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I am new to Generalized additive mixed models (GAMM) and I'm trying to model a behavioral response variable (time spent shading eggs by a nesting bird in minutes timeCS) in relation to several predictor variables: maximum temperature (maxT), species (categorical), the day of the year (jdate) and the age of the nest (ca). My data was based on repeated observations at several nests of shorebirds.

I have three random effects: nest id (nest), location (rm) and year. Nest is nested within rm and year; while rm and year are crossed.

Since I have multiple random effects, I plan to use gamm4 in R as my software package to conduct the GAMM. So far I believe the correct code to run this analysis with my data is

 gamm4 <- (timeCS~s(maxT)+ species + s(jdate) + s(ca), 
           random=~(1|year)+(1|rm)+(1|rm:nest)+(1|year:nest), 
           data=Dataset, family=gaussian(link ="identity"))

Is this correct? Should I specify smooth terms for my predictor variables? Can I run model selection based on AICc on GAMM?

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