I'm analysing correct response rate and response time of participants on a task. For the first one, I ran a mixed effect logistic regression:

glmer (CR ~ Group * Var2 * Var3 + NDG + (1 |ID),
                     data = df,
                     family = binomial (link = "logit")) 

When I have an interaction effect, I investigate simple effects and I also plot my data, for instance, box plot/bar plot for correct response rate according to Group and Var2 (and I put the little "*" for significant effects). However, the plot of correct response rate does not represent well my model outcomes (log odds). And for the interaction it can be rather misleading (as explained in this blog post).

What is the best way to represent my data in this case?

For the second one, I ran a GLMM with inverse gaussian distribution (after having read Lo and Andrews, 2015):

glmer (RT ~ GroupC * Var2 * Var3 + (1|ID),
                    data = TSTdf1,
                    family = inverse.gaussian (link = "identity"))

I this case, for an interaction effect I plot mean RT (with se) and graphically represent significant effect with "*". But again, my model is not comparing means (and means are not the best way to represent RT distribution). I was thinking about plotting flat violin which is better to my mind but I'm not sure it will be as easy to put my stars on it (with ggsignif). What would you recommend in this case?

A visual example would be appreciated (maybe with paper using this kind of visualisation) and any suggestion would be appreciated :-)))

(My supervisors like "*"... so that's why I need to put them on my plots)



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