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In my study, participants were presented with descriptions of several acts of interpersonal betrayal and asked if they would want wo find out about the betrayal if they had been the victim of it or if they would prefer to remain deliberately ignorant (Variable name: DI). Additionally, I varied the relationship with the perpetrator between experimental conditions (Condition: friend vs. stranger) and, among other things, measured the emotional costs associated with finding out about the betrayal (Costs).

I then ran a mixed generalized linear model with random effects for participants and scenarios, DI as the criterion, and costs and condition as predictors.

mreg = glmer(DI ~ (1|id)+1|Scenario)+Costs*Condition,
family = binomial('logit'),data=dfgDICg)

I find a significant interaction between condition (stranger) and costs and would like to further explore this interaction. Judging from the plot it seems as if the relationship between costs and DI is less pronounced in the stranger condition. Which post-hoc test would be most appropriate in this case? Do you have suggestions on how to implement it in R?

It would be great to get some feedback on this! Thank you very much in advance.

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If the interaction term is significant, then you already have evidence for a different association between outcome DI and Costs depending on Condition. As you modeled Costs as having a strict linear association with log-odds(DI), the magnitude of the interaction coefficient tells you how much the slope of that association changes between the 2 values of Condition.

Plots of the modeled probability of DI as a function of Costs, with separate curves for the 2 values of Condition, is one good way to illustrate your results. There are several packages for post-modeling analysis that can generate such displays. The emmeans package, for example, allows you to show results in the log-odds or the probability scale, with standard errors and the possibility for multiple-comparison corrections. It only returns results with the random effects set to 0, but that shouldn't be a problem for your application.

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