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BOX

The BOX command provides features for estimation with Box-Cox transformations. Models include the Classical Box-Cox, Extended Box-Cox, Box-Tidwell, combined Box-Cox and Box-Tidwell, Box-Cox Autoregressive and the Extended Box-Cox Autoregressive Model.

In general, the format is:

BOX depvar indeps / options

The available options are:

OPTION DESCRIPTION
accur Normally, SHAZAM will estimate lambda to an ACCURacy of 0.01. However, if this option is used, SHAZAM will iterate to an ACCURacy of 0.001 at some increase in computation time.
all Used to extend the Box-Cox model so that ALL variables receive the same power transformation (unless restricted). Without this option only the dependent variable is transformed. The extended Box-Cox model is far more difficult to estimate than the classical model. For example, the classical model usually requires only four iterations. The ALL option often requires twenty iterations.
anova Prints the ANalysis Of VAriance tables and the F-statistic for the test that all coefficients are zero. In some restricted models, the F-test from an ANOVA table is invalid. In these cases the F-statistic will not be printed, but may be obtained with the TEST command. Model Selection Tests are also printed.
auto Simultaneously estimate lambda and the first-order AUTOcorrelation parameter rho. The method is that of Savin and White [1978]. This option is very slow as over 100 iterations are required. An accuracy of 0.01 is obtained for lambda and rho (the ACCUR option is not available with this option). When using this option, the DROP, NMISS=, and GAP= options described in the chapter on AUTOCORRELATION MODELS may be used. The RHO= option described below can also be used. The lambda range for the AUTO option is preset at (-2 , 3.5) and may not be altered. It is important to check for corner solutions.
dn Uses a divisor of N instead of N-K when estimating the error variance.
dump Used with the AUTO option to get some intermediate output on the iterations to be DUMPed. This output is usually of little value, but sometimes contains useful information on the grid search.
full Attempts a combined Box-Cox and Box-Tidwell estimation so that all variables in the equation have different lambdas. This option can be rather slow as many iterations are required. The warning on Box-Tidwell regressions also applies for the FULL option. In fact, overflows are quite common with this option so it should be used with care. RESTRICT commands are not permitted. The ALL, AUTO, LAMBDA=, LAMS=, LAME= and LAMI= options must not be used with the TIDWELL or FULL options.
gf Prints Goodness of Fit tests for normality of residuals. Coefficients of skewness and excess kurtosis and the Jarque-Bera test for normality of the residuals are also computed.
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.
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.
noconstant Estimates a model with no intercept. The user should be aware that the Box-Cox model is not well defined for models without an intercept, and the model is generally not scale-invariant. A further result is that the likelihood function is not continuous at ??= 0; SHAZAM will use a value of 0.01 instead of 0.0. A Golden Section search algorithm will be 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.
restrict Forces linear parameter restrictions. The restrictions are specified with LAMBDA and/or RESTRICT commands. The RESTRICT option is not available with the FULL or TIDWELL options.
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.
tidwell Does a Box-TIDWELL regression instead of a Box-Cox regression. Only the independent variables will be transformed and each variable will have a different lambda. For details on the method see Box and Tidwell [1962]. All independent variables must be strictly positive for this technique. Users should be aware that, quite frequently, the Box-Tidwell method will not converge, thus causing the run to be terminated unsuccessfully. This happens most often in small samples where there is a high variance in one of the parameters. If this happens, the run might be successful if the data is scaled to a lower range (for example, divide all variables by 100). RESTRICT commands are not permitted. The ALL, AUTO, LAMBDA=, LAMS=, LAME= and LAMI= options must not be used with the TIDWELL or FULL options.
ut UnTransforms the observed and predicted dependent variables for purposes of computing and plotting the residuals. All values will then be in their original form. This is a useful option since the transformed residuals and predicted values usually are difficult to interpret. However, this option will raise computation time somewhat since an extra pass through the data is required. In addition, the untransformed residuals will no longer necessarily have a zero mean. Note that this option does not affect the regression results. Only the residual listing will be affected.
beg= Specifies the BEGinning observation to be used in estimation. This option overrides the SAMPLE command and defaults to the sample range in effect.
end= Specifies the ENDing observation to be used in estimation. This option overrides the SAMPLE command and defaults to the sample range in effect.
coef= Saves the COEFficients, the lambdas for each independent variable and the dependent variable, and ? if the AUTO option is used.
cov= Saves the COVariance matrix of coefficients in the variable specified.
lambda= Used to specify the value of LAMBDA desired by the user. Expensive iterations are eliminated with this option.
lame= The ending value of LAMbda (LAME=). This option is used with LAMI= and LAMS= to do a manual grid test for lambda. When the optimal lambda has been determined it can be specified on the LAMBDA= option. The manual grid search is rarely needed. It may be necessary if the iterative procedure fails. The manual grid search is not available when using the AUTO option.
lami= The Increment of LAMbda (LAMS=). This option is used with LAMS= and LAME= to do a manual grid test for lambda. When the optimal lambda has been determined it can be specified on the LAMBDA= option. The manual grid search is rarely needed. It may be necessary if the iterative procedure fails. The manual grid search is not available when using the AUTO option.
lams= The starting value of LAMbda (LAMS=). This option is used with LAMI= and LAME= to do a manual grid test for lambda. When the optimal lambda has been determined it can be specified on the LAMBDA= option. The manual grid search is rarely needed. It may be necessary if the iterative procedure fails. The manual grid search is not available when using the AUTO option.
noanova Specifies not to print Analysis of Variance tables and model selection tests
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.
rho= Specifies a fixed value for RHO to be used when the AUTO option is specified.

The available temporary variables on the BOX command are:

$ADR2, $ANF, $DF, $DW, $ERR, $K, $LLF, $N, $R2, $R2OP, $RAW, $RHO, $SIG2, $SSE, $SSR, $SST, $ZANF, $ZDF, $ZSSR and $ZSST