Initial values for drift diffusion model with continuous predictor

Interfaces brms
1

I have been following Henrik Singmann’s great drift diffusion model tutorial (using brms): http://singmann.org/wiener-model-analysis-with-brms-part-i/

It all works well with categorical predictors (x1:x2:x3, all x’s being categorical), e.g.

formula <- bf(RT | dec(Response) ~ 0 + x1:x2:x3 + (0 + x1:x3|p|SubjectID), 
               bs ~ 0 + x1:x2:x3 + (0 + x1:x3|p|SubjectID), 
               ndt ~  0 + x1:x2:x3,
               bias = 0.5)

However, if I have a numeric predictor (let’s assume linear for now), the model just cannot find valid initial values:

log(0) sampling errors (Log probability evaluates to log(0), i.e. negative infinity.)

I am probably overlooking something basic in how a continuous variable interacts with the x1:x2 notation and failing to account for that when defining initial values.

Here is our reproducible example:

  1. A sample dataset: Dropbox - exp1_subset.csv - Simplify your life
    The dataset is about a categorical perception task (discriminating between “Sendt” and “Tændt”), where the stimulus is along a graded continuum between the two extremes (Step codes for the position on the continuum). ResponseN is the response, RT_target is the RT. We have 2 additional binary categorical predictors (Language, indicating the native language of the participants; and Bias indicating which perception is supported by the context, a sentence in which the stimulus is situated).

  2. A R markdown with the code we used to set up formula, priors and initial values: Dropbox - File Deleted - Simplify your life

2

I don’t have time to look at the exact model and data right now, but possibly the scale of the continuous predictors is too large. Standardizing them might help.

3

thanks! The scale is 0-1, so that should not be an issue. I think what I’m missing is:
i) if we have a y ~ x1:x2 situation with categorical predictors (2 values for simplicity), we basically need 4 initial values.
ii) if we have y ~ x1:x2 situation with 1 categorical predictor and 1 continuous, I am not sure how the initial values structure should look like.

4

I often ask myself the same question. You can find out what model.matrix actually did by investigating the $X_<dpar> elements of the make_standata output.

5

Thanks! It took a while but by looking at this and trying out a wider range of initial values we managed to make it work.

6

Hi, I had the similar problem. If I use the below formula1.1, the brms sampling no problem. However, if use the below formula1.2, the brms can not sampling. In the formula block_name is a categorical predictor, and delta_Vself_Zscore & delta_Vother_Zscore are two continuous predictors.

formula1.1 <- bf(rt | dec(response) ~ 0 + block_name:delta_Vself_Zscore +
                   block_name:delta_Vother_Zscore +
                (0 + block_name:delta_Vother_Zscore|p|subjID), 
               bs ~ 0 + block_name + (0 + block_name|p|subjID), 
               ndt ~ 0 + block_name + (0 + block_name|p|subjID),
               bias ~ 0 + block_name + (0 + block_name|p|subjID))

formula1.2 <- bf(rt | dec(response) ~ 0 + block_name:delta_Vself_Zscore +
                   block_name:delta_Vother_Zscore +
                (0 + block_name:delta_Vself_Zscore  +
                   block_name:delta_Vother_Zscore|p|subjID), 
               bs ~ 0 + block_name + (0 + block_name|p|subjID), 
               ndt ~ 0 + block_name + (0 + block_name|p|subjID),
               bias ~ 0 + block_name + (0 + block_name|p|subjID))

Can you explain in detail how to solve this problem?