# [R] p-value for non-linear variable in overdispersed glm()

From: <tsnall_at_mappi.helsinki.fi>
Date: Sat 01 Oct 2005 - 01:29:59 EST

Dear all,
I am fitting an nonlinear glm() using optim() by first minimising glm(resp~ var1 + var2, family=binomial, data=data)\$deviance where var1= exp(-a1*dist1), and var2= exp(-a2*dist2), where a1 and a2 are parameters and dist1 and dist2 are independent variables.

Next, I calculate the value of var1 (and var2) by plugging in the value of al1 (and al2) that minimises deviance,
and fit glm(resp~ var1+var2 , family=binomial, data=data) Var1 in this model thus includes two parameters - the standard glm() coefficient and a1. This is (of course) not recognized by drop1().

Usually I extract a rough p-value for var1 in this model by 1-pchisq(scaled deviance,df=2)
This gives the p-value reported by drop1(): 1-pchisq(scaled deviance,df=1)

However, the model that I currently work on is overdispersed, and I have used family=quasibinomial. According to ?anova.glm the F-value should be used in likelihood-ratio tests of models fitted by quasibinomial. Again I want to extract a rough p-value and try the corresponding (I thought) for the overdispersed model:
1-pf(5.1,df1=2, df2=250)
[1] 0.006746671

which is lower than
1-pf(5.1,df1=1, df2=250)
[1] 0.02478842

which I didn't expect.

Could someone please give a clue on how to get the rough p-value for var1 in my overdispersed model?

Thanks!

Cheers,
Tord

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