# Compare the factor A between levels of factor B when an interaction exists, using emmeans

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?