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## TOBIT

The TOBIT command is available for regressions with limited dependent variables. The tobit model, also called a censored regression model, is designed to estimate linear relationships between variables when there is censoring from below and above. Censoring from above takes place when cases with a value at or above some threshold, all take on the value of that threshold, so that the true value might be equal to the threshold, but it might also be higher. In the case of censoring from below, values those that fall at or below some threshold are censored.

In general, the format is:

TOBIT 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. Uses normalised coefficients. conv= Sets the CONVergence criterion for the normalized coefficients. The default is .00000001 (that is, 1 x 10^-8). This is the same as using CONV=1E-8. cov= Saves the COVariance matrix of coefficients in the variable specified. Uses normalised coefficients. dump DUMPs the matrix of second derivatives, the moment matrices of limit and non-limit observations, and some other output that is probably not useful to the average user. end= Specifies the ENDing observation to be used in estimation. This option overrides the SAMPLE command and defaults to the sample range in effect. index= Saves the computed INDEX in the variable specified. iter= Sets the maximum number of ITERations allowed. The default is 25. limit= Specifies the LIMITing value of the dependent variable. The default is LIMIT= 0. list LISTs, for each observation, the value of the index I, the density and cumulative probabilities corresponding to the index I, and the observed, expected and conditional values of the dependent variable. No plot is produced. 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. negative The observed value of the dependent variable can be greater than or less than the limit value. 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. nonorm Used with WEIGHT= if you do not want normalized weights. Interpretation of output is sometimes difficult when weights are not normalized. Sometimes, the weights can be viewed as a sampling replication factor. Users are expected to know exactly what their weights represent. pcor Prints the CORrelation matrix of the normalized coefficients. pcov Prints the estimated asymptotic COVariance matrix of the normalized coefficients. The matrix is the inverse of the negative of the matrix of second derivatives of the log-likelihood function. In a large sample the normalized coefficients will be normally distributed. piter= Specifies the frequency with which ITERations are to be Printed. The default is PITER=1. If PITER=0 is specified, no iterations are printed. predict= Saves the PREDICTed expected values in the variable specified. stderr= Saves the values of the STanDard ERRors of the coefficients in the variable specified. Uses normalised coefficients. tratio= Saves the values of the T-RATIOs in the variable specified. Uses normalised coefficients. upper Used if the limit is an UPPER limit rather than a lower limit. weight= Specifies a variable to use as the weight for a WEIGHTed Least Squares regression. OLS with the WEIGHT= option is similar to a GLS regression with a diagonal Omega matrix. Users should also examine the NONORM, UT and REPLICATE options described above which can be used with the WEIGHT= option. More details and an example are given in the SHAZAM Reference Manual.