Marginal effect overlaps, unequal variances with random effects

Interfaces brms
1
  • Operating System: Win10 Enterprise 64bit
  • brms Version: 2.9.0

Couple of noob questions about usage of brms:

  1. I would like to know whether predicted points in marginal plots are “significantly” different from each other. Can “marginal_effects” return the precise overlap/difference of posterior distributions instead of just showing credible intervals (e.g., at 95%)? This is illustrated in the Figure 2 taken from “Ordinal models of psychology” paper. If not, how can I compute such overlaps? If overlap is, say below 5%, can we conclude that there is significant statistical marginal difference between groups, does it make sense?
    marginal_differences

  2. Model “fit_sc4” in paper “Ordinal models of psychology” (page 88) is an example of an ordinal model with unequal response variance with formula
    “bf(rating ~ 1 + belief) + lf(disc ~ 0 + belief, cmc = FALSE)”
    If we also include random effects “subject”, would this formula simply become
    “bf(rating ~ 1 + belief + (1|subject)) + lf(disc ~ 0 + belief + (1|subject), cmc = FALSE)”`

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I would avoid the term “significantly” in a Bayesian setting.

  1. You can compare these predictions by creating a small data sets with the conditions you are interested in, pass these to fitted(..., newdata = <your newdata>) and then compute the contrasts of different columns of the output. Be aware that the output will be a 3D array as described in the doc.

  2. Yes.