# What are fitted.values in Cumulative Link Mixed Models (CLMM) in R?

I am estimating a Cumulative Link Mixed Model (CLMM) in R on a dataset similar to the following:

Likert Age Income Location
Uncomfortable 65 High East
Comfortable 42 Low West
Comfortable 68 Low Center
Neutral 75 High East
... ... ... ...

The code I use to estimate the model is:

m = clmm(Likert ~ 1 + Age + Income + (1|Location), data = d,
threshold = "flexible")


My question is what do the fitted.values represent in this model? If I run fitted.values(m) a numeric list with values between 0 and 1 are outputted. How can I interpret these values?

The Ordinal package documentation defines fitted.values as

fitted values evaluated with the random effects at their conditional modes

but I don't understand what this really represents about my dependent variable.

• Apparently, fitted.values() of a polr object outputs a matrix, with a column for each level of the response. I don't know why CLMM only outputs a list! Sep 17, 2021 at 0:01
• As an aside what about location makes you treat it as a random effect? Oct 27, 2023 at 12:38

Looking through the vignette for the clm function (assuming clmm works similarly), clm_article.pdf, it looks like it's returning the predicted probability of the observed outcome level for each observation. As mentioned by Amir H, polr from MASS returns a matrix with the predicted probabilities of each possible outcome level (not just the observed level for that row).
• This predicted probably can be used for residuals for diagnostic purposes as in the Li-Shepherd residuals. But the polr output is more useful in practice since it provides the matrix of all predicted probabilities, i.e., you get as columns all values of $y$ with $\Pr(Y=y)$. Oct 27, 2023 at 12:37