# Linear mixed effects model structure feedback

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))


Or

m2 <- lmer(abundance ~ TRT*year + (TRT|site) + (period|site/sample)


where sample is the 14 sampling locations within treatment level, and period is the 3 bi-weekly samples within each year.

• Both models seem to encompass valid modelling assumption. More as personal comment, I would not include intercepts especially when looking at the period because there is no "intecept" as such case. Just to clarify this: do you have 2 distinct treatments levels per site plus no treatment at all, or a treatment\no treatment design? Don't be taken aside if the site-specific variation due to treatment comes out very low, you might encounter issues of identifiability between the site and site/sample random effects. – usεr11852 says Reinstate Monic Mar 29 '13 at 23:55
• This a treatment/no treatment design. The t values for m1 were pretty high for TRT, ~5-8 depending upon the abundance measure used as the response variable, and I just wanted feedback on whether we were handling the pseudoreplication in time and space correctly. The t values are lower for m2. We want to show a treatment effect, but I want to make sure the t values are not inflated due to incorrect handling of the pseudoreplication. – user23690 Mar 31 '13 at 1:47