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

[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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