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Re: st: linear test


From   Maarten buis <maartenbuis@yahoo.co.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: linear test
Date   Wed, 15 Nov 2006 17:43:30 +0000 (GMT)

--- M.Delprato@westminster.ac.uk wrote:
> I want to test if an explanatory variable has linear relationship
> with an dependent variable. Say, y = a + b1 x1 + b2 x2 + b3 x3 + e,
> and I want to know if the relationship between x3 and y is linear.
> Which test can I use?

I would start with the interoccular trauma test, i.e. just type
-scatter y x3- and look if the relationship seems linear to you. If you
are worried about controlling for the other variables you could plot
the residuals against x3 with -rvpplot x3-. 

If you want more formal tests then it really helps if you have an
alternative, for instance a quadratic relationship, or a spline. If the
former is the case I would first use -orthpoly- to create orthogonal
polynomials, that way the significance of the quadratic term can be
interpreted as a test whether the quadratic terms adds anything. If
your alternative is spline, I would use the marginal option. that way
the second term measures how much the effect changes befor and after
the knot, and the significance of that term tells you if that's
significant. Finally, you could look at the -estat ovtest-. 

However, I think graphs are the best way to find non-linearities and
assess whether they are big enough for you to worry about. I would only
use tests if I had a specific hypothesis about that non-linearity.

HTH,
Maarten

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting adress:
Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

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