Group and Individual Parameters in Regression

[JoeSu112]

Hi all, @frankmj, I am now trying to transition my data from HDDM to HSSM. I've asked about the interpretation of group- and subject-level parameters for `a ~ 1 + (1|subject) in the model (#345). However, I have new problems on the interpretation of group- and subject-level parameters in regression:

I put v ~ 1 + (beta1|subject) + (beta2|subject) + (beta3|subject) in the model, so that the drift rate is a combination of the intercept, beta1, beta2 and beta3. It's a bit different from above. The result table is as followed:

Header	Mean
v_Intercept	0.09406
v_1｜subject[1]	0.09397
v_1｜subject[2]	-0.03487
v_beta1｜subject[1]	0.29647
v_beta1｜subject[2]	0.21175
v_beta2｜subject[1]	0.22109
v_beta2｜subject[2]	0.08195
v_beta3｜subject[1]	-0.18794
v_beta3｜subject[2]	0.55229

There are v_Intercept, v_1｜subject[i], v_beta1｜subject[i], v_beta1｜subject[i], v_beta1｜subject[i] in the table. And I am wondering how I can get group and individual parameters of the intercept, beta1, beta2 and beta3.
Thanks for any help!!!

[gpagnier]

Hi,
There's a tutorial in the works that will address these questions but in the meantime I'll do my best to answer. When creating these models its generally a good idea to plot the graph of the model using graph() to see exactly what group/individual parameters you're asking the model to fit. If it's truly hierarchical, you can see this with graph() where there should be a mean and std (sigma) for the individual parameters.
In the equation you posted, it looks like you're only asking for a group effect of the intercept (represented by v_intercept). v_1|subject[1] represents the individual offset for subject[1] so the individual intercept for subject 1 in the example above would be v_Intercept + v_1|subject[1]. To get for the full group and individual effects for beta1 and beta2 you should define your regression equation to be:
v ~ 1 + beta1 + beta2 + (1|subject) + (beta1|subject) + (beta2|subject).
If you set hierarchical to True, HSSM will automatically turn any unspecified parameter into a regression with the terms 1 + (1|participant_id) . Remember that if you use this, you need to have a column denoting participant ids called 'participant_id'.