I used brms to implement a 2-level hierarchical logistic regression model.
I would like to describe the model details in my paper:
- Please confirm if the model specification and math description match
- What is the group-level design matrix Z? An example would make it clear.
The model specification is as follows:
fit <- brm(data = data, family = bernoulli, formula = y ~ 1 + X1 + X2 + (1 + X1 + X2 || group), prior = c(prior(normal(0, 5), class = Intercept), prior(cauchy(0, 5), class = sd), prior(normal(0, 5), class = b)) )
The model (math) description that I have so far:
\\ 2-level hierarchical logistic regression \\ i denotes the sample index \\ y is the binary outcome \\ group(i) denotes the group to which the sample i belongs \\ X[i] is the design matrix for sample i \\ ??? Z[group(i)] is the group-level design matrix ??? y[i] ~ Bernoulli(p[i]) p[i] = inverseLogit(beta0 + beta*X[i] + u0[group(i)] + u[group(i)]*Z[group(i)]) \\population-level intercept and coefficients \\ k denotes the covariate index beta0 ~ Normal(0,5) beta[k] ~ Normal(0,5) \\ group-level intercept and coefficients \\ j denotes the group index, k denotes the covariate index u0[j] ~ Normal(0, sd^2) u[j][k] ~ Normal(0, sd^2) \\ group-level standard deviation sd ~ HalfCauchy(0, 5)
Your help is much appreciated.
- Operating System: Windows 10
- brms Version: 2.10.0