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# Re: st: Incomplete Beta Function

 From Maarten Buis To statalist@hsphsun2.harvard.edu Subject Re: st: Incomplete Beta Function Date Mon, 18 Feb 2013 15:51:18 +0100

```Nick was very clear, repeat:

"Please note further that you are asked to use full real names on
Statalist: neither Catia nor nicostat qualifies."

-- Maarten

On Mon, Feb 18, 2013 at 3:13 PM,  <nicostat@gmail.com> wrote:
> 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
>> tell us more before we can help you.
>>
>> -- 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
>>>> you will want to have access to:
>>>> <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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>>> *
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>>
>>
>>
>> --
>> ---------------------------------
>> Maarten L. Buis
>> WZB
>> Reichpietschufer 50
>> 10785 Berlin
>> Germany
>>
>> http://www.maartenbuis.nl
>> ---------------------------------
>> *
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>
> *
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--
---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

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

*
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```

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