Problem with Linear mixed Model in Split-plot design

Hello all,

I am working on a field project where we are evaluating different fertilizer sources (4) applied at 3 different rates! I designed my experiment as a split-plot design with fertilizer source being my main plot factor and rate being as my sub-plot factor. I wanted to see if there is an effect of fertilizer source, rate, and fertilizersource*rate on plant yield. I created my model but I am not sure if it right. Plus I wanted to see if there is any difference between the blocks (total 4) with fertilizer source and rate.
Can anyone please help me!?

Here is my code for Anova and TukeyHSD:
CISER3<-lme(Yield~Fertilizer+Rate+Fertilizer:Rate, random = ~1|Block/Fertilizer,data = CISER)

test4_HSDpost<-cld(emmeans(CISER3,~Fertilizer:Rate,type ="response"),tukey="adjust")

Please let me know if it is wrong! Again, I want to count on variation at block level with fertilizer and rate.


A reproducible example, called a reprex with a small amount of representative data (which need not be actual data, just in the same form) will help attract more answers.


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