PROC NLIN Example with Parameter Profiling and Bootstrap

The script fits an exponential model to a dataset. It uses the NLIN procedure not only to estimate the model parameters but also to evaluate their stability and sensitivity. The PROFILE statement is used to examine the profile likelihood of two of the parameters, while the BOOTSTRAP statement performs a resampling analysis to provide robust confidence intervals and graphical diagnostics on the estimators.

Data Analysis

Type : CREATION_INTERNE

The 'clarke1987a' dataset is created directly within the script using a DATA step and a 'datalines' statement.

1 Code Block

DATA STEP Data

Explanation :
This code block creates the SAS table 'clarke1987a' in the WORK library. The table contains two numeric variables, 'x' and 'y', whose data is read directly from the input stream via the 'datalines' statement.

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1	DATA clarke1987a;
2	INPUT x y;
3	DATALINES;
4	1 3.183
5	2 3.059
6	3 2.871
7	4 2.622
8	5 2.541
9	6 2.184
10	7 2.110
11	8 2.075
12	9 2.018
13	10 1.903
14	11 1.770
15	12 1.762
16	13 1.550
17	;
18

2 Code Block

PROC NLIN

Explanation :
This block activates ODS graphics generation, then executes the non-linear regression procedure (NLIN). It defines the initial parameter values (parms), specifies an exponential model (model), and requests two advanced analyses: a likelihood profiling for 'theta1' and 'theta3' (profile) and a bootstrap analysis with 2000 resamples to obtain confidence intervals and diagnostic plots (bootstrap). ODS graphics are then deactivated.

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1	ods graphics on;
2	PROC NLIN DATA=clarke1987a plots(stats=none)=diagnostics;
3	parms theta1=-0.15
4	theta2=2.0
5	theta3=0.80;
6	profile theta1 theta3 / range = -6 to 2 BY 0.2 all;
7	bootstrap / nsamples = 2000 seed=123 bootplots bootci bootcov;
8	model y = theta3 + theta2exp(theta1x);
9	RUN;
10	ods graphics off;

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