Tobit regression

[Hiam Saghir]

Hello all,

I am new to Tobit regression and I have few questions in relation to a dataset I am analyzing.

I have a dataset where the dependent variable is continuous with left censoring (concentrations below machine's detection limit). The dependent variable is also not normally distributed. I have transformed the dependent variable to the log scale and applied tobit regression. My questions are as follows:

1- Is it possible to back transform the beta coefficients generated by Tobit using exp(beta)?
2-Can I use these beta coefficients (generated by tobit) to interpret the data in a similar way to a regular linear regression?

Thanks!
H

[Carlo Lazzaro]

Hiam:
I fail to get your concern about -depvar- departure from normality.
Is it a prerequisite of -tobit-?

[Hiam Saghir]

Isn't normality a prerequisite for a best fit line? SO I have transformed the data because regardless of the censoring the data is not normally distributed. What do you think is best to do?

[Carlo Lazzaro]

Hiam:
if you refer to OLS, normality pertains to the residual distribution.
That said, it may well be that -ln- transformation increases the fit of your model (say, reducing heteroskedasticity).
Or, that you may have a better fit with quadratic relationship between some predictors and the dependent variable.
I would also considering (as in all regression models) the risk of omitted variable bias.
As far as the interpretation is concerned, by logging the dependent variable (and keeping, I guess, all the predictors in their original metrics), you have a so called log-linear regression model.
The interpretation of the contribution of each predictor in explaining the variation of the dependent variable (when adjusted for the other predictors) is different from the one forOLS without logged dependent variable: a change in X by 1 unit is associated with a [exp(beta)-1] change in Y.

[Hiam Saghir]

Hi Carlo,

Thank you for your reply.
But how do I deal with the data left censoring?
Hiam

[Carlo Lazzaro]

Hiam:
as you posted, -tobit. is the right tool there.
The interpretation of coefficients for OLS with looged depvar holds for -tobit-, too.