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 nonevents. 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 loglikelihood for each observation, or the negative log of the probability of getting the observed response.
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Select Analyze > Modeling > Nonlinear.

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Click OK.

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Click Go.

The same problem can be handled differently by defining a model column formula that absorbs the logistic function. Also, define a loss function that uses the model to form the probability for a categorical response level. Model2 Y holds the model, and the loss function is Loss2.
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Display the Logistic w Loss.jmp sample data table again.

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Select Analyze >Modeling > Nonlinear.

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Select the Second Derivatives option.

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Click OK.

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Type 1000 for the Iteration Stop Limit.

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Click Go.

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:
The average number of ingots ready is the product of the number tested and the probability that an ingot is ready for use given the amount of time it was heated and soaked. Using a probit model, the P column contains the model formula:
The argument to the Normal Distribution function is a linear model of the treatments.
To specify binomial errors, the loss function, Loss, has the formula
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Select Analyze > Modeling > Nonlinear.

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Select the Numeric Derivatives Only option.

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Click OK.

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Click Go.

The platform used the Numerical SR1 method to obtain the parameter estimates shown in Solution for the Ingots2 Data.
, n = 0, 1, 2, …
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 cargocarrying 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 –loglikelihood) is in the Poisson column. To fit the model, follow the steps below:
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Select Analyze > Modeling > Nonlinear.

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Click OK.

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Set the Current Value (initial value) for b0 to 1, and the other parameters to 0 (Enter New Parameters).

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Click Go.

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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.
Complete Example Using the Fit Curve Personality in Nonlinear Regression with BuiltIn Models to fit the model. This example shows how to save the prediction formula from Fit Curve and then set parameter limits in Nonlinear.
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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.
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Select Analyze > Modeling > Nonlinear.

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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.
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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.

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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.