The NLIN Procedure

Confidence Intervals

Parameter Confidence Intervals

The parameter confidence intervals are computed using the Wald-based formula:

$\text{[math]}$

where $\text{[math]}$ is the $\text{[math]}$ th parameter estimate, $\text{[math]}$ is its estimated approximate standard error, $\text{[math]}$ is a $\text{[math]}$ statistic with $\text{[math]}$ degrees of freedom, $\text{[math]}$ is the number of observations, and $\text{[math]}$ is the number of parameters. The confidence intervals are only asymptotically valid. The significance level $\text{[math]}$ used in the construction of these confidence limits can be set with the ALPHA= option in the PROC NLIN statement; the default value is $\text{[math]}$ .

Model Confidence Intervals

Model confidence intervals are output when an OUT= data set is specified and one or more of the keywords LCLM, UCLM, LCL, UCL, L95M=, U95M=, L95=, and U95= is specified. The expressions for these terms are as follows:

	$\text{[math]}$	$\text{[math]}$
	$\text{[math]}$	$\text{[math]}$
	$\text{[math]}$	$\text{[math]}$
	$\text{[math]}$	$\text{[math]}$
	$\text{[math]}$	$\text{[math]}$
	$\text{[math]}$	$\text{[math]}$
	$\text{[math]}$	$\text{[math]}$
	$\text{[math]}$	$\text{[math]}$

where $\text{[math]}$ is the leverage, $\text{[math]}$ , and $\text{[math]}$ is the $\text{[math]}$ th row of $\text{[math]}$ . These results are derived for linear systems. The intervals are approximate for nonlinear models. The value $\text{[math]}$ in the preceding formulas for LCLM, UCLM, LCL, and UCL can be set with the ALPHA= option in the PROC NLIN statement or with the ALPHA= option in the OUTPUT statement. If both ALPHA= options are specified, the option in the OUTPUT takes precedence.