# Tobit-like model for dependent variable with upper limits

Following the wiki page and the form of the likelihood function for a generalized Tobit model presented here, I am thinking about applying a model of this type to a problem I'm facing but need some help in the interpretation.

I have a variable $Y$ which I assume to linearly depend on $X$ via a parameter $\beta$. My model is

$$Y = X\beta + \epsilon_i$$

The problem is that some observed values I have for $Y$, the $y_i$'s, are upper limits. Can I extend the concept of "censored data" to this case and use the Tobit model to perform the linear regression?

Do you have any thoughts on the possibility of further inclunding a categorical moderator variable in the regression? Is this possible?

Thanks.

• Try this answer: stats.stackexchange.com/questions/83047/…. Also, this exact problem is very common in survival analysis (because the trial usually ends before everyone is dead), so you might try searching on that. The model you would use is not normally called a Tobit model, though it is really the same thing. – Bill May 9 '14 at 15:01
• @Bill, thank you for pointing me in the right direction. I got it to work, and even included the categorical variable. – joaoFaria May 10 '14 at 22:10