Fitting Curves and Surfaces Using SAS Software - ISS - University of ...

Fitting Curves and Surfaces Using SAS Software
Version 1.1 (February 2007)
Inverse quadratic polynomial Y= 1/( β0 + β1/X + β2X)
Both REG and NLIN are useful when you know the functional form of the model you want to fit. However,
when you have no prior knowledge about the model, or when you know that the data cannot be represented
by a model with a fixed number of parameters, two other procedures can be used – LOESS and TPSPLINE.
PROC LOESS uses a non-parametric method called Loess Smoothing for estimating regression surfaces.
This approach makes no assumptions about the parametric form of the regression surface and as a result
offers greater flexibility for model fitting. In particular, the LOESS procedure is suitable when there are outliers
in the data and a robust fitting method is necessary.
The TPSPLINE procedure uses a method called penalised least squares to fit non-parametric and semiparametric
models. TPSPLINE uses thin-plate smoothing splines to approximate smooth multivariate functions
observed with noise. The degree of smoothing can be controlled using the generalised cross validation
function (GCV).
The GAM procedure fits Generalised Additive Models as defined by Hastie and Tibshirani (1990). These
models are extensions of the generalised linear model, allowing functions to take the place of individual
explanatory variables in the model.
A full description of these procedures is beyond the scope of this text. The user is referred to the SAS/STAT
User Guide (available within the online Help system within SAS) for details. The examples below illustrate their
use on the sample data sets described in the Annex.
3.1 Parametric Modelling using REG and NLIN
Example 2: A Comparison of REG, NLIN and I=SPLINE
PROC REG and PROC NLIN are the main procedures for curve fitting when a functional form for a suitable
curve can be found. This example shows how to use both REG and NLIN and compares a variety of curves
fitted to the same data.
(i) Open the file curve.sas. The program, shown below, creates a small data set used for the example.
data curve1;
input x y @@;
xsq=x*x;
datalines;
0.3 0.2 0.5 0.33 1.0 0.5 1.5 0.6 2.0 0.67 2.5 0.72 3.0 0.75 4.0 0.8
5.0 0.85 6.0 0.87 7.0 0.89 8.0 0.9 9.0 0.91 12.0 0.92 13.0 . 14.0 . 15.0 .
;
run;
(ii) Submit the program by pressing F8.
The last three observations are included with missing values for Y. It will be instructive to see how well
each model performs in estimating values of Y for these observations.
A very simple approach would be to use the SYMBOL statement to fit a simple polynomial to the data.
(iii) Open the file splineq.sas. This program uses I=RQ to fit a quadratic to the data.
(iv) Submit the program by pressing F8. The results should correspond to the display shown below.
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Version 1.1 (Feb 2007) tut125.doc