Variational Bayes for linear mixed model (random intercept only).

Variational Bayes for linear mixed model (random intercept only).

Usage

vb_lmm_randint(
  X,
  Z,
  y,
  mu_beta,
  sigma_beta,
  mu,
  sigma,
  Aeps = 1,
  Beps = 1,
  Au = 1,
  Bu = 1,
  Bqeps = 1,
  Bqu = 1,
  tol = 1e-08,
  maxiter = 100L,
  verbose = FALSE,
  trace = FALSE
)

Arguments

X

The design matrix

Z

Group design matrix

y

The response vector

mu_beta

The prior mean for beta

sigma_beta

The prior covariance for beta

mu

Initial value for mu

sigma

Initial value for sigma

Aeps

The prior shape for sigma_eps

Beps

The prior scale for sigma_eps

Au

The prior shape for sigma_u

Bu

The prior scale for sigma_u

Bqeps

The intial value for Bqeps

Bqu

The initial value for Bqu

tol

Tolerance level

maxiter

Maximum iterations

verbose

Print trace of the lower bound to console. Default is FALSE.

trace

Print a trace of `mu` to console.

Value

A list containing:

converged

Indicator for algorithm convergence.

elbo

Vector of the ELBO sequence.

mu

The optimised value of mu.

Sigma

The optimised value of Sigma.

Examples

library(nlme)
X <- model.matrix( ~ age + factor(Sex, levels = c("Female", "Male")), data = Orthodont)
Z <- kronecker(diag(1, 27), rep(1, 4))
y <- Orthodont$distance
mu0 <- rep(0, ncol(X))
S0 <- diag(1e8, ncol(X))
mu <- rep(0, ncol(X) + ncol(Z))
S <- diag(1, ncol(X) + ncol(Z))
A <- 1/100
B <- 1/100
fit <- vb_lmm_randint(X, Z, y, mu0, S0, mu, S, A, B, A, B, verbose = TRUE)
#> Iter:   1; ELBO = -312.245477
#> Iter:   2; ELBO = -260.313773
#> Iter:   3; ELBO = -259.935380
#> Iter:   4; ELBO = -259.914549
#> Iter:   5; ELBO = -259.912980
#> Iter:   6; ELBO = -259.912836
#> Iter:   7; ELBO = -259.912821
#> Iter:   8; ELBO = -259.912819
#> Iter:   9; ELBO = -259.912819
#> Iter:  10; ELBO = -259.912819
#> Iter:  11; ELBO = -259.912819