AW: st: RE: testing for significant changes in r squared within

["Jan Mammen" <jan.mammen@googlemail.com>]

prior studies in this field have analyzed the relationship online with
linear terms, but as there are good reasons to assume a more complex
relationship, I thought a step by step analysis would be useful. From your
point of view, would a simple likelihood-ratio test to compare the three
models be of any use?

Best
Jan

-----Ursprüngliche Nachricht-----
Von: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Nick Cox
Gesendet: Mittwoch, 23. Februar 2011 16:23
An: 'statalist@hsphsun2.harvard.edu'
Betreff: RE: st: RE: testing for significant changes in r squared within

You are making it sound much better than in your first post. In fact if the
theory is at all sound, just using a linear term sounds a silly null
hypothesis, so why any need to take it seriously? 

Nick 
n.j.cox@durham.ac.uk 

Jan Mammen

> Hello Nick, hello Maarten
> thanks very much for your quick responses,  the cubic term is insofar
justified as it can be argued that low level of my independent variable lead
to an increase in risk, while moderate level lead to a decrease and high
level should again lead to an increase. In the full model all three terms
are significant at p<0.005, The F-Test of all three coefficients has a value
of p<0.0002.
> In search for papers which analysis similar relationships I found the
mentioned paper and thought that the presented procedure could serve as a
further test to show that the model specification with all three terms is
more suitable. I will try out mkspline.

> 2011/2/23 Nick Cox <n.j.cox@durham.ac.uk>
>>
>> This sounds backwards to me.
>>
>> 1. Usually assessing whether adding the quadratic and cubic terms is
worthwhile is a standard problem which should yield to -test-. Does anything
in your set-up rule that out?
>>
>> 2. Much depends on how the extra terms behave. Perhaps they are just
correction terms that give you some curvature where you need it. However,
cubics rarely possess any theoretical rationale and they can behave very
poorly in other respects.
>>
>> 3. Whether a polynomial with terms higher than linear fits better is only
a very limited stab at exploring nonlinearity, as many other functional
forms might need to be considered.
>>
>> 4. Treating R^2 as a test statistic (rather than a descriptive measure)
seems at best an indirect way of answering your real question. You seem to
want to copy someone's else procedure at the expense of answering your own
question directly.
>>
>> Nick
>> n.j.cox@durham.ac.uk
>>
>> Jan Mammen
>>
>> I have a panel data model in which  the dependent variable is firm
>> risk and one independent variable the degree of multinationality of
>> the firm. I would like to test the hypothesis of a nonlinear
>> relationship by adding first a linear term, afterwards the squared and
>> finally the cubic term of multinationality. I am looking for a
>> possibility to show that the inclusion of the squared and cubic term
>> significantly improves the model. As I am using a fixed effects model
>> my first guess was to look for changes in R² within. In the article
>> Strategic Management Article (2008, Issue 2) "WITHIN-INDUSTRY
>> DIVERSIFICATION AND FIRM PERFORMANCE IN THE PRESENCE OF NETWORK
>> EXTERNALITIES: EVIDENCE FROM THE SOFTWARE INDUSTRY" written by
>> Tanrverdi and Lee the authors test the changes in R² within for
>> significance. Unfortunately the authors do not provide abundant
>> information how this test is performed.
>>
>> As far as I have understood I would first have to simulate the
>> distribution of R² within to be able to test the change for
>> significance. I would be very grateful if anybody could tell me if
>> this guess is right or has any suggestion for literature in which such
>> a test or rather the procedure is described.

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