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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