The Nonlinear Fit red triangle menu contains the following options:
Parameter Bounds
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
Shows or hides the Iterations table. Once this option is selected, the platform records subsequent iterations in the table.
Numeric Derivatives Only
Specifies that only numeric derivatives are used in the fitting method. 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 either Gauss-Newton (for regular least squares) or Newton-Raphson (for models with loss functions) as the optimization method.
QuasiNewton SR1
Specifies QuasiNewton SR1 as the optimization method. This method avoids recalculating the derivatives at each iteration.
QuasiNewton BFGS
Specifies QuasiNewton BFGS as the optimization method. This method is best for large numbers of parameters.
Accept Current Estimates
Produces the solution report using the current estimates, even if the estimates did not converge.
Show Derivatives
Shows the derivatives of the nonlinear formula in the JMP log. See Statistical Details on 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 or hides 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 or hides the Contour Profiler. The Contour profiler shows two-dimensional contours as well as three dimensional mesh plots.
Surface Profiler
Shows or hides a three-dimensional surface plot. This option is available only for models with two or more X variables.
Parameter Profiler
Shows or hides a prediction profiler that profiles the SSE or loss as a function of the parameters.
Parameter Contour Profiler
Shows or hides a contour profiler that profiles the SSE or loss as a function of the parameters.
Parameter Surface Profiler
Shows or hides a three-dimensional surface plot that profiles the SSE or loss as a function of the parameters. This option is available only for models with two or more parameters.
Profile Likelihood
(Available only if Nonlinear is launched with a loss function that contains two or more parameters.) Shows or hides a plot of the relative likelihood function, scaled to have a maximum value of one, across values of a single parameter while all other parameters are optimized to minimize the loss function. The intersection of the curve with the confidence level lines form a likelihood confidence interval for the parameter setting. You can change the parameter of interest by clicking on the parameter list above the plot. Use the Update Region button to update the plot after making adjustments to the horizontal axis.
Change Settings
Opens a window that enables you to control the resolution of the grid used to compute the profile.
Profile Likelihood Contour
(Available only if Nonlinear is launched with a loss function that contains three or more parameters.) Shows or hides the likelihood confidence contours for the relative likelihood function across two parameters while all other parameters are optimized to minimize the loss function. You can change the two parameters of interest by clicking on the parameter lists above the plot. Use the Update Region button to update the plot after making adjustments to the horizontal axis.
Change Settings
Opens a window that enables you to control the resolution of the grid used to compute the contours.
SSE Grid
Creates a grid of values around the solution estimates and computes 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 the radio button for a particular model to display that model in the Plot and the parameter estimates in the Control Panel.
Custom Estimate
Estimates a user-defined 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 Estimation Profiler
Enables you to construct a profiler for a custom expression. This type of profiler is useful for nonlinear models that you have specified. You provide an expression involving parameters and at least one factor. There is also an option to apply a transformation to the expression. After you click OK, you specify the initial values for the factors. The profiler for the expression is based on the current parameter estimates across a range of the factors. The profiler is set at the specified initial values. You can add several custom profilers using the Custom Estimation Profiler option. Each custom profiler red triangle menu contains options for the profiler graph and factor settings. See “Profiler” in Profilers. To remove a profiler, click the corresponding red triangle and select Remove Profiler. See Create Custom Profiler.
Note: By default, the profiler axis ranges for the expression and the factors might be narrow. You can adjust the range by double clicking an axis and specifying new minimum and maximum values.
Custom Inverse Prediction
Estimates an X value for each specified response value. Standard errors and confidence limits for the estimated X values are also calculated. 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.
Show Prediction Expression
Shows or hides the prediction model or the loss function in the report.
Save Pred Confid Limits
Saves new columns to the data table. The new columns contain the asymptotic confidence limits for the model prediction. This is the confidence interval for the average response value at a given X value.
Save Indiv Confid Limits
Saves new columns to the data table. The new columns contain the asymptotic confidence limits for an individual prediction. This is the confidence interval of an individual response value at a given X value.
Save Formulas
Gives options for saving model results to data table columns:
Save Prediction Formula
Saves a new formula column to the data table. The new column contains the prediction formula using the current parameter estimates.
Save Std Error of Predicted
Saves a new formula column to the data table. The new column contains the formula of the standard error for a model prediction. This is the standard error for predicting the average response value for a given X value. 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 a new formula column to the data table. The new column contains the formula of the standard error for an individual prediction. This is the standard error for predicting an individual response 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 a new formula column to the data table. The new column contains the formula for computing the residuals.
Save Pred Confid Limit Formula
Saves new formula columns to the data table. The new columns contain the formulas to calculate the confidence interval for a model prediction. This is a confidence interval for the average response value at a given X value.
Save Indiv Confid Limit Formula
Saves new formula columns to the data table. The new columns contain the formulas to calculate the confidence interval for an individual prediction. This is a confidence interval of an individual response value for a given X values.
Save Inverse Prediction Formula
Saves new formula columns to the data table. The new columns contain the 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
Saves new formula columns to the data table. The new columns contain formulas for the prediction and standard error for evaluating an X variable given the response variable and either other X values in the data or a constant. This option is equivalent to Save Inverse Prediction Formula in simple cases. However, this option 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 option, a window 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 window. 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.
Save Estimates to Table
Creates a new data table that contains the parameter estimates.