We are investigating the effects of a treatment (versus untreated control) on insect abundance. The study consists of 5 geographically separated study site replicates. Treatments were applied to 1 ~500 acre area at each location. Insects were collected from 14 randomly selected locations within the treatment area at each site, and were compared to samples collected from 14 randomly selected untreated reference area locations at each site. Samples were collected during 3 biweekly periods each year. So there are 840 observations for the entire study (2 years x 5 sites x 2 treatment levels/site x 14 sampling plots/treatment x 3 sampling periods/year).
We are proposing to analyze these data with linear mixed effects models with treatment and years as the fixed effects, and site/sample location as random effects. Year is included as a fixed effect primarily because there are only 2 levels. I would appreciate feedback on whether either of the following models using lmer in the R lmer4 package are an appropriate starting point for analyzing these data:
m1 <- lmer(abundance ~ TRT*year + (period|site/sample))
m2 <- lmer(abundance ~ TRT*year + (TRT|site) + (period|site/sample)
sample is the 14 sampling locations within treatment level, and
period is the 3 bi-weekly samples within each year.