--- 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
*----------- begin example ---------------
clear
program drop _all
set more off
input prop str1 site variety
0.0005 A 1
0.0000 A 2
0.0000 A 3
0.0010 A 4
0.0025 A 5
0.0005 A 6
0.0050 A 7
0.0130 A 8
0.0150 A 9
0.0150 A 10
0.0000 B 1
0.0005 B 2
0.0005 B 3
0.0030 B 4
0.0075 B 5
0.0030 B 6
0.0300 B 7
0.0750 B 8
0.0100 B 9
0.1270 B 10
0.0125 C 1
0.0125 C 2
0.0250 C 3
0.1660 C 4
0.0250 C 5
0.0250 C 6
0.0000 C 7
0.2000 C 8
0.3750 C 9
0.2625 C 10
0.0250 D 1
0.0050 D 2
0.0001 D 3
0.0300 D 4
0.0250 D 5
0.0001 D 6
0.2500 D 7
0.5500 D 8
0.0500 D 9
0.4000 D 10
0.0550 E 1
0.0100 E 2
0.0600 E 3
0.0110 E 4
0.0250 E 5
0.0800 E 6
0.1650 E 7
0.2950 E 8
0.2000 E 9
0.4350 E 10
0.0100 F 1
0.0500 F 2
0.0500 F 3
0.0500 F 4
0.0500 F 5
0.0500 F 6
0.1000 F 7
0.0500 F 8
0.5000 F 9
0.7500 F 10
0.0500 G 1
0.0010 G 2
0.0500 G 3
0.0500 G 4
0.5000 G 5
0.1000 G 6
0.5000 G 7
0.2500 G 8
0.5000 G 9
0.7500 G 10
0.0500 H 1
0.1000 H 2
0.0500 H 3
0.0500 H 4
0.2500 H 5
0.7500 H 6
0.5000 H 7
0.7500 H 8
0.7500 H 9
0.7500 H 10
0.1750 I 1
0.2500 I 2
0.4250 I 3
0.5000 I 4
0.3750 I 5
0.9500 I 6
0.6250 I 7
0.9500 I 8
0.9500 I 9
0.9500 I 10
end
encode site, gen(sitenum)
gen byte left = sitenum <= 4
program define zibeta_lf
*! MLB 0.0.1 13 Aug 2009
version 8.2
args lnf logitmu lnphi zb
tempvar zero nonzero mu phi
quietly gen double `zero' = invlogit(`zb')
quietly gen double `nonzero' = invlogit(-`zb')
quietly gen double `mu' = invlogit(`logitmu')
quietly gen double `phi' = exp(`lnphi')
quietly replace `lnf' = ln(`nonzero') + ///
lngamma(`phi') - ///
lngamma(`mu'*`phi') - ///
lngamma((1-`mu')*`phi') + ///
(`mu'*`phi'-1)*ln($ML_y) + ///
((1-`mu')*`phi'-1)*ln(1-$ML_y) ///
if $ML_y > 0
quietly replace `lnf' = ln(`zero') if $ML_y == 0
end
xi i.site i.variety
ml model lf zibeta_lf (logitmu: prop = _I*) /lnphi (zg:left), robust
ml check
ml search
ml maximize
exit
*--------------- end example ----------------------
-----------------------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany
http://home.fsw.vu.nl/m.buis/
-----------------------------------------
*
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