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rmodelanovatukey

Do I have to make another model to perform a Tukey test when the anova shows that only the factors are significant and not their interaction?

I'm doing repeated measurements ANOVA in R with libraries:

library(ordinal)
library(car)
library(RVAideMemoire)

I have two groups: months and distance and the dependent variable is CO2:

distance month CO2

0 metres july 234

I've made a clmm model for CO2 explained by distance, month and interaction betwee month and distance:

model_CO2 = clmm(CO2.f ~ month + distance + month:distance + (1|nest),
             data = field_data,
             threshold = "equidistant")

The results show that both month and distance are significan, but not there interaction. Now, I want to perform a Tukey test with this information, so my idea is to perform a Tukey test for each factor separatedly.

My question is:

Do I have to make another model, where I separate each factor? Or can I just perform the Tukey test using the model I created but only considering one factor?

Example:

Using the initial model:

library(emmeans)
library(lsmeans)

Tmonth = lsmeans(model_CO2,
        ~ month)
multcomp::cld(Tmonth,
              alpha = 0.05,
              Letters = letters,
              adjust = "tukey")

Creating a new model only for month and then performing a Tukey test:

model_CO2m = clmm(CO2.f ~ month + (1|nest),
                 data = field_data,
                 threshold = "equidistant")
Tmonth = lsmeans(model_CO2m,
        ~ month)
multcomp::cld(Tmonth,
              alpha = 0.05,
              Letters = letters,
              adjust = "tukey")

Thanks in advance!

Solution

  • I think some people would recommend that you do. But no, you don't have to, in that the estimated marginal means that you are comparing are well-defined; the interaction effects are just averaged over.

    I would recommend that you plot the estimates for the factor combinations, though -- using emmip() for example -- so that you clearly understand what the estimates are that are being averaged.

    Note

    I just noticed in the question that you took a factor completely out of the model. I definitely recommend against doing that. Each factor contributes a significant main effect, so they both belong in the model. If you are to consider a reduced model here, only consider the one with both main effects but no interaction.