I have a GAM /regression model which is originally defined as:
log10(Y)~s(log10(X1))+s(log10(X2))+s(log10(X3)) #using R mgcv
The response needs to be back transformed. As simply doing
exp(Y) would give a biased result, I do the bias correction via:
Now it seems that for the data on log10-log10 the assumption of a gaussian error is not correct and I still have very heavy tails. The scat() family from mgcv (https://rdrr.io/cran/mgcv/man/scat.html) provides optimal qqplots for the model. It is based on the t-distribution.
How would now a bias correction look like for a t-distribution ? Is there one at all?
P.S. I also tried to model:
Y~s(log10(X1))+s(log10(X2))+s(log10(X3)) #using R gamlss and a lognormal error distribution Y~s(log10(X1))+s(log10(X2))+s(log10(X3)) #using R mgcv and a Gamma error distribution with log link
none of those gave as good models i.e. qqplots as the scat family on log10(Y) so how would a bias correction for scat() i.e. the t-distribution look like?