I am modeling wheat yields over time at several locations using mixed models in R (lmer function). My selected model is as follows:
M0<-lmer(Yield ~ Year2 + SYST + (1|LOCATION) + (0 + Year2|LOCATION), data = Wheat)
where SYST is a categorical treatment with two levels. The summary of the random and fixed effect output is:
Random effects: Groups Name Variance Std.Dev. LOCATION (Intercept) 0.05587 0.2364 LOCATION.1 Year2 0.02277 0.1509 Residual 0.04195 0.2048 Number of obs: 2904, groups: LOCATION, 6 Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) 0.46254 0.10934 5.10000 4.230 0.00801 ** Year2 -0.11881 0.07365 5.50000 -1.613 0.16267 SYSTCP -0.10589 0.01797 2889.80000 -5.893 4.23e-09 *** Year2:SYSTCP 0.04626 0.02989 2889.90000 1.548 0.12182
Now, in simple linear models the common rule of thumb is to "ignore" significant main effects of a treatment if there are significant interaction effects present. In that case we would look at treatment effects for different levels of the other term in the interaction.
Question 1: Is the random effect of slope for Year2 at each LOCATION analogous to a fixed interaction effect of Year2:LOCATION?
Question 2: If the answer to the first question is "yes", then should I "ignore" the fixed main effect of Year2 and explore the possibility significance within individual LOCATIONS?
Question 3: This is what I am ultimately trying to understand...based on my results, can I collapse the data across Years and simply present wheat yields at different Locations and treatments?
Here is a graph of the data by Year, SYST, and LOCATION. As you can see it does look like at least two locations have significant slopes (DO & LU).