lmm_improper: Fit a linear mixed model with an improper prior.

In asbates/geblm: Geometrically Ergodic Bayesian Linear Models

Description

Fits a Bayesian linear mixed model with a flat prior on beta and improper gamma prior on the precision lambda for the fixed effects and error term. A standard reference prior for lambda is used by default. The formula syntax is the same as lme4::lmer which is used to obtain the model matrices. Only a singleintercept is supported for the random effects.

Usage

lmm_improper(data, formula, burnin = 5000, iterations = 5000,
  thin = 1, lambda_prior_shape, lambda_prior_rate, start_theta)

Arguments

data	A data frame.
formula	A formula describing the model fit. Passed to lme4::lmer to construct model matrices.
burnin	Number of burn in iterations
iterations	Number of sampling iterations
thin	Number of thinning iterations
lambda_prior_shape	(Optional) Shape parameter for the prior on the precision of the error term and random effects, in that order. Defaults to c(0, -0.5).
lambda_prior_rate	(Optional) Rate parameter for the prior on the precision of the error term and random effects, in that order. Defaults to c(0, 0).
start_theta	(Optional) Starting vector for θ = (β' u')', the concatenation of the fixed and random effects coefficients. Defaults to the frequentist estimate.

Value

A list containing MCMC samples from the posterior distributions of the fixed effects, random effects, and standard deviations for the error term and fixed effects.

@return An object of class geblm containing samples from the posterior distributions of the fixed effects, random effects, and standard deviations of the fixed effects and errors.

Warning

We leave it to the user to ensure only a single intercept is specified in the model formula.

References

Roman, J. C. and Hobert, J. P. (2012). Convergence analysis of the Gibbs sampler for Bayesian general linear mixed models with improper priors. Annals of Statistics, 40 2823–2849.

asbates/geblm documentation built on Nov. 12, 2019, 5:23 p.m.