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

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Fitting Curves and Surfaces Using SAS Software Version 1.1 (February 2007) Contents 1. Introduction ............................................................................................................................................ 3 1.1 Documentation ........................................................................................................................... 3 1.2 Getting Started ........................................................................................................................... 4 2. Using Interpolating Splines in SAS/GRAPH ........................................................................................... 4 3. SAS/STAT Modelling Procedures .......................................................................................................... 5 3.1 Parametric Modelling using REG and NLIN ............................................................................... 6 3.2 Non-Parametric Modelling using Loess Smoothing .................................................................. 10 3.3 Semi-Parametric Modelling using Thin-Plate Splines ............................................................... 13 3.4 Generalised Additive Models ................................................................................................... 17 References ..................................................................................................................................................... 19 Annex ............................................................................................................................................................. 20 Format Conventions In this document the following format conventions are used: Menu items and commands that you must type Name in are shown in bold Keys that you press and options that you or select are enclosed in angle brackets. Feedback If you notice any mistakes in this document please contact the Information Officer. Email should be sent to the address info-officer@leeds.ac.uk Copyright This document is copyright University of Leeds. Permission to use material in this document should be obtained from the Information Officer (email should be sent to the address info-officer@leeds.ac.uk) Information Systems Services Page 2 of 22 Version 1.1 (Feb 2007) tut125.doc
Fitting Curves and Surfaces Using SAS Software Version 1.1 (February 2007) 1. Introduction In studies involving continuous valued variables, a common requirement is the ability to predict the value of one variable given the value of another variable. As a first step, the relationship between a pair of variables can be examined using a scatter plot. It may be sufficient to obtain a visual impression of the relationship between the variables by smoothing the data - for example, by using a smoothing spline, specified on a SYMBOL statement. Alternatively, it may be required, to obtain a deeper understanding about how changes in one variable (referred to as the independent or explanatory variable) influence values of another variable, referred to as the dependent variable. For values of the independent variable within the range of the current data, this is referred to as interpolation. For values of the independent variable outside the range of the current data, the problem is referred to as extrapolation. Whilst the use of the SYMBOL spline facility may be adequate for visual interpolation, it does not provide numerical representations of interpolated values and cannot be relied upon for extrapolation. Consider the two graphs below. Both curves appear to fit the data equally well. In the first graph, y increases exponentially as x increases – in the second graph y tails off asymptotically as x increases. Which curve represents ‘the best fit’? The answer is, of course, that there is no such thing as an absolute best fit. This demonstrates an idea central to curve fitting – that an understanding of the nature of the variables is essential if meaningful predictions are to be made. If it is known that y settles down to a finite value as x increases, a functional form expressing that relationship is essential if extrapolations are to be made. Thus, an alternative to the simple smoothing approach is the modelling approach in which a mathematical function, based upon knowledge of the data, is sought to describe the relationship between the two variables. This document looks at a range of methods available in SAS for smoothing and modelling data. A familiarity with the basics of SAS/GRAPH is assumed. 1.1 Documentation The main reference documentation for the facilities described in this document are as follows: • SAS/GRAPH Reference Manual Vols. 1 & 2 • SAS/STAT Reference Manual Vols. 1 & 2 The Reference Manuals are also available in the on-line Help system. The SAS Sample Library, accessible from within a SAS session, also contains the numerous examples found in the above volumes. Information Systems Services Page 3 of 22 Version 1.1 (Feb 2007) tut125.doc
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