[R-sig-ME] Random effect in GAM

[Vaniscotte Amélie]

Dear R users,

I am using the mgcv package in R to model the ratio of damaged culture 
hectares by wild boar in each french department according to some 
environmental covariates(cf data attached). I used a using a Beta 
distribution for the response.

For each department, the damages are estimated in 3 different culture 
types (« Culture »). Also, the department are clustered into landscape 
types (« Cluster »). Since I wanted to get the effect of the Culture 
type and the Landscape, I keep those variables as fixed effects in the 
model.

Also, since we have 5 repetitions in time of the response and of some 
covariates measurement per department and culture type, I put a random 
effect on the Department per Culture type and put the year as fixed 
effect as well.

The model takes the form :

gam_tot <-gam(resp ~ Culture + Cluster:Culture + s(Year,k=4, by=Culture) 
+ s(X1, by=Culture) + s(X2, by=Culture) + s(Depts, bs="re", by=Culture) 
, family=betar(link="logit"),method="REML",data=data,select=FALSE)

Then, I estimated the part of the model explained deviance provided by 
each covariate. For that, I run the model without the given covariate 
(keeping smooth parameters constant between models), and compute the 
difference in deviance between the Full model (with the given covariate) 
and the penalized model (without the given covariate): (Full model 
Deviance – Penalized model Deviance) / Full Model Deviance

 From that, I get a huge proportion of Deviance explained by the random 
effect (Department) of about 30 %, while the others covariates explained 
less than 1 %.

At this point, I have few questions :

     Do you think my model formula is correct regarding my data and 
questions ?

     Is my estimate of explained deviance correct ? In that case, how 
can I explain such a discrepancy between the part of explained deviance 
by random and fixed effects ?

Thanks for your help,

Amélie