Re: st: ZOIB procedure

[Maarten Buis <maartenlbuis@gmail.com>]

On Sun, Sep 18, 2011 at 11:51 PM, Prerna S <maruiprerna@gmail.com> wrote:
> I am using zoib (Stata 11.2) to estimate 2 proportions. I have 3 questions.

-zoib- is a user written program. The Statalist FAQ asks you to
specify where you got it from. This is not to annoy you, but to help
you. Experience learns us that there are often different versions of
user written software floating around in cyber space. How can we help
you if we do not know which version you are talking about? I am
assuming you are talking about -zoib- as available from SSC.

> 1. The model that I am attempting to estimate looks like the following.
>
> p1 = a1 + a2X + e1
> p2 = b1 + b2X + e2
>
> where pi is the proportion of income from source i.
>
> Is there any procedure that approximates an SUR for zoib that I can
> use? I tried the suest option but it does not offer a test statistic
> and the results under suest appear to be the same as without suest. I
> am unsure if this implies that SUR does not matter or if I missed
> something.

-suest- only changes the variance covariance matrix, such that you can
perform tests across models. Like the -vce(robust)- option, they do
not change the estimated coefficients. To perform those tests, you
need specify them yourself using -test-. For more see the manual
entries of -suest- and -test-.

I am guessing, but it seems to me you are worried about correlation of
error terms across income sources. This is a hard problem, in part
because proportions are inherently (negatively) correlated. If one
proportion increases, than the rest will have to decrease. Some work
has been done by Aitchison (2003), but he sacrifices an interpretable
effect of explanatory variables on the proportion in order to get the
correlations right. This is fine if you are mainly interested in those
correlations, but a problem otherwise.

Alternative solutions are -dirifit- and -fmlogit-. The former makes
the strong assumption that the correlations between proportions are
only due to that automatic correlation that occurs between
proportions. -fmlogit- uses a quasi-likelihood argument to by-pass
that entire problem. Both -dirifit- and -fmlogit- can be downloaded
from SSC. They are discussed in this talk at the 2010 German Stata
Users' meeting: <http://ideas.repec.org/p/boc/dsug10/04.html>.

> 2.  Wooldridge (2002) suggests using Smith-Blundell/Rivers Vuong
> method that for dealing with endogeneity with respect to fractional
> logit and tobit. Is this for some reason unsuitable for zoib?

The Statalist FAQ asks you to provide full references rather than a
name/year reference.

> 3.  I would like to investigate the usual problems like
> multicollinearity, heteroscedasticity, non-normality. Is there a
> resource that I might refer to for regression diagnostics for zoib?

The usual problems are only usual in the linear regression case. You
will need to redefine them when dealing with other types of models.
Multicolinearity is never a problem, it is just an unfortunate
historical accident that it ended up in that row of "problems".
Heteroskedasticity, is in and of itself not a problem when dealing
with a (zero-one-inflated) beta distribution, as that distribution
allows for heteroskadasticity. This leaves the question open whether
it does so correctly. Normality is only a problem when you assume a
normal distribution, which is obviously not the case when you estimate
a zero-one-inflated beta distribution. This leaves the question
whether your data is well enough approximated with a zero-one-inflated
beta distribution. In short you need to rethink what those "problems"
mean in the context of your model. A good source is chapter 4 of
Hardin and Hilbe (2007).

Hope this helps,
Maarten (author of -zoib-)

Aitchison (2003) The Statistical Analysis of Compositional Data.
Caldwell, NJ: The Blackburn Press.

James W. Hardin and Joshep M. Hilbe (2007) "Generalized Linear Models
and Extensions", second edition. College Station, TX: Stata Press.
<http://www.stata.com/bookstore/glmext.html>

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany


http://www.maartenbuis.nl
--------------------------

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