[R] Tobit model fluid milk consumption

Terry Therneau therneau at mayo.edu
Fri Dec 4 16:07:32 CET 2009

First, note that all attachments are removed from messages sent to
R-help, please use plain text only.  I took the time to bring up the
attachment in a web browser (there is a link to it), but you are
unlikely to get a lot of readers when the question is captured as a pdf.

 1. Tobit regression on the raw data:
   The "scale" is the residual standard deviation, or estimate of
"sigma" in the usual linear models terminology.
   For linear regression with uncensored data, the estimate of scale is
independent of the estimate of the other coefficients, and can be
computed at the end.  For censored data this is not so, the scale and
the coefficients must be estimated together.  During the maximization
step the routine uses log(scale), it forces positive coefficients and
also works better numerically; as a consequence the full
variance/covariance matrix includes both beta and log(scale).

2. Tobit regression on the rescaled data.
  You must have rescaled both x and y, since the estimated residual
variance changed.
  I see multiple disadvantages, and no advantages, to regression on
rescaled data.  I know it is common in some fields, but why?  With
respect to your questions on how to interpret rescaled coefficients, I
don't know how to interpret them either.

 3. The "residual" for a censored observation is not a well defined
quantity.  Hence both the computation and meaning of R^2 are unclear to

Terry Therneau

  Terry Therneau

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