Hi everyone,

I am fitting cumulative models to analyse ordinal data with #brms. I want to set a region of practical equivalence (ROPE) and see if the highest density interval corresponding to my parameter is inside or outside this ROPE. However I can’t find guidelines for this. Does anyone has experience with this kind of approach (cumulative models + ROPE) ? How should we interpret ordinal regression parameters obtained with brms and what would be a good way to set a ROPE in this context ? @matti @Solomon @paul.buerkner maybe ?

- I would like to specify the rope depending on my variables (simplified example) :

- Predictor → pseudo-continuous transformed as a z-score → range ~ [-2.5 ; 2.5]
- DV → ordinal measure : 9 possibles values (from 1 to 9)

With the following reasoning :

a) range of predictor = 5.

b) smaller observable variation on the DV = 1

c) Smallest Effect size of interest (SESOI) = 1/5 = 0.2

d) SESOI/2 = 0.1 (we keep a safety margin because parameter values between 0.1 and 0.2 could potentially be of interest)

e) ROPE = -0.1, 0.1

However I am not sure of this kind of reasoning with an ordinal model.

- If the solution 1 is not possible, what about “classical” ROPEs ?

From Region of Practical Equivalence (ROPE) we can read :

"Kruschke (2018) suggests that the ROPE could be set, by default, to a range from -0.1 to 0.1 of a standardized parameter (negligible effect size according to Cohen, 1988).

- For linear models (lm) , this can be generalised to:

[−0.1∗SDy,0.1∗SDy]

*-For logistic models , the parameters expressed in log odds ratio can be converted to standardized difference through the formula:

π/√3

(see the effectsize package, resulting in a range of -0.18 to -0.18 . For other models with binary outcome, it is strongly recommended to manually specify the rope argument. Currently, the same default is applied that for logistic models."

I would be tented to choose the second option because of the logistic nature of the ordinal model, but if I read well Bürkner & Vuorre (2019) or Understanding the disc parameter in ordered logit models - #5 by matti / https://groups.google.com/g/brms-users/c/SdXC3T9U9hU, the parameters given by brms for ordinal models are standardised parameters, and then we should choose the first option ?

Thanks a lot !

Brice

ref :

Bürkner, P.-C., & Vuorre, M. (2019). Ordinal Regression Models in Psychology: A Tutorial. *Advances in Methods and Practices in Psychological Science* , *2* (1), 77–101. https://doi.org/10.1177/2515245918823199