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

[Ebru Ozturk <ebru_0512@hotmail.com>]

Do you mean that the model violates the Tobit assumptions in any case and I should swithc to a different model?

Thank you, Ebru

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