# [R] degrees of freedom question

Greg Tarpinian sasprog474 at yahoo.com
Thu Aug 23 03:54:49 CEST 2007

```    R2.3, WinXP

Dear all,

I am using the following functions:

f1 = Phi1+(Phi2-Phi1)/(1+exp((log(Phi3)-log(x))/exp(log(Phi4)))
f2 = Phi1+(Phi2-Phi1)/(1+exp((log(Phi3)-log(r)-log(x))/exp(log(Phi4)))

subject to the residual weighting

Var(e[i]) = sigma^2 * abs( E(y) )^(2*Delta)

Here is my question, in steps:

1.  Function f1 is separately fitted to two different datasets
corresponding to two different dose response curves.  These
fits are unweighted.
2.  Function f2 is fitted to the pooled data such that the two
dose response curves are assumed to differ _only_ in log(r).
This fit is also unweighted.
3.  The residuals from #2 are used to estimate an appropriate
sigma^2 and Delta to use in weighting.
4.  The functions described in #1 and #2 are refitted, but this
time weighted using the information gathered in #3.
5.  How many degrees of freedom should be allocated to the
weighted residual sums of squares?  (There are three such
SSE's, one for each individual model, and one for the overall
joint model)