Hi,
I am currently trying to build a regression model for calibration of
HPLC outputs. I decided to use a multiplicative error model:
Y_i = (a*X_i + b)*eps_i
where the eps_i ~ iid N(0, s^2). Now I am having a hard time estimating
my parameters ;) So the idea was to apply log() to both sides:
Z_i = log(Y_i) = log(a*X_i + b) + log(eps_i)
Now the additive errors are lognormally distributed and I could
formulate this as a GLM
Z_i = g^(-1)(a*X_i + b) + iota_i
where iota_i are lognormal and the link function g(x) is exp(x) as
g^(-1) = log. So wouldn't the corresponding call for R have to be
something like:
glm(z ~ x, data=data.frame(x=x, z=log(y)), family=lognormal(link='exp'))
this however is not working (there is no lognormal family and no exp
link function ^^. How do I estimate those parameters? This seems to be a
pretty standard problem to me...
Thanks for your comments!
Kevin
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