[R] multiplicative error
David Winsemius
dwinsemius at comcast.net
Sun Jul 13 00:00:48 CEST 2014
On Jul 12, 2014, at 4:25 AM, Kevin Kunzmann wrote:
> 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...
I would have imagined that this would do what was described in the beginning:
glm( y ~ x, data=data.frame(x,y), family="quasipoisson")
# family="poisson" would choke on non-integer y.
Link is `log` by default for this family and the model is multiplicative with poisson errors. It's admittedly not exactly log-normal errors, but should be sufficiently similar.
--
David Winsemius
Alameda, CA, USA
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