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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).

enter image description here

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