Modeling bimodal duration data with categorical predictors with brms

Modeling
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1

Hello!

I have collected some eye-tracking data within a three-factorial experiment design. My response variable is the start time of looking at some object (called as Gaze Onset) during the task of picture description. My Gaze Onsets follow a bimodal distribution for which I actually have found an explanatory variable (Gaze Label, the name of the object my participants look at the picture, see the Figure).

GazeOnset_distributions
GazeOnset_distributions2700×1500 68.8 KB

My problem is that when I specify this explanatory variable as a co-variate in my Bayesian regression model, the sampler still does not detect the two modes of the response variable (see the posterior predictive check below).

GazeOnset_posteriorPredictiveCheck
GazeOnset_posteriorPredictiveCheck2700×1500 16.1 KB

Looking into different examples of models of bimodal distributions (e.g. https://psyarxiv.com/cdxv3/), the inclusion of an explanatory variable of the two modes should take care of the bimodal distribution in the sampler. I am new to Bayesian data analysis. Therefore, I am still modelling my data with unrestricted priors. Here’s the specification of my model.

myBrmsModel = brm(GazeOnset ~ identity*doubleActor*load +
                    GazeLabel +
                    (1+identity*doubleActor*load|participantID) +
                    (1+identity*doubleActor*load|item) +
                    (1|trialIndex),
                  family = shifted_lognormal(),
                  data = test)

I have already implemented the shifted_lognormal family suggested in this post: Regression Models for Duration Data. The mixture family did not work for my data as the convergence got really bad. Would you have any more ideas how could I capture the two modes of my response variable, please? Since I’m not a programming queen, I would appreciate the bits and pieces of concrete code.

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Hi guys,

Meanwhile I took the courage and set some uninformative or regularizing priors and switched to the mixture modelling:

mix <- mixture(exgaussian, exgaussian)
prior <- c(
  prior(normal(0, 1000), Intercept, dpar = mu1),
  prior(normal(1000, 1000), Intercept, dpar = mu2))

and I defined a simpler model with my controlled factors only:

myBrmsModel <- brm(bf(GazeOnset ~ identity*doubleActor*load),
                   data = test,
                   family = mix,
                   prior = prior,
                   control = list(adapt_delta = 0.99),
                   init = 0,
                   iter = 5000)

With these changes, I indeed got brms to sample from a bimodal posterior:

GazeOnset_posteriorPredictiveCheck_updated
GazeOnset_posteriorPredictiveCheck_updated2700×1500 43 KB

But now I have another burning question. Could you help me to add in the random effects structure together with the priors? I have uploaded the subset of my data this time as well.

The desired random effects structure:

(1+identity*doubleActor*load|participantID) +
                        (1+identity*doubleActor*load|item)+
                         (1|trialIndex)

The data:
22-07-26_gazeOnsetsSubset.txt (60.8 KB)

I’m indeed a newbie here and would be extremely thankful for your help!

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