Nonlinear

Example 1

Summary: Perform a nonlinear regression model using the Nonlinear function.

Code:

// Open data table
dt = Open("$Sample_Data/Design Experiment/Reaction Kinetics.jmp");
// Model
Nonlinear(
    Y( :Observed Yield ),
    X( :Yield Model )
);

Example 2

Summary: Fit a full nonlinear Mitscherlich growth curve model using the Nonlinear platform.

Code:

// Open data table
dt = Open("$Sample_Data/Nonlinear Examples/Algae Mitscherlich.jmp");
// Full nonlinear model
Nonlinear(
    Y( :Algae density ),
    X( :Mitscherlich ),
    Finish
);

Example 3

Summary: Fit a reduced nonlinear model with equal alphas for algae density.

Code:

// Open data table
dt = Open("$Sample_Data/Nonlinear Examples/Algae Mitscherlich.jmp");
// Reduced nonlinear model-with equal alphas
Nonlinear(
    Y( :Algae density ),
    X( :equal alphas ),
    Finish
);

Example 4

Summary: Create a nonlinear regression model to analyze algae density using the Algae Mitscherlich dataset with equal betas.

Code:

// Open data table
dt = Open("$Sample_Data/Nonlinear Examples/Algae Mitscherlich.jmp");
// Reduced nonlinear model-with equal betas
Nonlinear(
    Y( :Algae density ),
    X( :equal betas ),
    Finish
);

Example 5

Summary: Northwest plots the distribution of shoot lengths in a satellite image.

Code:

// Open data table
dt = Open("$Sample_Data/Nonlinear Examples/CES Production Function.jmp");
// Nonlinear
Nonlinear(
    Y( :"log($ value)"n ),
    X( :Model )
);

Example 6

Summary: Fit a nonlinear Meyers Model to the given dataset using the Newton method.

Code:

// Open data table
dt = Open("$Sample_Data/Nonlinear Examples/Chemical Kinetics.jmp");
// Meyers Model Fit
Nonlinear(
    Y( :"Velocity (y)"n ),
    X( :"Model (x)"n ),
    Newton,
    Finish
);

Example 7

Summary: Perform nonlinear regression using a disjoint linear model to analyze yield data.

Code:

// Open data table
dt = Open("$Sample_Data/Nonlinear Examples/Corn.jmp");
// Nonlinear - disjoint linear
Nonlinear(
    Y( :yield ),
    X( :linear ),
    Plot( 1 )
);

Example 8

Summary: Fit a nonlinear disjoint quadratic model to analyze yield data using the Quasi-Newton SR1 algorithm.

Code:

// Open data table
dt = Open("$Sample_Data/Nonlinear Examples/Corn.jmp");
// Nonlinear - disjoint quadratic
Nonlinear(
    Y( :yield ),
    X( :quad ),
    Plot( 1 ),
    QuasiNewton SR1
);

Example 9

Summary: Fit a nonlinear model to the data using the Model Y variable, with the loss function specified as negative log-likelihood, using the Newton method for optimization and omitting the final plot.

Code:

// Open data table
dt = Open("$Sample_Data/Nonlinear Examples/Logistic w Loss.jmp");
// Nonlinear with ModelY and Loss
Nonlinear(
    X( :Model Y ),
    Loss( :Loss ),
    Second Deriv Method( 1 ),
    Loss is Neg LogLikelihood( 1 ),
    Newton,
    Finish,
    Plot( 0 )
);

Example 10

Summary: Perform a nonlinear analysis with the response variable designated as Model2 Y and the loss function specified as Loss2, utilizing gradient-based optimization techniques and Newton's method.

Code:

// Open data table
dt = Open("$Sample_Data/Nonlinear Examples/Logistic w Loss.jmp");
// Nonlinear with Model2 Y and Loss2
Nonlinear(
    X( :Model2 Y ),
    Loss( :Loss2 ),
    Relative Gradient( 0.000000001 ),
    Gradient Limit( 0.000000001 ),
    CL Limit( 0.00000001 ),
    Numeric Derivatives Only( 1 ),
    Loss is Neg LogLikelihood( 1 ),
    Newton,
    Finish,
    Plot( 0 )
);

Example 11

Summary: Perform nonlinear regression analysis without a model column using Newton's method in the Nonlinear platform.

Code:

// Open data table
dt = Open("$Sample_Data/Nonlinear Examples/Logistic w Loss.jmp");
// Nonlinear with no Model Column
Nonlinear(
    Loss( :Loss with No Model Column ),
    Second Deriv Method( 1 ),
    Loss is Neg LogLikelihood( 1 ),
    Newton,
    Finish,
    Plot( 0 )
);

Example 12

Summary: Fit nonlinear Poisson regression using the Newton-Raphson method.

Code:

// Open data table
dt = Open("$Sample_Data/Ship Damage.jmp");
// Nonlinear
Nonlinear(
    X( :model ),
    Loss( :Poisson ),
    Loss is Neg LogLikelihood( 1 ),
    Newton,
    Finish,
    Plot( 0 )
);