Hi all, I would like to report two models I have estimated in brms and am hoping someone here can help me with the equation. I have given it a go but don’t know anyone I could ask directly, so I am hoping for the help of the community. I appreciate that this is quite long though…

**Cross-classified model with students (L1) nested in the cross-classification of teachers (L2) and classrooms (L2)**

Brms model is:

Y ~ 0 + Intercept + V1_cgm + V2_cgm + V3_cwc + V4_cwc + V5_cwc + V6_cwc +V7_cwc + V8_cgm + (0 + Intercept + V1_cgm + V2_cgm + V3_cwc + V4_cwc + V5_cwc + V6_cwc + V7_cwc |p| T1_ID) + (0 + Intercept + V1_cgm + V2_cgm + V3_cwc + V4_cwc + V5_cwc + V6_cwc + V7_cwc |q| C1_ID), family = skew_normal())

Where

V1-V7 are student-level variables (L1), modelled as random effects

V8 is a teacher/classroom level variable (L2)

T1_ID is the teacher unit

C1_ID is the classroom unit

cgm = grand-mean centered

cwc = centered within cluster

This is what I have got:

The formula at Level 1 is

and, at Level 2

**2)** **Cross-classified multiple membership model with students (L1) nested in the cross-classification of teachers (L2) and classrooms (L2), whereby students can belong to multiple teachers and classrooms**

Y ~ 0 + Intercept + V1_cgm + V2_cgm + V3_cgm + (0 + Intercept + V1_cgm + V2_cgm |p| mm(T1_ID, T2_ID, T3_ID, T4_ID, weights = cbind(W_T1, W_T2, W_T3, W_T4))) + (0 + Intercept + V1_cgm + V2_cgm |q| mm(C1_ID, C2_ID, C3_ID, C4_ID, weights = cbind(W_C1, W_C2, W_C3, W_C4))), family = skew_normal())

Where

V1 and V2 are student-level variables (L1), modelled as random effects

V3 is a teacher/classroom level variable (L2)

T1_ID is the teacher unit

C1_ID is the classroom unit

cgm = grand-mean centered

And the equation I have got so far is

The formula at Level 1 is

and, at Level 2

where,

If someone takes the time to look through these, many thanks in advance!

PS. So sorry for the formatting - I gave my best