How to use multi-level model with predictors using ulam?

[HidekiOkabayashi]

I am very interested in your book, "Statistical Rethinking."
I would like to use ulam for multi-level model with several predictors.

I construct a multi-level model for 420 couples’ marital satisfaction.

There are 420 couples (husband and wife).
Each of two individuals within a couple responded to 3 items of marital satisfaction.
So, 420 couples x 2 (husband and wive) x 3 (items) = 2,520 rows of data were created.
About gender, husband = -0.5, wife = 0.5.

I referred to a univariate Hierarchical Linear Model for dyads (Sayer & Klute, 2005) and tried to construct a following model.

Marital Satisfaction ij = beta 0j + beta 1j * Gender ij + r ij,
beta 0j = gamma 00 + gamma 01 * Marital Hassle + u 0j

i = 6 = 2 * 3 items
j = 420

In ulam, I wrote a following code.
It worked successfully. But, is this model right?

level 1 linear model for within_dyads variation

mu <- (a_bar+v[CoupleID,1]) + (b_bar+v[CoupleID,2])*gender,

level 2 linear model for between-dyads variation

a_bar <- aa_bar + bMH*M_hassle,

Although I thought “a_bar” as a dependent variable of level 2 linear model. If so, it should be a vector [420]. But it was a vector [2520].
But, each consecutive 6 values are the same. So, actually there is 2520 / 6 = 420.

Is this model right or not? I am confused.
I attached the full model and data structure as follows.
If not, would you please tell me how to set multi-level model using ulam?

Thank you very much in advance.

< literature >
Sayer, A.G., & Klute, M. M. (2005). Analyzing Couples and Families: Multilevel Methods. In V. L. Bengston, A. C., Acock, K. R., Allen, Dilworth-Anderson, P., & Klein, D.M. (Eds.) Sourcebook of family theory and research (pp. 289-313).

full model description

multi-level model

m001nc <- ulam(
alist(
# likelihood
M_sat ~ dnorm(mu, sigma),
sigma ~ dexp(1),

# level 1 linear model for within_dyads variation
mu <- (a_bar+v[CoupleID,1]) + (b_bar+v[CoupleID,2])*gender,
  transpars> matrix[420,2]: v <-
  compose_noncentered(sigma_v, L_Rho_v, z_v),
matrix[2, 420]: z_v ~ dnorm(0,1),
vector[2]: sigma_v ~ dexp(1),
cholesky_factor_corr[2]: L_Rho_v ~ lkj_corr_cholesky(2),

# level 2 linear model for between-dyads variation
a_bar <- aa_bar + bMH*M_hassle,

# priors
aa_bar ~ dnorm(0,1),
bMH    ~ dnorm(0,0.5),
b_bar  ~ dnorm(0,0.5),

# generated quantities
gq> matrix[2,2]: Rho_v  <<- Chol_to_Corr(L_Rho_v),
gq> vector[420]: b <<- b_bar+v[,2]
), data=dat_list, chains=4, cores=4, log_lik=T)

data list

dat_list <- list(
CountryID = d5$Country,
CoupleID = d5$CoupleID,
TypeID = d5$Type,
gender = d5$gender,
H_Age = standardize(d5$H_Age),
W_Age = standardize(d5$W_Age),
H_health = standardize(d5$H_health),
W_health = standardize(d5$W_health),
income = standardize(d5$income),
M_hassle = standardize(d5$M_hassle),
item = d5$item,
M_sat = standardize(d5$M_sat)
)

data structure

List of 12
$ CountryID: int [1:2520] 1 1 1 1 1 1 1 1 1 1 ...
$ CoupleID : int [1:2520] 1 1 1 1 1 1 2 2 2 2 ...
$ TypeID : int [1:2520] 4 4 4 4 4 4 5 5 5 5 ...
$ gender : num [1:2520] -0.5 -0.5 -0.5 0.5 0.5 0.5 -0.5 -0.5 -0.5 0.5 ...
$ H_Age : num [1:2520] 0.852 0.852 0.852 0.852 0.852 ...
$ W_Age : num [1:2520] 0.558 0.558 0.558 0.558 0.558 ...
$ H_health : num [1:2520] -1.36 -1.36 -1.36 -1.36 -1.36 ...
$ W_health : num [1:2520] 1.95 1.95 1.95 1.95 1.95 ...
$ income : num [1:2520] 1.61 1.61 1.61 1.61 1.61 ...
$ M_hassle : num [1:2520] 0.719 0.719 0.719 0.719 0.719 ...
$ item : int [1:2520] 1 2 3 1 2 3 1 2 3 1 ...
$ M_sat : num [1:2520] -0.195 1.004 1.004 1.004 1.004 ...