Question regarding parameters in hierarchical model

[SaschaFroelich]

My apologies if this is not HSSM-specific. I have looked at the bambi-notebooks, but so far, I didn't find the answer to this question.

I formulate my model hierarchically for 10 participants, and a factor jokercondition, which has 3 levels (A, B, and C). Then for the model parameters I include something like this, in the case of v:

include=[
    {
        "name": "v",
        "formula": "v ~ 1 + jokercondition + (0 + jokercondition|participant_id)",
        "prior": {
            "jokercondition|participant_id": {"name": "Normal", 
                                  "mu": {"name": "Normal", "mu": 2., "sigma": 1.},
                                  "sigma": {"name": "HalfNormal", "sigma": .3}},
            "Intercept": {"name": "Normal", "mu": 1, "sigma": 2, "initval": 1},
        },
        "link": "identity",
    }

So then there are the following output parameters relating to v:

v_Intercept
v_jokercondition[B]
v_jokercondition[C]
v_jokercondition|participant_id[A, 1.0]
v_jokercondition|participant_id[A, 2.0]
v_jokercondition|participant_id[A, 3.0]
v_jokercondition|participant_id[A, 4.0]
v_jokercondition|participant_id[A, 5.0]
v_jokercondition|participant_id[A, 6.0]
v_jokercondition|participant_id[A, 7.0]
v_jokercondition|participant_id[A, 8.0]
v_jokercondition|participant_id[A, 9.0]
v_jokercondition|participant_id[A, 10.0]
v_jokercondition|participant_id[B, 1.0]
v_jokercondition|participant_id[B, 2.0]
v_jokercondition|participant_id[B, 3.0]
v_jokercondition|participant_id[B, 4.0]
v_jokercondition|participant_id[B, 5.0]
v_jokercondition|participant_id[B, 6.0]
v_jokercondition|participant_id[B, 7.0]
v_jokercondition|participant_id[B, 8.0]
v_jokercondition|participant_id[B, 9.0]
v_jokercondition|participant_id[B, 10.0]
v_jokercondition|participant_id[C, 1.0]
v_jokercondition|participant_id[C, 2.0]
v_jokercondition|participant_id[C, 3.0]
v_jokercondition|participant_id[C, 4.0]
v_jokercondition|participant_id[C, 5.0]
v_jokercondition|participant_id[C, 6.0]
v_jokercondition|participant_id[C, 7.0]
v_jokercondition|participant_id[C, 8.0]
v_jokercondition|participant_id[C, 9.0]
v_jokercondition|participant_id[C, 10.0]
v_jokercondition|participant_id_mu[A]
v_jokercondition|participant_id_mu[B]
v_jokercondition|participant_id_mu[C]
v_jokercondition|participant_id_sigma[A]
v_jokercondition|participant_id_sigma[B]
v_jokercondition|participant_id_sigma[C]

If I interpret this correctly, the level A of the factor jokercondition on the subject-level is taken into v_Intercept. So is then v_jokercondition|participant_id_mu[A] the mean of the group-level distribution of v_Intercept? If not, how do these outputs have to be interpreted?

Best,
Sascha

[frankmj]

You probably want instead to do v ~ 1 + jokercondition + (1 + jokercondition|participant_id) That way you will also have subject specific intercepts (which will be the values for the reference condition A). And then v_intercept will be the mean of the group in that condition, and the mu’s of the other conditions will be group distributions of within subject differences relative to that

…

On Fri, Aug 9, 2024 at 8:20 AM Sascha Frölich ***@***.***> wrote: My apologies if this is not HSSM-specific. I have looked at the bambi-notebooks <https://bambinos.github.io/bambi/notebooks>, but so far, I didn't find the answer to this question. I formulate my model hierarchically for 10 participants, and a factor jokercondition, which has 3 levels (A, B, and C). Then for the model parameters I include something like this, in the case of v: include=[ { "name": "v", "formula": "v ~ 1 + jokercondition + (0 + jokercondition|participant_id)", "prior": { "jokercondition|participant_id": {"name": "Normal", "mu": {"name": "Normal", "mu": 2., "sigma": 1.}, "sigma": {"name": "HalfNormal", "sigma": .3}}, "Intercept": {"name": "Normal", "mu": 1, "sigma": 2, "initval": 1}, }, "link": "identity", } So then there are the following output parameters relating to v: v_Intercept v_jokercondition[B] v_jokercondition[C] v_jokercondition|participant_id[A, 1.0] v_jokercondition|participant_id[A, 2.0] v_jokercondition|participant_id[A, 3.0] v_jokercondition|participant_id[A, 4.0] v_jokercondition|participant_id[A, 5.0] v_jokercondition|participant_id[A, 6.0] v_jokercondition|participant_id[A, 7.0] v_jokercondition|participant_id[A, 8.0] v_jokercondition|participant_id[A, 9.0] v_jokercondition|participant_id[A, 10.0] v_jokercondition|participant_id[B, 1.0] v_jokercondition|participant_id[B, 2.0] v_jokercondition|participant_id[B, 3.0] v_jokercondition|participant_id[B, 4.0] v_jokercondition|participant_id[B, 5.0] v_jokercondition|participant_id[B, 6.0] v_jokercondition|participant_id[B, 7.0] v_jokercondition|participant_id[B, 8.0] v_jokercondition|participant_id[B, 9.0] v_jokercondition|participant_id[B, 10.0] v_jokercondition|participant_id[C, 1.0] v_jokercondition|participant_id[C, 2.0] v_jokercondition|participant_id[C, 3.0] v_jokercondition|participant_id[C, 4.0] v_jokercondition|participant_id[C, 5.0] v_jokercondition|participant_id[C, 6.0] v_jokercondition|participant_id[C, 7.0] v_jokercondition|participant_id[C, 8.0] v_jokercondition|participant_id[C, 9.0] v_jokercondition|participant_id[C, 10.0] v_jokercondition|participant_id_mu[A] v_jokercondition|participant_id_mu[B] v_jokercondition|participant_id_mu[C] v_jokercondition|participant_id_sigma[A] v_jokercondition|participant_id_sigma[B] v_jokercondition|participant_id_sigma[C] If I interpret this correctly, the level A of the factor jokercondition on the subject-level is taken into v_Intercept. So is then v_jokercondition|participant_id_mu[A] the mean of the group-level distribution of v_Intercept? If not, how do these outputs have to be interpreted? Best, Sascha — Reply to this email directly, view it on GitHub <#541>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAG7TFAEHWUDJWYO6EZM3C3ZQSX2BAVCNFSM6AAAAABMILTUT2VHI2DSMVQWIX3LMV43ASLTON2WKOZSGQ2TONZZHAYTSNY> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[digicosmos86]

I'll move this general question to discussions so we can use issues to track bugs and feature requests