When a Linear Model Just Won't Do: Fitting Nonlinear Models in JMP

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This presentation was given live at JMP Discovery Summit 2013 in San Antonio, Texas, USA. To sign up to attend this year's conference, visit http://jmp.com/summit

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When a Linear Model Just Won't Do: Fitting Nonlinear Models in JMP

  1. 1. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. WHEN A LINEAR MODEL JUST WON’T DO FITTING NONLINEAR MODELS IN JMP SUE WALSH – JMP TECHNICAL SUPPORT
  2. 2. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. MODELS LINEAR VERSUS NONLINEAR MODELS • A linear regression model is linear in the parameters. That is, there is only one parameter in each term of the model and each parameter is a multiplicative constant on the independent variable(s) of that term. • A nonlinear model is nonlinear in the parameters.
  3. 3. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. LINEAR MODELS EXAMPLES
  4. 4. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. NONLINEAR MODELS EXAMPLES
  5. 5. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. NONLINEAR MODELS MODEL SPECIFICATION In order for each nonlinear model to be analyzed, you must specify: • the model equation • names and starting values of the parameters to be estimated.
  6. 6. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. NONLINEAR MODELS CONVERGENCE ISSUES Convergence might not be attained under certain conditions. These might include the following: • incorrect specification of the model • poor initial starting values • over-defined model • insufficient data.
  7. 7. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. NONLINEAR MODELS THE JMP PLATFORM There are three different ways to fit nonlinear models in JMP: • Fit Curve • Model Library • Column Formula
  8. 8. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. NONLINEAR MODELS EXAMPLE: DRUG LEVEL A drug is tested to determine the level of the drug over time. The drug is administered orally and the level of the drug in the blood stream is measured at various times after administration.
  9. 9. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. NONLINEAR MODELS ONE COMPARTMENT ORAL DOSE MODEL
  10. 10. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. NONLINEAR MODELS EXAMPLE: ENZYMATIC REACTION The initial velocity of an enzymatic reaction is believed to be related to the substrate concentration. Use the nonlinear platform to explore the relationship between velocity and concentration.
  11. 11. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. NONLINEAR MODELS EXAMPLE: CALCIUM IONS An experiment was conducted to examine the relationship between the amount of time cells are held in a calcium suspension and the amount of radioactive calcium in the cells. NOTE: This experiment was conducted by Howard Grimes, Idaho State University, and the data is used with his permission.
  12. 12. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. NONLINEAR MODELS 4 PARAMETER WEIBULL MODEL
  13. 13. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. NONLINEAR MODELS 4 PARAMETER WEIBULL MODEL (ALTERNATE FORM)
  14. 14. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. NONLINEAR MODELS EXAMPLE: TULIP GROWTH An experiment was conducted to examine the relationship between the concentration of plant growth inhibitor used and the height of tulip plants at the time of flower. NOTE: This experiment was conducted by Brian Krug, University of New Hampshire, and the data used with his permission.
  15. 15. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. NONLINEAR MODELS SEGMENTED MODEL
  16. 16. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. NONLINEAR MODELS SEGMENTED MODEL
  17. 17. Copyr ight © 2012, SAS Institute Inc. All rights reser ved. NONLINEAR MODELS CONCLUSION There are three different ways to fit nonlinear models in JMP: • Fit Curve • Model Library • Column Formula

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