Modeling and Multivariate Methods - SAS

270 Performing Nonlinear Regression Chapter 9
Additional Examples
The platform used the Quasi-Newton SR1 method to obtain the parameter estimates shown in Figure 9.19.
Figure 9.19 Solution for the Ingots2 Data
Poisson Loss Function
A Poisson distribution is often used to model count data.
e – μ μ n
P( Y = n)
= -------------- , n = 0, 1, 2, …
n!
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.
6. Click Go.
7. Select the Confidence Limits button.
The Solution report is shown in Figure 9.20. The results include the parameter estimates and confidence
intervals, and other summary statistics.