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# Re: st: Incomplete Beta Function

 From nicostat@gmail.com To statalist@hsphsun2.harvard.edu Subject Re: st: Incomplete Beta Function Date Mon, 18 Feb 2013 14:13:28 +0000

```Sorry about that. Starting from the model:
I have a discontinuity  distribution of my dependent variable y  that
are scores. I have  several thresholds, where I cannot observe the
real value of y, so is latent.
To illustrate, consider a simple case where there is only one
threshold at 50. Let y and y∗ be the
observed and latent scores, respectively. If y∗ ≥ 50 then y = y∗
always. If y∗ < 50, we observe y = 50
with a probability F (y∗/50), approaching 1 as y∗ → 50 from below, and
we observe y = y∗ with a
probability 1 − F (y∗/50). Thus,
y =y∗ if y∗ < 50 and d = 0
y=50 if y∗ < 50 and d = 1
y=y∗ if y∗ ≥ 50
where the rounding indicator d is drawn conditionally on y∗ < 50 as
d = 1[u ≤ F (y∗/50)]
and u is a (0, 1) uniform error. Also d = 1(y∗ − ε ≥ 0) where ε = 50F −1 (u).
One way to proceed is to specify a normal regression equation for y∗
and a Beta cdf for F (.), so that
y∗ = xβ + σv
F (y∗/50) = Iy∗/50 (a, b)
where Ir (a, b) is the incomplete Beta function ratio with parameters a and b.

I want to implement this model in Stata, how i can do it. The
parameters (β, σ, a, b) can be estimated by maximum likelihood.
there is some code or i need to write my code?

Hope is more clear
Catia

2013/2/18 Maarten Buis <maartenlbuis@gmail.com>:
> On its own the incomplete beta function is not a model, so you need to
>
> -- Maarten
>
> On Mon, Feb 18, 2013 at 12:12 PM,  <nicostat@gmail.com> wrote:
>> Thanks Maarteen,
>> yes  I need to estimate the parameters a and b of this beta incomplete
>> function by ml.
>> Thanks
>> Catia
>>
>> 2013/2/18 Maarten Buis <maartenlbuis@gmail.com>:
>>> On Sun, Feb 17, 2013 at 9:15 PM,  <nicostat@gmail.com> wrote:
>>>> I would like to estimate incomplete Beta function such as this below
>>>> trough maximum likelihood I can performance this in Stata?
>>>>
>>>> (y*/50) = I (a, b)
>>>> where I(a, b) is the incomplete Beta function ratio with parameters a and b.
>>>
>>> What is your question? Do you want to incomplete Beta function? Than
>>> type in Stata: -findit incomplete beta function-. Do you want to
>>> estimate the paramters a and b? Than you need to write down your
>>> log-likelihood function and use -ml- to maximize that. In that case
>>> <http://www.stata.com/bookstore/maximum-likelihood-estimation-stata/>.
>>>
>>> -- Maarten
>>>
>>>
>>>
>>> -- Maarten
>>>
>>> ---------------------------------
>>> Maarten L. Buis
>>> WZB
>>> Reichpietschufer 50
>>> 10785 Berlin
>>> Germany
>>>
>>> http://www.maartenbuis.nl
>>> ---------------------------------
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>
>
>
> --
> ---------------------------------
> Maarten L. Buis
> WZB
> Reichpietschufer 50
> 10785 Berlin
> Germany
>
> http://www.maartenbuis.nl
> ---------------------------------
> *
> *   For searches and help try:
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```