How can I select a ROPE range for a logistic model based on odds ratios

[a_t]

Thank you for your response, @Solomon! I truly appreciate you and this community, as I am learning Bayesian modeling alone without having anybody near me to ask such questions.

@Solomon

How exactly do you want to express your outcome? As an odds ratio? As a difference in probabilities? As one probability expressed as a percent change relative to another probability? Something else?

My initial idea was as an odds ratio.
By me stating

increases the odds of the outcome value by 20% or more

I intended to express the differences in odds ratio (1.2 times+) compared to a control condition (e.g., no intervention).

I am using the brms code something like as follows:
fit = brm ( outcome ~ intervention + pretest_outcome + (1|participant) + (intervention | item), family = "bernoulli",...)
where intervention was dummy coded as 0 for control and 1 for intervention. outcome is a correct/incorrect response on a cognitive task (e.g., math questions) after the treatment (intervention vs. no intervention). We did the same test for the outcome variable as a pretest beforehand, hence pretest_outcome in the model.

So I maybe should have stated like…?
I want to examine whether the intervention increases/decreases the ODDS of the outcome value (i.e., success/fail rate) 1.2 times or more/less compared to the control condition; if not, the intervention does not make a meaningful difference.

then, setting rope to be:
upper: ln(1.20) = 0.1823215568
lower: ln(0.8) = -0.2231435513
Am I understanding this right?

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Me, for example, I always prefer probability contrasts, which is one probability minus another probability. I believe this is sometimes called a risk difference (though the jargon of “risk” is a poor fit for my discipline). Other folks, however, love those odds ratios.

Thank you for the suggestion. I am wondering if this corresponds to the comments made here (ROPE range specification for binary models)?

@martinmodrak

Change in log-odds is the same multiplying the odds, so if say baseline odds are 1:1 and 11:10 is the maximal odds you consider practically equivalent for a treatment, you can compute the relevant value of the ROPE for the coefficient as \log \left(\frac{\frac{11}{10}}{\frac{1}{1}} \right) = \log(\frac{11}{10}) - \log(1) \simeq 0.095log(111011)=log(1110)−log(1)≃0.095\log \left(\frac{\frac{11}{10}}{\frac{1}{1}} \right) = \log(\frac{11}{10}) - \log(1) \simeq 0.095. Note, however, that this requires speaking about relative risk, which is not always the best target. In other words, you are saying that multiplying the odds by 1.11.11.1 is practically equivalent regardless of the baseline odds, so with the same ROPE, if the baseline odds are 1:100 the practically equivalent range would end at 11:1000.

So, with this approach, we need to know the baseline odds to start with right? In my experiment, I do not know how well the control condition performs on the outcome value beforehand. Even in such a case, can I still use the probability contrasts?