In greta: Simple and Scalable Statistical Modelling in R

Random intercept-slope model (with correlated effects)

A hierarchical, Bayesian linear regression model using the iris data, with random intercepts and slopes for each of the three species. The slopes and intercepts for each species are correlated in this example.

# model matrix
modmat <- model.matrix(~ Sepal.Width, iris) 
# index of species
jj <- as.numeric(iris$Species)

M <- ncol(modmat) # number of varying coefficients
N <- max(jj) # number of species

# prior on the standard deviation of the varying coefficient
tau <- exponential(0.5, dim = M)

# prior on the correlation between the varying coefficient
Omega <- lkj_correlation(3, M)

# optimization of the varying coefficient sampling through
# cholesky factorization and whitening
Omega_U <- chol(Omega)
Sigma_U <- sweep(Omega_U, 2, tau, "*")
z <- normal(0, 1, dim = c(N, M)) 
ab <- z %*% Sigma_U # equivalent to: ab ~ multi_normal(0, Sigma_U)

# the linear predictor
mu <- rowSums(ab[jj,] * modmat)

# the residual variance
sigma_e <- cauchy(0, 3, truncation = c(0, Inf))

#model
y <- iris$Sepal.Length
distribution(y) <- normal(mu, sigma_e)