The Logistic w Loss.jmp data table in the Nonlinear Examples sample data folder has an example for fitting a logistic regression using a loss function. The Y column contains ones for events and zeros for non-events. The Model Y column has the linear model, and the Loss column has the loss function. In this example, the loss function is the negative log-likelihood for each observation, or the negative log of the probability of getting the observed response.
 1 Select Help > Sample Data Library and open Nonlinear Examples/Logistic w Loss.jmp.
 2 Select Analyze > Modeling > Nonlinear.
 3 Assign Model Y to the X, Predictor Formula role.
 4 Assign Loss to the Loss role.
Nonlinear Launch Window
 5 Click OK.
Nonlinear Fit Control Panel
 6 Click Go.
Solution Report
 1 Display the Logistic w Loss.jmp sample data table again.
 2 Select Analyze >Modeling > Nonlinear.
 3 Assign Model2 Y to the X, Predictor Formula role.
 4 Assign Loss2 to the Loss role.
 5 Select the Second Derivatives option.
Nonlinear Launch Window for Second Derivatives
 6 Click OK.
 7 Type 1000 for the Iteration Stop Limit.
Specify the Stop Limit
 8 Click Go.
The Standard Error is different
The Ingots2.jmp sample data table includes the numbers of ingots tested for readiness after different treatments of heating and soaking times. The response variable, NReady, is binomial, depending on the number of ingots tested (Ntotal) and the heating and soaking times. Maximum likelihood estimates for parameters from a probit model with binomial errors are obtained using:
 • numerical derivatives
 • the negative log-likelihood as a loss function
 • the Newton-Raphson method.
Normal Distribution(b0+b1*Heat+b2*Soak)
The argument to the Normal Distribution function is a linear model of the treatments.
 1 Select Analyze > Modeling > Nonlinear.
 2 Assign P to the X, Predictor Formula role,
 3 Assign Loss to the Loss role.
 4 Select the Numeric Derivatives Only option.
 5 Click OK.
 6 Click Go.
Solution for the Ingots2 Data
where μ can be a single parameter, or a linear model with many parameters. Many texts and papers show how the model can be transformed and fit with iteratively reweighted least squares (Nelder and Wedderburn 1972). However, in JMP it is more straightforward to fit the model directly. For example, McCullagh and Nelder (1989) show how to analyze the number of reported damage incidents caused by waves to cargo-carrying vessels.
The data are in the Ship Damage.jmp sample data table. The model formula is in the model column, and the loss function (or –log-likelihood) is in the Poisson column. To fit the model, follow the steps below:
 1 Select Analyze > Modeling > Nonlinear.
 2 Assign model to the X, Predictor Formula role.
 3 Assign Poisson to the Loss role.
 4 Click OK.
 5 Set the Current Value (initial value) for b0 to 1, and the other parameters to 0 (Enter New Parameters).
Enter New Parameters
 6 Click Go.
 7 Click the Confidence Limits button.
The Solution report is shown in Solution Table for the Poisson Loss Example. The results include the parameter estimates and confidence intervals, and other summary statistics.
Solution Table for the Poisson Loss Example
Complete Example Using the Fit Curve Personality in Nonlinear Regression with Built-In Models to fit the model. This example shows how to save the prediction formula from Fit Curve and then set parameter limits in Nonlinear.
 1 From the Logistic 4P red triangle menu, select Save Formulas > Save Parametric Prediction Formula.
A new column named Toxicity Predictor appears in the data table.
 2 Select Analyze > Modeling > Nonlinear.
 3 Assign Toxicity to the Y, Response role.
 4 Assign Toxicity Predictor to the X, Predictor Formula role.
 5 Assign Formulation to the Group role.
 6 Click OK.
The Nonlinear Fit window appears (Nonlinear Fit Control Panel). In the Control Panel, parameter values and locking options are shown. The letters listed before each parameter correspond to variables from the Prediction Model in the Fit Curve function.
Nonlinear Fit Control Panel
 7 Select the red triangle menu next to Nonlinear Fit and then select Parameter Bounds.
 8 Set the lower bounds for the parameters as shown in Setting Parameter Bounds. You know from prior experience that the maximum toxicity of the drug is at least 1.1.
Setting Parameter Bounds
 9 Click Go.
The final parameter estimates are shown in the Solution report, along with other fit statistics (Nonlinear Fit Plot and Parameter Estimates). The fitted model is shown on the plot.
Nonlinear Fit Plot and Parameter Estimates