# Linear mixed model construction validation

I have 6 groups of fish made up of 8 individuals. Each group is tested three times under different treatments. These group level treatments are hungry , satiated and mixed in which half of the individuals were hungry and half satiated. I want to test for the effect of group treatment (3 levels, hungry, satiated and mixed) as well as individual state hungry or satiated. I've run a linear mixed model on just the mixed group treatment where State was the fixed factor and my random factors were Group and Individual ID nested inside Group. My dependent variable is mean_speed.

mHvsS = lmer(mean_speed ~ State + (1|Group) + (1|Group/ID), REML=F,
data=HungryVsSatiated)


but how do appropriately add the Group level treatment (3 factors hungry, satiated and mixed) into the model? Is this correct?

mHvsS=lmer(mean_speed ~ Treatment + State + Treatment:State + (1|Group) + ((1|Group/ID),
REML=F, data=HungryVsSatiated)


Or does State need to be nested within Treatment as a random factor? I probably also have to throw in Day as a random factor, correct?