The NLIN Procedure

BOOTSTRAP Statement

BOOTSTRAP </ options> ;

A BOOTSTRAP statement requests bootstrap estimation of confidence intervals, the covariance matrix, and the correlation matrix of parameter estimates. To produce the plots that are are controlled by the BOOTSTRAP statement, ODS Graphics must be enabled. If the main data set contains observations that PROC NLIN deems unusable, the procedure issues a message that these observations are excluded from the bootstrap resampling. PROC NLIN ignores the BOOTSTRAP statement for nonconvergent and singular models.

Table 67.4 summarizes the options available in the BOOTSTRAP statement.

Table 67.4: Summary of Options in BOOTSTRAP Statement

Option	Description
BOOTCI	Produces bootstrap confidence intervals of the parameters
BOOTCORR	Produces a bootstrap correlation matrix estimate table
BOOTCOV	Produces a bootstrap covariance matrix estimate table
BOOTDATA=	Specifies the bootstrap output data set
BOOTPLOTS	Produces plots of the bootstrap parameter estimates
DGP=	Specifies the bootstrap data generating process (DGP)
NSAMPLES=	Specifies the number of bootstrap sample data sets (replicates)
SEED=	Provides the seed that initializes the random number stream

BOOTCI <(BC | NORMAL | PERC | ALL)>

produces bootstrap-based confidence intervals for the parameters and adds columns that contain these values to the “Parameter Estimates” table. You can specify the following types of bootstrap confidence intervals:

BC: produces bias-corrected confidence intervals.
NORMAL: produces confidence intervals based on the assumption that bootstrap parameter estimates follow a normal distribution.
PERC: produces percentile-based confidence intervals.
ALL: produces all three confidence intervals.

The ALPHA= option in the PROC NLIN statement sets the level of significance that is used in constructing these bootstrap confidence intervals. By default, without the BOOTCI option, PROC NLIN produces bias-corrected (BC) confidence intervals and adds a column that contains the standard deviation of the bootstrap parameter estimates to the “Parameter Estimates” table. For more information, see the section Bootstrap Resampling and Estimation.

BOOTCORR

produces the “Bootstrap Correlation Matrix” table, which contains a bootstrap estimate of the correlation matrix of the parameter estimates. For more information, see the section Bootstrap Resampling and Estimation.

BOOTCOV

produces the “Bootstrap Covariance Matrix” table, which contains a bootstrap estimate of the covariance matrix of the parameter estimates. For more information, see the section Bootstrap Resampling and Estimation.

BOOTDATA=SAS-data-set

specifies the SAS data set that contains the bootstrap sample data when you use a BOOTSTRAP statement. For more information about this data set, see the section Output Data Sets.

BOOTPLOTS <(HIST | SCATTER | ALL)>

produces ODS graphics of bootstrap parameter estimates. You can specify the following types of plots:

HIST: produces histograms of the bootstrap parameter estimates.
SCATTER: produces pairwise scatter plots of the bootstrap parameter estimates.
ALL: produces both plots.

By default, if ODS Graphics is enabled, PROC NLIN produces histograms of the bootstrap parameter estimates.

DGP=RESIDUAL <(scaling-option)> | WILD

specifies the bootstrap data generating process (DGP). DGP=RESIDUAL requests the residual bootstrap, and DGP=WILD requests the wild bootstrap. The scaling-option determines the type of residual scaling to be performed for DGP=RESIDUAL.

Table 67.5: Scaling Options Available for DGP=RESIDUAL

Keyword	Description
ADJSSE	Simple uniform scaling
JAC	Scaling based on Jacobian leverage
RAW	No scaling
TAN	Scaling based on tangential leverage

By default, if the BOOTSTRAP statement is specified with no DGP= option or if no scaling-option is specified for DGP=RESIDUAL, PROC NLIN performs a residual bootstrap with simple scaling (ADJSSE) for unweighted least squares and a wild bootstrap (WILD) for weighted least squares. For more information, see the section Bootstrap Resampling and Estimation.

NSAMPLES=n

specifies the number of bootstrap sample data sets (replicates). By default, NSAMPLES=1000. For more information, see the section Bootstrap Resampling and Estimation.

SEED=n

provides the seed that initializes the random number stream for generating the bootstrap sample data sets (replicates). If you do not specify the SEED= value or if you specify a value less than or equal to 0, the seed is generated from reading the time of day from the computer’s clock. The largest possible value for the seed is $2^{31}-1$ . The _SEED_ in the data set that is produced by the the BOOTDATA= option contains the value that is used as the initial seed for a particular replicate.

You can use the SYSRANDOM and SYSRANEND macro variables after a PROC NLIN run to query the initial and final seed values. However, using the final seed value as the starting seed for a subsequent analysis does not continue the random number stream where the previous analysis left off. The SYSRANEND macro variable provides a mechanism to pass on seed values to ensure that the sequence of random numbers is the same every time you run an entire program.