Many thanks for the suggestions.
Do you mean Lognormal and using the standardised observed data (RTs) ? If that’s so, I do not think that’ll work. A Lognormal only takes positive values, but standardised RTs have both negative and positive values (after all, the point of standardising is placing the mean of the distribution at zero). Hence, standardised RTs + Lognormal should result in NaN values in the RT parameter, as shown by a mod.check_test_point():
Out[5]:
alpha_m -0.92
alpha_s_log__ -0.77
alpha_t -5.51
beta_m -0.92
beta_s_log__ -0.77
beta_t -5.51
sigma_log__ -1.06
RT NaN
Name: Log-probability of test_point, dtype: float64
So the sampling would break-down immediately. There’s a whole discussion about the consequences of standardisation as a data transformation procedure, but that’s besides the point. I don’t think any variable would change your model, if the model is though as the structure which holds variables and parameters. But data transformations may change results and thus change inference, thus we change the model (i.e. distributions in the model) to adapt better to those data (if I don’t understand that wrongly). But I guess that’s also besides the point. Back to the suggestion, if you refer to standardising the worry-socre variable, I think that wouldn’t change things much, as the main issue is about using theoretically ‘appropriate’ vs ‘inappropriate’ distributions for the observed data (RTs in this case).
Regarding your second suggestion. If I take the log of the RT variable, the tail of the distribution shifts (goes towards negative), but because RTs are generally skewed (in this case with median ~380ms and SD ~ 310ms), the tail should contain very few negative values. So, in practice, running a StudentT model with log(RT) gives basically the same results as the Lognormal model. I’m not sure whether I follow what you mean by
“…it also doesn’t have the issue of allowing for negative reaction times.”
As far as I understand, a StudentT distribution will always allow for negative values (unless you bound, truncate or fold it). Actually, wouldn’t the point of taking the log of RTs be to have negative values so the StudentT adapts better?
Thanks again.