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## ROBUST

The ROBUST command is designed to circumvent some limitations of traditional parametric and non-parametric methods. Certain methods of regression, such as ordinary least squares, have favourable properties if their underlying assumptions are true, but can give misleading results if those assumptions are not true. Robust regression methods are designed to be not overly affected by violations of assumptions by the underlying data-generating process.

In general, the format is:

ROBUST depvar indeps / options

The available options are:

 OPTION DESCRIPTION beg= Specifies the BEGinning observation to be used in estimation. This option overrides the SAMPLE command and defaults to the sample range in effect. coef= Saves the COEFficients in the variable specified. If there is an intercept it will be stored as the last coefficient. conv= Used with the MULTIT= option described below to specify a convergence criterion delta to stop the iterative procedure used to obtain the estimates. The default is CONV=0.01. cov= Saves the COVariance matrix of coefficients in the variable specified. diff= Specifies a value of d to use with the LAE and THETA= options and for methods that use linear functions of regression quantiles. The parameter d is the differential used when selecting ordered residuals to use in computing the covariance matrix. The default value for d is (N-K-1) / 6 (rounded down to the nearest integer). However, the maximum permitted value for d is N-theta/2(rounded down to the nearest integer). If you specify DIFF=-1 the method of Bofinger  and Siddiqui  is used. If DIFF=-2 SHAZAM will use the method suggested by Hall and Sheather  and Siddiqui . end= Specifies the ENDing observation to be used in estimation. This option overrides the SAMPLE command and defaults to the sample range in effect. fivequan Uses the five quantile values in computing regression quantiles. gastwirt Uses the Gastwirth weighting scheme in computing regression quantiles. graph Prepares Graphs of the residuals and the fitted values. iter= Used with the MULTIT= option described below to specify the maximum number of iterations allowed in the iterative procedure used to obtain the estimates. The default is ITER=10. lae Specifies that least absolute error (LAE) estimation is desired. This is the default method. Also see the DIFF= option. lininv Used when the dependent variable is LINear, but the independent variables are in INVerse form. This type of model is known as the reciprocal model. This option only affects the calculation of the elasticities. NOTE: This option does not transform the data. The data must be transformed by the user with the appropriate GENR commands or the Data Editor. See the chapter ORDINARY LEAST SQUARES in the SHAZAM Reference Manual. linlog Used when the dependent variable is LINear, but the independent variables are in LOG form. This option only affects the calculation of the elasticities. NOTE: This option does not transform the data. The data must be transformed by the user with the appropriate GENR commands or the Data Editor. See the chapter ORDINARY LEAST SQUARES in the SHAZAM Reference Manual. list LISTs and plots the residuals and predicted values of the dependent variable and residual statistics. When LIST is specified RSTAT is automatically turned on. loginv Used when the dependent variable is in LOG form, and the independent variables are in INVerse form. loglin Used when the dependent variable is in LOG form, but the independent variables are LINear. This option only affects the calculation of the elasticities. NOTE: This option does not transform the data. The data must be transformed by the user with the appropriate GENR commands or the Data Editor. See the chapter ORDINARY LEAST SQUARES in the SHAZAM Reference Manual. loglog Used when the dependent variable is in LOG form, and the independent variables are in LOG form. This option only affects the calculation of the elasticities. NOTE: This option does not transform the data. The data must be transformed by the user with the appropriate GENR commands or the Data Editor. See the chapter ORDINARY LEAST SQUARES in the SHAZAM Reference Manual. max Prints Analysis of Variance Tables, Variance-covariance matrix, Correlation matrix, Residuals, Residual Statistics and Goodness of Fit Test for Normality. This option is equivalent to using the ANOVA, LIST, PCOV, PCOR and GF options. Users should be sure the MAX output is necessary, otherwise unnecessary calculations are required. multit= Specifies the degrees of freedom parameter to be used for the multivariate-t error distribution. See also the UNCOR, CONV=, and ITER= options which can be used with the MULTIT= option. noconstant There will be NO CONSTANT (intercept) in the estimated equation. This option is used when the intercept is to be suppressed in the regression or when the user is supplying the intercept. This option should be used with caution as some of the usual output may be invalid. In particular, the usual R^2 is not well defined and could be negative. However, when this option is used, the raw moment R^2 may be of interest. The ANALYSIS OF VARIANCE - FROM MEAN table will not be computed if this option is used. pcor Prints the CORrelation matrix of the estimated coefficients. This should not be confused with a correlation matrix of variables which can be obtained with a STAT command. pcov Prints the COVariance matrix of coefficients. This should not be confused with the covariance matrix of variables which can be obtained with the STAT command. predict= Saves the PREDICTed values of the dependent variable in the variable specified. resid= Saves the values of the RESIDuals from the regression in the variable specified. rstat Prints Residual Summary STATistics. The output includes the Durbin-Watson statistic and related residual test statistics. It also includes the Runs Test. When the LIST option is specified RSTAT is automatically turned on. stderr= Saves the values of the STanDard ERRors of the coefficients in the variable specified. theta= Specifies a single value of theta to use for the regression quantile method. thetab Specifies beginning (THETAB=) estimate used for a grid search over THETA. A sequence of regression quantile estimates is generated and coefficient estimates are obtained as the average (equal weights) If options (THETAB=), ending (THETAE=), and increments (THETAI=) are specified the THETA= option is ignored. thetae Specifies ending (THETAE=) used for a grid search over THETA. A sequence of regression quantile estimates is generated and coefficient estimates are obtained as the average (equal weights) If options (THETAB=), ending (THETAE=), and increments (THETAI=) are specified the THETA= option is ignored. thetai Specifies increment (THETAI=) used for a grid search over THETA. A sequence of regression quantile estimates is generated and coefficient estimates are obtained as the average (equal weights) If options (THETAB=), ending (THETAE=), and increments (THETAI=) are specified the THETA= option is ignored. tratio= Saves the values of the T-RATIOs in the variable specified. trim Specifies the value of the TRIMming proportion alpha to use for the trimmed least squares estimation method. The value specified for alpha should be between 0 and 0.5. A listing of the observation numbers for the deleted observations is printed unless the SET NOWARN command has been used. tukey Uses the Tukey Trimean weighting scheme in computing regression quantiles. uncor Used with the MULTIT= option to specify that the uncorrelated error model is requested. If this option is not used the independent error model is assumed.