when a linear model just won't do: fitting nonlinear models in jmp
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Copyr i g ht © 2012, SAS Ins t i tu t e Inc . A l l r ights reser ve d .
WHEN A LINEAR MODEL JUST WON’T DO
FITTING NONLINEAR MODELS IN JMPSUE WALSH – JMP TECHNICAL SUPPORT
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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.
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LINEAR MODELS EXAMPLES
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NONLINEAR
MODELSEXAMPLES
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NONLINEAR
MODELSMODEL 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.
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NONLINEAR
MODELSCONVERGENCE 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.
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NONLINEAR
MODELSTHE JMP PLATFORM
There are three different ways to fit nonlinear models in JMP:
• Fit Curve
• Model Library
• Column Formula
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NONLINEAR
MODELSEXAMPLE: 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.
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NONLINEAR
MODELSONE COMPARTMENT ORAL DOSE MODEL
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NONLINEAR
MODELSEXAMPLE: 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.
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NONLINEAR
MODELSEXAMPLE: 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.
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NONLINEAR
MODELS4 PARAMETER WEIBULL MODEL
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NONLINEAR
MODELS4 PARAMETER WEIBULL MODEL (ALTERNATE FORM)
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NONLINEAR
MODELSEXAMPLE: 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.
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NONLINEAR
MODELSSEGMENTED MODEL
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NONLINEAR
MODELSSEGMENTED MODEL
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NONLINEAR
MODELSCONCLUSION
There are three different ways to fit nonlinear models in JMP:
• Fit Curve
• Model Library
• Column Formula
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