factor_analysis: Runs gibbs sampler for a factor model.

In dcbdan/s525: Implementation of common Bayesian models

Description

The model is as follows:

y_i = Λ η_i + ε_i

ε_i \sim N_p(0, Σ)

where Σ = diag(σ_1^2, ..., σ_p^2).

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 for conditional posteriors.

Usage

factor_analysis <- function(
  Y,
  k,
  niter = 1000,
  shape_psi = 1/2,
  rate_psi = 1/2,
  shape_sigma2 = 1,
  rate_sigma2 = 0.2,
  nonzero_structure = NULL)

Arguments

Y	n by p 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_sigma2	shape parameter for sigma2. Can be a p vector
rate_sigma2	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

sigma	An niter x p matrix of posterior values
eta	An niter x n x k array of posterior values
lambda	An niter x p x k array of posterior values

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