[R] Testing general hypotheses on regression coefficients

[Søren Højsgaard]

AFAICS you are not testing a linear hypothesis (which is of the form Lb=b0 where L is a matrix and b=(a,B1,B2,B3,B3) is the parameter vector).

If, for simplicity, your model is E(y) = a + bx then -a/b is the x-value for which y is zero.

When you turn to estimates then u = -a/b is the ratio of two (typically correlated) normal variables and such a ratio is *not* normal. (Just think of the Cauchy distribution.)

One approach is to calculate the approximate variance of u and then construct a Wald test or similar while hoping for the best. Alternatively one could perhaps try with a parametric bootstrap test. 

Just ideas. Good luck.
Søren




-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Chris
Sent: 6. september 2014 04:17
To: r-help at stat.math.ethz.ch
Subject: [R] Testing general hypotheses on regression coefficients

Hi.

Say I have a model like

y = a + B1*x1 + B2*x2 + B3*x3 + B4*x4 + e

and I want to test

H0: B2/B1 = 0

or

H0: B2/B1=B4/B3

(whatever H1). How can I proceed?

I now about car::linearHypothesis, but I can't figure out a way to do the tests above.

Any hint?

Thanks.

C

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