Logistic regression with block correction for ordinal response

Question

I have a categorical response (ordinal, lets call it A) collected from a complete randomized block design experiment where the explanatory variable is treatment. How do I account for the between block variation? I have found models that do this for dichotomous response variables but my response has >2 levels, treatment is also categorical and has 10 levels and there are 8 separate blocks. Could I hypothetically run a logistic regression and add the separate block factors to account for the variation?

The treatment variable has 10 levels but I could separate them so that I compare them 2 at a time, control vs some treatment. Would it be reasonable to run a GLMM model using treatment as a response? So that level changes in the categorical variable, A, affect the odds of having received treatment or is there some fallacy in this?

Answer 1

Could you not run a LMM or GLMM with block as a random effect? Random effects are often added to control for pseudo-replication.

The testFactors function from the package phia seems appropriate for your post-hoc analysis. "This function is specially indicated for post-hoc analyses of models with factors, to test pairwise comparisons of factor levels..." Package 'phia'

Lets say your treatment levels are 1,2,3,4,5,6,7,8,9, and 10. Try:

library('lme4')
model<-lmer(data=mydata, A~treatment+(1|block))

library('phia')
treat1.vs.treat2 <- list(treatment=c("1", "2"))
testFactors(model, treat1,vs,treat2)
treat2.vs.treat3<-list(treatment=c("2","3"))
testFactors(model, treat2.vs.treat3)

etc...