged. Collinearity diagnostics are also automatically printed if the estimation fails to converge.
CORR: prints the correlation matrices of the residuals and parameters. Using CORR is the same as using both CORRB and CORRS.
CORRB: prints the correlation matrix of the parameter estimates.
CORRS: prints the correlation matrix of the residuals.
COV: prints the covariance matrices of the residuals and parameters. Specifying COV is the same as specifying both COVB and COVS.
COVB: prints the covariance matrix of the parameter estimates.
COVS: prints the covariance matrix of the residuals.
DW: prints Durbin-Watson d statistics, which measure autocorrelation of the residuals. When the residual series is interrupted by missing observations, the Durbin-Watson statistic calculated is dprimesym as suggested by Savin and White (1978). This is the usual Durbin-Watson computed by ignoring the gaps. Savin and White show that it has the same null distribution as the DW with no gaps in the series and can be used to test for autocorrelation using the standard tables. The Durbin-Watson statistic is not valid for models containing lagged endogenous variables.
FSRSQ: prints the first-stage R² statistics for instrumental estimation methods. These R²s measure the proportion of the variance retained when the Jacobian columns associated with the parameters are projected through the instruments space.
GODFREY
GODFREY= n: performs Godfrey's tests for autocorrelated residuals for each equation, where n is the maximum autoregressive order, and specifies that Godfrey's tests be computed for lags 1 through n. The default number of lags is one.
NORMAL: performs tests of normality of the model residuals.
PRINTALL: specifies the printing options COLLIN, CORRB, CORRS, COVB, COVS, DETAILS, DW, and FSRSQ.
WHITE: specifies White's test.

Options to control iteration output

Details of the output produced are discussed in the section "Iteration History".

I: prints the inverse of the crossproducts Jacobian matrix at each iteration.
ITALL: specifies all iteration printing-control options (I, ITDETAILS, ITPRINT, and XPX). ITALL also prints the crossproducts matrix (labeled CROSS), the parameter change vector, and the estimate of the cross-equation covariance of residuals matrix at each iteration.
ITDETAILS: prints a detailed iteration listing. This includes the ITPRINT information and additional statistics.
ITPRINT: prints the parameter estimates, objective function value, and convergence criteria at each iteration.
XPX: prints the crossproducts Jacobian matrix at each iteration.

Options to Control the Minimization Process

The following options may be helpful when you experience a convergence problem:

CONVERGE= value1
CONVERGE= (value1, value2): specifies the convergence criteria. The convergence measure must be less than value1 before convergence is assumed. value2 is the convergence criterion for the S and V matrices for S and V iterated methods. value2 defaults to value1. See "The Convergence Criteria" for details. The default value is CONVERGE=.001.
HESSIAN= CROSS | GLS | FDA: specifies the Hessian approximation used for FIML. HESSIAN=CROSS selects the crossproducts approximation to the Hessian, HESSIAN=GLS selects the generalized least-squares approximation to the Hessian, and HESSIAN=FDA selects the finite difference approximation to the Hessian. HESSIAN=GLS is the default.
LTEBOUND= n: specifies the local truncation error bound for the integration. This option is ignored if no ODE's are specified.
MAXITER= n: specifies the maximum number of iterations allowed. The default is MAXITER=100.
MAXSUBITER= n: specifies the maximum number of subiterations allowed for an iteration. For the GAUSS method, the MAXSUBITER= option limits the number of step halvings. For the MARQUARDT method, the MAXSUBITER= option limits the number of times ${\lambda}$ can be increased. The default is MAXSUBITER=30. See "Minimization Methods" for details.
METHOD= GAUSS | MARQUARDT: specifies the iterative minimization method to use. METHOD=GAUSS specifies the Gauss-Newton method, and METHOD=MARQUARDT specifies the Marquardt-Levenberg method. The default is METHOD=GAUSS. See "Minimization Methods" for details.
MINTIMESTEP= n: specifies the smallest allowed time step to be used in the integration. This option is ignored if no ODE's are specified.
NESTIT: changes the way the iterations are performed for estimation methods that iterate the estimate of the equation covariance (S matrix). The NESTIT option is relevant only for the methods that iterate the estimate of the covariance matrix (ITGMM, ITOLS, ITSUR, IT2SLS, IT3SLS). See "Details on the Covariance of Equation Errors" for an explanation of NESTIT.
SINGULAR= value: specifies the smallest pivot value allowed. The default 1.0E-12.
STARTITER= n: specifies the number of minimization iterations to perform at each grid point. The default is STARTITER=0, which implies that no minimization is performed at the grid points. See "Using the STARTITER option" for more details.

Other Options

Other options that can be used on the FIT statement include the following that list and analyze the model: BLOCK, GRAPH, LIST, LISTCODE, LISTDEP, LISTDER, and XREF. The following printing control options are also available: DETAILS, FLOW, INTGPRINT, MAXERRORS=, NOPRINT, PRINTALL, and TRACE. For complete descriptions of these options, see the discussion of the PROC MODEL statement options earlier in this chapter.

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