Nonlinear Platform Options

The Nonlinear Fit red triangle menu has the following options:

Sets bounds on the parameters. When the option is selected, editable boxes appear in the Control Panel. Unbounded parameters are signified by leaving the field blank.

Plot

Shows or hides a plot of the X and Y variables for models with only one X variable. The model shown on the plot is based on the current values of the parameters. To change the current values of the parameters, use the sliders or edit boxes beneath the plot. If you specify a Group variable at launch, then a curve shows for each group.

Iteration Options

Specifies options for the fitting algorithm.

Iteration Log

Records each step of the fitting process in a new window.

Numeric Derivatives Only

Useful when you have a model that is too messy to take analytic derivatives for. It can also be valuable in obtaining convergence in tough cases.

Expand Intermediate Formulas

Tells JMP that if an ingredient column to the formula is a column that itself has a formula, to substitute the inner formula, as long as it refers to other columns. To prevent an ingredient column from expanding, use the Other column property with a name of “Expand Formula” and a value of 0.

Newton

Specifies whether Gauss-Newton (for regular least squares) or Newton-Raphson (for models with loss functions) is the optimization method.

QuasiNewton SR1

Specifies QuasiNewton SR1 as the optimization method.

QuasiNewton BFGS

Specifies QuasiNewton BFGS as the optimization method.

Accept Current Estimates

Tells JMP to produce the solution report with the current estimates, even if the estimates did not converge.

Show Derivatives

Shows the derivatives of the nonlinear formula in the JMP log. See Notes Concerning Derivatives, for technical information about derivatives.

Unthreaded

Runs the iterations in the main computational thread. In most cases, JMP does the computations in a separate computational thread. This improves the responsiveness of JMP while doing other things during the nonlinear calculations. However, there are some isolated cases (models that have side effects that call display routines, for example) that should be run in the main thread, so this option should be turned on.

Profilers

Provides various profilers for viewing response surfaces.

Profiler

Shows the Prediction Profiler. The Profiler lets you view vertical slices of the surface across each x-variable in turn, as well as find optimal values of the factors.

Contour Profiler

Shows the Contour Profiler. The Contour profiler lets you see two-dimensional contours as well as three dimensional mesh plots.

Surface Profiler

Creates a three-dimensional surface plot. This option is available only for models with two or more X variables.

Parameter Profiler

Shows the Prediction Profiler and profiles the SSE or loss as a function of the parameters.

Parameter Contour Profiler

Shows the Contour Profiler and contours the SSE or loss as a function of the parameters.

Parameter Surface Profiler

Creates a three-dimensional surface plot and profiles the SSE or loss as a function of the parameters. This option is available only for models with two or more parameters.

SSE Grid

Create a grid of values around the solution estimates and compute the error sum of squares for each value. The solution estimates should have the minimum SSE. When the option is selected, the Specify Grid for Output report is shown with these features:

Parameter

Lists the parameters in the model.

Min

Displays the minimum parameter values used in the grid calculations. By default, Min is the solution estimate minus 2.5 times the ApproxStdErr.

Max

Displays the maximum parameter value used in the grid calculations. By default, Max is the solution estimate plus 2.5 times the ApproxStdErr.

Number of Points

Gives the number of points to create for each parameter. To calculate the total number of points in the new grid table, multiply all the Number of Points values. Initially Number of Points is 11 for the first two parameters and 3 for the rest. If you specify new values, use odd values to ensure that the grid table includes the solution estimates. Setting Number of Points to 0 for any parameter records only the solution estimate in the grid table.

When you click Go, JMP creates the grid of points in a new table. A highlighted row marks the solution estimate row if the solution is in the table.

Revert to Original Parameters

Resets the platform to the original parameter values (the values given in the formula column parameters).

Remember Solution

Creates a report called Remembered Models, which contains the current parameter estimates and summary statistics. Results of multiple models can be remembered and compared. This is useful if you want to compare models based on different parameter restrictions, or models fit using different options. Click on the radio button for a particular model to display that model in the Plot and the parameter estimates in the Control Panel.

Custom Estimate

Gives an estimate of a function of the parameters. You provide an expression involving only parameters. JMP calculates the expression using the current parameter estimates, and also calculates a standard error of the expression using a first-order Taylor series approximation.

Custom Inverse Prediction

Estimates the X value for a given Y value. It also calculates a standard error for the estimated X. JMP must be able to invert the model. The standard error is based on the first-order Taylor series approximation using the inverted expression. The confidence interval uses a t-quantile with the standard error, and is a Wald interval.

Save Pred Confid Limits

Saves asymptotic confidence limits for the model prediction. This is the confidence interval for the average Y at a given X value.

Save Indiv Confid Limits

Saves asymptotic confidence limits for an individual prediction. This is the confidence interval for an individual Y value at a given X value.

Save Formulas

Gives options for saving model results to data table columns:

Save Prediction Formula

Saves the prediction formula with the current parameter estimates.

Save Std Error of Predicted

Saves the standard error for a model prediction. This is the standard error for predicting the average Y for a given X. The formula is of the form Sqrt(VecQuadratic(matrix1,vector1)). matrix1 is the covariance matrix associated with the parameter estimates, and vector1 is a composition of the partial derivatives of the model with respect to each parameter.

Save Std Error of Individual

Saves the standard error for an individual prediction. This is the standard error for predicting an individual Y value for a given X value. The formula is of the form Sqrt(VecQuadratic(matrix1,vector1)+mse). matrix1 is the covariance matrix associated with the parameter estimates, vector1 is a composition of the partial derivatives of the model with respect to each parameter, and mse is the estimate of error variance.

Save Residual Formula

Saves the formula for computing the residuals.

Save Pred Confid Limit Formula

Saves the formula to calculate the confidence interval for a model prediction. This is a confidence interval for the average Y for a given X.

Save Indiv Confid Limit Formula

Saves the formula to calculate the confidence interval for an individual prediction. This is a confidence interval for an individual Y for a given X.

Save Inverse Prediction Formula

Saves formulas for the inverse of the model, the standard error of an inverse prediction, and the standard error of an individual inverse prediction.

Save Specific Solving Formula

Equivalent to Save Inverse Prediction Formula in simple cases. However, this command allows the formula to be a function of several variables and allows expressions to be substituted. This feature works only for solving easily invertible operators and functions that occur just once in the formula.

After selecting this command, a dialog appears that enables you to select the variable to solve for. You can also edit the names of the columns in the resulting table. You can also substitute values for the names in the dialog. In these cases, the formula is solved for those values.

Note: The standard errors, confidence intervals, and hypothesis tests are correct only if least squares estimation is done, or if maximum likelihood estimation is used with a proper negative log-likelihood.

Show Prediction Expression

Shows the prediction model or the loss function at the top of the report.