Example of Inverse Prediction
In the Logistic platform, you can use the Crosshair tool to visually approximate an inverse prediction. If your response has exactly two levels, the Inverse Prediction option enables you to request an exact inverse prediction. Inverse prediction gives you an estimated value of the X variable that corresponds to a given probability of the target level of the Y variable, as well as a confidence interval for that estimate.
1. Select Help > Sample Data Folder and open Penicillin.jmp.
2. Select Analyze > Fit Y by X.
3. Select Response and click Y, Response.
4. Select ln(dose) and click X, Factor.
Notice that JMP automatically fills in Count for Freq. Count was previously assigned the role of Freq.
5. From the Target Level list, select Cured.
6. Click OK.
Crosshair Tool
7. Click the Crosshair tool.
8. Place the crosshair at about 0.5 on the vertical (Response) probability axis on the left side of the plot.
9. Move the crosshair intersection to the prediction line, and read the In(dose) value that shows below the crosshair.
Figure 8.10 Example of Crosshair Tool on Logistic Plot
In this example, a rabbit with a ln(dose) of approximately -0.9 is equally likely to be cured as it is to die. To obtain a precise inverse prediction, use the Inverse Prediction option.
Inverse Prediction Option
10. Click the Logistic Fit red triangle menu and select Inverse Prediction (Figure 8.11).
11. Type 0.95 for the Confidence Level.
12. Select Two sided for the confidence interval.
13. Request the response probability of interest. Type 0.5 and 0.9 for this example, which indicates you are requesting the values for ln(dose) that correspond to a 0.5 and 0.9 probability of being cured.
Figure 8.11 Inverse Prediction Window
14. Click OK.
Figure 8.12 Example of Inverse Prediction Plot
The estimates of the values of the X variable and the corresponding confidence intervals are shown in the Inverse Prediction report in both tabular and graphic format. For example, the value of ln(dose) that results in a 90% probability of being cured is estimated to be between -0.526 and 0.783.