Example of Analyzing Left-Censored Data
In the Fit Parametric Survival platform, you can specify left-censored observations using two response columns. This example fits a Tobit model, which assumes left-censoring at zero.
Note: The Tobit model is popular in economics for responses that must be positive or zero, with zero representing a censored point. It assumes a normal distribution that is censored at zero. An observation of zero is considered to be left-censored.
In this example, you create a new column that indicates observations for which left censoring has occurred. For left-censored observations, the new column contains a missing value. Otherwise, it contains the observed value of durable. The new column is then used as the left side of interval-censored observations, and the existing column durable is used as the right side of the intervals.
1. Select Help > Sample Data Folder and open Reliability/Tobit2.jmp.
Create the Left Censoring Column:
2. Select Cols > New Columns.
3. Type durable0 for Column Name.
4. Select Column Properties and click Formula.
5. Select Conditional > If and select durable.
6. Select Comparison > a == b, type 0, and press Enter.
7. Select the box labeled “else clause” and select durable.
Figure 15.13 shows the completed formula.
Figure 15.13 Column Formula for durable0
8. Click OK.
9. Click OK.
Fit the Tobit Model:
10. Select Analyze > Reliability and Survival > Fit Parametric Survival.
11. Select YLow and YHigh in the Time to Event role.
12. Click Remove.
13. Select durable0 and click Time to Event.
14. Select durable and click Time to Event.
You must use two response columns to specify left-censored observations. The direction of censoring is determined by the order of the columns in the Time to Event role.
15. Change the Distribution type to Normal.
Notice that JMP automatically fills in age and liquidity as model effects, because they are designated as effects in the Model script in the data table.
16. Click Run.
Figure 15.14 Tobit Model Results
The report shows the estimated Tobit model fit. Note in the upper right part of the report that there are 13 left-censored observations. This is a good way to check that you have correctly specified the left censoring.