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The Liver Cancer.jmp sample data table contains liver cancer Node Count values for 136 patients. It also includes measurements on six potentially related variables: BMI, Age, Time, Markers, Hepatitis, and Jaundice. These columns are described in Column Notes in the data table.
This example develops a prediction model for Node Count using the six predictors. Node Count is modeled using a Poisson distribution.
1.
Select Help > Sample Data Library and open Liver Cancer.jmp.
2.
Select Analyze > Fit Model.
3.
Select Node Count from the Select Columns list and click Y.
4.
Select BMI through Jaundice and click Macros > Factorial to Degree.
5.
Select Validation from the Select Columns list and click Validation.
6.
From the Personality list, select Generalized Regression.
8.
Click Run.
9.
The Solution Path is shown in Figure 7.1. The paths for terms that have nonzero coefficients are highlighted. Think of the solution paths as moving from right to left across the plot, as the solutions shrink farther from the MLE. A number of terms have paths that shrink them to zero fairly early.
Figure 7.1 Solution Path for Lasso Fit with Nonzero Terms Highlighted
The Parameter Estimates for Original Predictors report (Figure 7.2) shows the parameter estimates for the uncentered and unscaled data. The 11 terms with nonzero parameter estimates are highlighted. These include interaction effects. In the data table, all six predictor columns are selected because every predictor column appears in a term that has a nonzero coefficient.
11.
Click on the row for (Age - 56.3994)*Markers[0-1] in the Parameter Estimates for Original Predictors report.
Figure 7.2 Parameter Estimates Report with Nonzero Terms Highlighted
12.
Click the red triangle next to Adaptive Lasso with Validation Column and select Save Columns > Save Prediction Formula and Save Columns > Save Variance Formula.
Two columns are added to the data table: Node Count Prediction Formula and Node Count Variance.
13.
Right-click either column heading and select Formula to view the formula. Alternatively, click on the plus sign to the right of the column name in the Columns panel.
The prediction formula in the Save Prediction Formula column applies the exponential function to the estimated linear part of the model. The prediction variance formula in Node Count Variance is given by the identical formula, because the variance of a Poisson distribution equals its mean.

Help created on 3/19/2020