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# RE: st: ZOIB procedure

 From Cameron McIntosh To STATA LIST Subject RE: st: ZOIB procedure Date Mon, 19 Sep 2011 09:12:16 -0400

```Prerna,

Sorry, my answer below wasn't very good. The straight-up logistic regression approach would be best if you had binomial data (alive or dead, diseased or healthy). For proportions, Warton et al. (2011) recommend a logit transformation to achieve linearity. You could then run a linear model in -gllamm-, while allowing cov(e1,e2) and back-transform the predicted values (yhats). Exponentiating these should return the geometric mean value of the yhats, and the geometric mean and median are (asymptotically) equivalent. Thus, you would get predicted median values, which are often of more interest in the study of income than the mean.

Cam

> From: maruiprerna@gmail.com
> Date: Mon, 19 Sep 2011 07:09:46 -0400
> Subject: Re: st: ZOIB procedure
> To: statalist@hsphsun2.harvard.edu
>
> Hello Cam,
>
> Tobit would be inappropriate for the data I am using because the data
> are not censored, rather they are defined over [0,1]. From a quick
> glance, it appears that arcsine is appropriate for binomial data,
> which again my data are not. However, I am unfamilar with arcsine and
> gllamm so I'll look over the references provided. Thank you.
>
> Prerna
>
>
>
> On 18 September 2011 20:02, Cameron McIntosh <cnm100@hotmail.com> wrote:
> > Hi Prerna,
> >
> > I have been wondering about simultaneous equation models (SEMs) that integrate Beta regression links, but I don't think anyone has done the computer implementation on this yet. That would solve your problem a bit more elegantly than SUR approaches as you could easily allow corr(e1,e2). That would certainly be a good R project. :)
> >
> > Anyway, you may want to just switch to a logit or tobit model. Natural scientists (especially in biology and ecology) have long favoured arcsine(square root) transformations for dealing with proportions but this has been criticized recently by:
> > Warton, D.I., & Hui, F.K.C. (2011). The arcsine is asinine: the analysis of proportions in ecology. Ecology, 92(1), 3–10. http://www.esajournals.org/doi/pdf/10.1890/10-0340.1
> >
> > who recommend logistic regression for analyzing proportions. You could estimate an SEM with logit links in gllamm, allow corr(e1,e2) and also instrument X if it's endogenous and if you have some defensible instruments in your data set.
> > My two cents,
> >
> > Cam
> >
> >> From: maruiprerna@gmail.com
> >> Date: Sun, 18 Sep 2011 17:51:07 -0400
> >> Subject: st: ZOIB procedure
> >> To: statalist@hsphsun2.harvard.edu
> >>
> >> Dear Statalisters,
> >>
> >> I am using zoib (Stata 11.2) to estimate 2 proportions. I have 3 questions.
> >>
> >> 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.
> >>
> >> 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?
> >>
> >> 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?
> >>
> >>
> >> Thank you for you time.
> >>
> >> Prerna Marui
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```