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# Re: st: nonlinear N effect

 From Maarten Buis To statalist@hsphsun2.harvard.edu Subject Re: st: nonlinear N effect Date Wed, 6 Mar 2013 14:33:23 +0100

```I suspect that the null hypothesis you state is probably not the null
hypothesis you want to test. Alternative null hypotheses (unfortunate
choice of words, I know) would be: "the curve is N shaped" or "the
curve is N shaped and the turning point happen at 5% and 25%".

Once you have chosen your model and your null hypothis, you should
rephrase the hypothesis in terms of the parameters of your model. Than
the test is often a straightforward call to -test- or -testnl-.

-- Maarten

On Wed, Mar 6, 2013 at 2:09 PM, Boris Peko wrote:
> My analysis is effect on managerial ownership on company's value and I
> use panel models.
> Ho is that man.own has unlinear effect (N-shape) on company's value.
> Other authors have predetermined inflection (or turning) points of 5%
> and 25% but I want to find out
> techniques to find those points.
>
> 2013/3/6 Maarten Buis <maartenlbuis@gmail.com>:
>> On Wed, Mar 6, 2013 at 12:14 PM, Boris Peko wrote:
>>> Hi! I have a non-linear effect but not U-shape or reverse U-shape.
>>> Effect is N-shaped, dependent variable rises, then fell, then rises.
>>> How can I test that in Stata?
>>> More important, what method should I use if I do not want to use
>>> predetermined inflection point?
>>
>> The test depends on the _exact_ null hypothesis and the method you
>> used to estimate your model.
>>
>> One possibility would be to add a third degree polynomial (cubic
>> curve), which could be an N-shaped curve. The extrema of this curve
>> have a closed form solution, so you can quickly look if the turning
>> point happen within the range of the data. -orthpoly- could be useful
>> for reducing multicolinearity and improving the stability of the
>> estimates. However, a cubic curve is often too restrictive and too
>> sensitive to outliers for my taste, just as a second degree polynomial
>> (quadratic curve) is often too restrictive and too sensitive to
>> outliers for hypothesised U-shaped and reverse U-shaped curves.
>>
>> A better alternative would probably be -fracpoly-, but this also
>> depends on all kinds of details of your data, the substantive
>> background of your study, tribal habits within your
>> (sub-(sub-))discipline, etc..
>>
>> Hope this helps,
>> 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
---------------------------------
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```