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I have a model with the following formula:

percent_discoloration ~ cv * year + zone_line

where percent_discoloration is my response (a plant disease), cv is the cultivar (18 different levels), year (two years) and zone_line is a binary variable.

I'm trying to compare the different level of cultivars (cv) to check which one has lower or higher precited mean diseases.

I have all the cv levels replicated for each year, as you can see in the contingency table:

                  year
cv                 2012 2013
  CPLRC5007          40   30
  CPLRC5663          40   40
  DK4866             40   40
  DT97-4290          40   40
  Exp1_Stine39LA02   40   40
  Exp2_XC3810        40   40
  Jack               40   40
  JTN-4307           40   29
  JTN-5208           40   40
  JTN-5308           40   39
  K07-1544           40   40
  LS980358           40   39
  MorsoyRT5388N      40   40
  NKBrandS39-A3      40   39
  Osage              40   40
  Pharaoh            40   40
  R01581F            40   40
  Spencer            40   40

As cv is interacting with year, I created adjusted means splitting by year as follows:

emm <- emmeans(mod, specs = ~cv | year, type = 'response')

In this way, I have two tables: one for year=2012 and another for year=2013.
Here are the omitted tables:

year = 2012:
 cv               response     SE  df asymp.LCL asymp.UCL
...
...
 Spencer            0.2567 0.0253 Inf    0.2103    0.3093

year = 2013:
 cv               response     SE  df asymp.LCL asymp.UCL
...
...
 Spencer            0.0736 0.0116 Inf    0.0538    0.0999

So within the years, I can compare which cultivars were better or worse.

The question is: Can I compare a cultivar between years?
For example, is it valid to compare cv=Spencer between 2012 and 2013 and conclude that this cultivar had a higher predicted mean disease in 2013 than in 2012?

I saw one answer (here) and was confused about whether is the same case as mine.
Following the answer above, we have:

emm_int <- emmeans(mod, ~cv * year, type = 'response')

This produces the following omitted table:

cv               year response     SE  df asymp.LCL asymp.UCL
 ...
 ...
 Spencer          2012   0.2567 0.0253 Inf    0.2103    0.3093
 ...
 ...
 Spencer          2013   0.0736 0.0116 Inf    0.0538    0.0999

In this way, I have the two estimates for cv=Spencer. Is that a valid approach to compare between years?

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