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Re: st: Normally distributed error term & testing normality of


From   "JVerkuilen (Gmail)" <jvverkuilen@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Normally distributed error term & testing normality of
Date   Sun, 14 Oct 2012 21:12:59 -0400

On Sun, Oct 14, 2012 at 11:06 AM, Ebru Ozturk <ebru_0512@hotmail.com> wrote:
>
> But, the issue is not for me whether to use -glm- or -tobit-. I want to learn how I can test Tobit specifications graphically.
>
> For instance, in linear regression they generate residuals and check it by -qnorm- or -pnorm- (qnorm e). Also, to check heteroscedasticity they make a graph of the residuals of the model against the predicted values.
>
> So, if the residuals will not be normal because of censoring, what should I look at? What should I use instead of residuals in Tobit?

I think the general problem is that residuals aren't separable from
the model, so there is an unavoidable issue of whether to use -glm- or
-tobit- at least in any real problem. They are functions of the
predictions made and hence conditional on the model. One model may
perform much better and thus have better behaved residuals than a
different one. Trying to assess this graphically seems like trying to
get a family sedan to drive like a sportscar. You can keep working at
that problem and maybe get a reasonable approximation to it or you can
switch to a model that doesn't make those assumptions.

That said, I guess you could beak the problem into two pieces. Piece 1
is a probit (or logit) of censored vs. not censored. Assess whether
this is fitting reasonably well using the tools for probit models.
Piece 2 is conditional on piece 1. The observed data are still not
normal, but you might be able to find a reasonable model for them. As
I said, I am not confident this would work, but one could try it.

One big issue that Tobit model seems to ignore is that the things that
predict being censored and the things that predict values for
noncensored cases don't have to be the same thing. A model like -zip-
(or an adaptation of it) seems like it has some potential in this
regard.
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