Hi Francesco,

You can fit a multinomial logistic regression for your nominal response. An example on how you can fit this in R is given below.

https://stats.idre.ucla.edu/r/dae/multinomial-logistic-regression/

You can also consider a GEE modeling approach using the gee package in R.

Good luck with your work!

Hello Francesco DʼAmore

https://cran.r-project.org/web/packages/mlogit/ - see vignette "The random parameters (or mixed) logit model"

https://cran.r-project.org/web/packages/gmnl/ - alternative(?)

Maybe you can turn your response into scores and use the Kruskal-Wallis like Scheirer–Ray–Hare test.

Eliana, Anton, and Igor, thank you very much for your replies.

In the past, while doing some searches on this topic, I came across both multinomial logistic regression and generalised estimating equations. However, it is still not clear to me whether these approaches (or any other) actually allow considering my specific case (1 between-subjects factor with 2 levels and 2 within-subjects factors with 4 levels each). In fact, online I could find several presentations of these approaches, but they were rather formal and used relatively simple designs as examples. Can anybody suggest a reference that is focussed on practical applications and uses more complex designs as examples?

Francesco

you can use multiple regression

my best wishes to you

Thank you صلاح الدين عواد الكبيسي