Hello,

I'd like to know if predicted values from  a Poisson mixed model require
back-transformation to get the 'real' predicted values or if this is
done automatically? I assume that the predicted values are already
back-transformed since my results are similar to the annual means.

My model for estimating bird trends in lme4 is as such:

lme3<-lmer(Abundance ~ Year +  (1|Observer) + (1|Site/Station),
data=SWTH, family = poisson(link=log))

I then took the coefficients from the mixed model and used them in a GLM
to derive the predicted values.
dd <-fixef(lme3) # gives coefficients
                      
lme_glmDEY <- glm(Abundance ~ Year, data=SWTH, family = poisson(link =
log)) # for poisson distribution
lme_glmDEY$coefficients <- dd  

# create a data set of predicted values
pred <- as.data.frame(predict(lme_glmDEY, SWTH , "response", se.fit=T))
pred_val <- as.data.frame(cbind(SWTH,pred))
 
So, do I have to perform a back-transformation on the predicted values
(ie., using exp())? 

Thanks,

Kevin

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