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Re: zero inflated beta [was: st: Information request]


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: zero inflated beta [was: st: Information request]
Date   Mon, 17 Aug 2009 15:19:04 -0400

Fabio Zona et al.:
There is no intrinsic problem with a lot of zeros in the fractional
logit model; those people could simply have very small bonuses in
expectation due to covariate patterns (with an expected bonus of 17
cents, you will realize a zero quite often). You could also run a
-poisson- regression (or equivalent -glm- model) of bonus on log total
compensation and other X (you can constrain the coef on log total
compensation to be one if necessary).  This is a more robust model,
and has a natural IV version at -ivpois- (on SSC) or using -gmm- (in
Stata 11), which you will want, since there is no way this type of
model is free from endogeneity problems.

On Mon, Aug 17, 2009 at 11:51 AM, Verkuilen, Jay<JVerkuilen@gc.cuny.edu> wrote:
> The ZI-Beta model is very hard to identify, too. The problem is that the beta includes a J-shaped distribution. It's hard to know if this will work.
>
> The main issue that the original poster should consider is if having no bonus is qualitatively different than having some. If the same basic set of regressors predict bonus size, just "cheat" the values away a little by, say, linearly transforming all bonuses towards .5 by a small amount and use beta regression normally.
>
> If not, some kind of system approach becomes necessary and, well, that's going to get ugly.
>
> JV
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Maarten buis
> Sent: Thursday, August 13, 2009 4:34 AM
> To: statalist@hsphsun2.harvard.edu
> Subject: zero inflated beta [was: st: Information request]
>
> --- On Wed, 12/8/09, Fabio Zona wrote:
>> I am in the unfortunate situation of running a regression
>> analysis, whereby:
>> - my dependent variable is a proportion (percentage of
>> bonus on total compensation of top managers of 178
>> corporations),
>> - the majority (more than 50%) of my managers does not have
>> any bonus, so the proportion is exact ZERO, that is, my
>> dependent variable has many exact zeros.
>>
>> How can I estimate this model? do you know the command I
>> should use in Stata?
>> I know that I cannot use the fractional logit because I
>> have many zeros. I have not found any zero-inflated logistic
>> regression for situations whereby y are proportion
>
> A zero inflated fractional logit model is hard to identify. A
> zero-inflated beta is probably better, but there is obviously
> a price (there is no such thing as a free lunch...), and that
> is more restrictive assumptions.
>
> Below is a quick stab at implementing such a model. I haven't
> done any checking or certification on it, so it is up to you
> to determine whether this is program actually does what it is
> supposed to do. As a first step I would build a simulated
> dataset where you know what the parameters should be and
> check whether this program actually finds those.
>
> Hope this helps,
> Maarten
<snip>

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