Modeling and Multivariate Methods - SAS

268 Performing Nonlinear Regression Chapter 9
Additional Examples
Additional Examples
This section provides several examples of the broad usefulness of the Nonlinear platform.
Maximum Likelihood: Logistic Regression
In this example, we show several variations of minimizing a loss function. The loss function is the negative
of a log-likelihood function, thus producing maximum likelihood estimates.
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 is the proportion of ones for equal-sized
samples of x values. 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.
Run the model by following the steps below:
1. Select Analyze >Modeling > Nonlinear.
2. Assign Model Y to the X, Predictor Formula role.
3. Assign Loss to the Loss role.
4. Click OK.
5. Click Go.
The parameter estimates are shown in the Solution report. See Figure 9.18.
Figure 9.18 Solution Report
The Loss value in the Solution report is the negative log-likelihood evaluated at the parameter estimates.
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.