Reaction time Gaussian and Lognormal distribution two different results

Hi, I have a problem with modeling reaction time data in brms. I modeled a reaction time on a continuous variable for three conditions. I used the default brms priors but set two different kinds of families. In one model, I set family = lognormal(), in a second model I set the family = gaussian(). I then plotted the estimated regressions against the averaged raw data. I noticed that the model with the lognormal family underestimates the intercepts (i.e., the regression lines fall below the mean value of the averaged raw data).
In contrast, the model with the gaussian family performs a correct estimation. I thought the lognormal family was the right one for my reaction time data since it excludes values below 0 (which are unlikely in reaction time data) and has a right-skewed distribution.

Any thoughts on why this could happen?

P.S. I’ve transformed the intercepts and slopes of the lognormal model through the exp() function so that to be able to plot them against the raw data.

RT_Regression_gaussian.pdf (95.2 KB)
RT_Regression_lognormal.pdf (95.6 KB)

Without your code it’s difficult to say what might be happening, but note that if Y is lognormally distributed such that log(Y) = X is normally distributed, then exp(X) is the median of Y, not the mean. Thus, your regression lines are showing the median of your reaction time data, not the mean. See here for formulas to get the mean of Y.


That make sense! Many thanks!