I need to give a quick description of Tobit Regression (TR), including how
it differs from ordinary least squares (OLS). I am an ecologist who knows
just enough about remote sensing and statistics to be dangerous in both.
Now I have found myself doing a remote sensing project where I have used TR:
survreg(Surv()). As far as I can tell, no form of Censored Regression has
been used in analyzing satellite imagery, so the manuscript I am working on
will effectively be introducing TR to the remote sensing community. The
manuscript has gone through peer review, and the strongest comment was that
I need to give a short description of TR compared to OLS.
While I think I've got a reasonable understanding of how to use it, I must
admit that I know nothing about the mathematics behind TR.
Some references mention it being a combination of OLS and Probit Analysis.
At least one econometrics book describes estimating an normal mean from data
with a censored or truncated normal distribution. I also find lots of
mentionings of y (dependant variable) being a 'latent' variable, though I
cannot seem to find a definition for 'latent variable' anywhere, though my
guess is that it simply is another way of referring to a censored or
truncated variable. I've also seen mentionings of the use of the Tobit
Model in Bayesian statistics... so maybe Tobit refers only to a linear model
with a censored outcome and there may be multiple ways of getting to that?
Here are some specific questions, in case that makes it easier to reply:
(1) Does 'Tobit' refer only to y* = Bx + E where y* is censored, or does it
also refer to the method for estimating the coefficients of significant
variables? (Is it the model or the regression method?)
(2) What is a 'latent' variable?
(3) In the use of survreg(Surv()), are both OLS and Probit Analysis
involved?
(4) If OLS is involved, are there modifications made to estimating the
means? Is this where Probit Analysis is involved?
(5) I've also seen mentionings of maximum likelihood (ML), and ML values are
given in the survreg output for the base and full models. Where does ML get
involved in the calculations?
Thanks!
-Eric
---
Eric B. Peterson, Ph.D.
Vegetation Ecologist & Lichenologist
Nevada Natural Heritage Program
and (adjunct) UNR Dept. NRES
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