factor_analysis_with_regression: Runs gibbs sampler for a factor model with regression on the...

In dcbdan/s525: Implementation of common Bayesian models

Description

The model is as follows:

y_i = α + Λ η_i + ε_i,

η_i = Bx_i + δ_i

ε_i \sim N_p(0, τ^{-1})

δ_i \sim N_k(0, I)

where τ = diag(τ_1, ..., τ_p).

See Joyee Ghosh & David B. Dunson (2009) Default Prior Distributions and Efficient Posterior Computation in Bayesian Factor Analysis, Journal of Computational and Graphical Statistics, 18:2, 306-320, DOI: 10.1198/jcgs.2009.07145.

Usage

factor_analysis_with_regression <- function(
  Y,
  X,
  k,
  niter = 1,
  shape_psi = 1/2,
  rate_psi = 1/2,
  shape_tau = 1,
  rate_tau = 0.2,
  coef_multiplier = 10,
  nonzero_structure = NULL)

Arguments

Y	n by p matrix
X	n by f matrix
k	number of factors
niter	number of iterations for the gibbs sampler to run.
shape_psi	shape parameter for psi. Can be a scalar or a k vector
rate_psi	rate parameter for psi. Can be a k vector
shape_tau	shape parameter for sigma2. Can be a p vector
rate_tau	rate parameter for sigma2. Can be a p vector
nonzero_structure	A boolean p x k matrix. If the i, jth spot is TRUE, then λ_{ij} is free. If the i, jth spot is FALSE, then λ_{ij} is zero. If not set, then a lower triangular matrix is used.

Value

alpha	An niter x p matrix of posterior values
lambda	An niter x p x k array of posterior values
tau	An niter x p matrix of posterior values
eta	An niter x n x k array of posterior values
B	An niter x k x f array of posterior values

dcbdan/s525 documentation built on May 19, 2019, 10:48 p.m.