[R] multiplicative error

Kevin Kunzmann kevinkunzmann at gmx.net
Sat Jul 12 13:25:34 CEST 2014


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!


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