[R-sig-ME] Changing reference level in clmm() ordinal regression

[Jessie Barker]

I have a couple of questions that I asked on StackExchange and someone
suggested that I ask this mailing list. The post on StackExchange is here (
https://stats.stackexchange.com/questions/304092/changing-reference-level-in-clmm-ordinal-regression-in-r),
but I am summarizing it below:

I’m analyzing data from a questionnaire where participants had to rank
three answers to each question (e.g. 1 = most likely, 3 = least likely).
They had to give a different rank to each answer, so each question has one
answer ranked 1, one ranked 2, and one ranked 3. The set of three answers
is the same for each questions, and there were seven questions.

I want to know whether participants give different ranks to different
answers, and whether that is affected by question. Here's my model:

model1 <- clmm(rank ~ answer + answer:question + (1+answer|participant),
data = mydata)

(I don’t have question as a fixed effect, because for each question
participants had to give a 1, 2 and 3 rank, so question alone does not
affect rank.)

My first question is whether I’ve set up the model correctly, as I don’t
have any experience with ordinal regression. When I look at coef(model1),
all participants seem to have the same intercepts and coefficients for the
different answers, which is not what I thought should happen (I thought I
was setting up a model with random intercepts and random slopes).

My second question is about changing the reference level of question and
answer. When I look at summary(model1), it uses answer a1 and question q1
as the reference levels, so I ran the model again using different answers
and questions as reference levels.

When I run the model again using a different answer as the reference level,
the coefficients for the fixed effects are the same, but the random effects
and threshold coefficients are quite different.
When I run the model using a different question as the reference level, the
coefficients for the fixed effects are quite different, but the random
effects are exactly the same, and the threshold coefficients relatively
similar.

Could someone please help me understand what’s going on here?

Thanks in advance,
Jessie Barker

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