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Re: st: logY, Tobit and the prediction of Y
Mathew Stalker replied to Christer Thrane:
My initial model is:
Y = a + b1x1 + controls + e
where Y is expenditures on a commodity and x1 is income.
Since there are a lot of zeroes, I use the Tobit apporach. However, since
the log-linear model performed better than the linear, I use the former
(Before the log transformation of Y, I follow convention and set zeroes
Accordingly, the estimated Tobit model is:
logY = a + b1x1 + controls + e
I want to predict the value of Y (not logY) for certain values of income
(and put it in a graph); that is, both the conditional Y (i.e. the Y
that the threshold value of 0 was passed) and the unconditional (latent)
value of Y.
Does anyone know how to do this?
The prediction of Y from your model would simply be the exponential of the
However, you should note that the log of zero is minus infinity, so in your
log model no observations where Y is zero will be included. Is this really
what you want?
Replacing 0s by 1s is clearly not very satisfactory. Using generalised
linear models with log link makes _that_ unnecessary.
glm Y <predictors>, link(log)
This approach has two extra advantages. First, it automatically
yields predictions on the scale of the response, here Y.
Second, the back-transformation approach mentioned by
Mathew raises bias issues, well documented in some
literatures (for some reason, there is masses on
this within health economics) which don't arise in the GLM
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