LN_hierarchical {BayesLN}

Bayesian estimation of a log - normal hierarchical model

Description

Function that estimates a log-normal linear mixed model with GIG priors on the variance components, in order to assure the existence of the posterior moments of key functionals in the original data scale like conditioned means or the posterior predictive distribution.

Usage

LN_hierarchical(
  formula_lme,
  data_lme,
  y_transf = TRUE,
  functional = c("Subject", "Marginal", "PostPredictive"),
  data_pred = NULL,
  order_moment = 2,
  nsamp = 10000,
  par_tau = NULL,
  par_sigma = NULL,
  var_pri_beta = 10000,
  inits = list(NULL),
  verbose = TRUE,
  burnin = 0.1 * nsamp,
  n_thin = 1
)

Arguments

formula_lme

A two-sided linear formula object describing both the fixed-effects and random-effects part of the model is required. For details see lmer.

data_lme

Optional data frame containing the variables named in formula_lme.

y_transf

Logical. If TRUE, the response variable is assumed already as log-transformed.

functional

Functionals of interest: "Subject" for subject-specific conditional mean, "Marginal" for the overall expectation and "PostPredictive" for the posterior predictive distribution.

data_pred

Data frame with the covariate patterns of interest for prediction. All the covariates present in the data_lme object must be included. If NULL the design matrix of the model is used.

order_moment

Order of the posterior moments that are required to be finite.

nsamp

Number of Monte Carlo iterations.

par_tau

List of vectors defining the triplets of hyperparaemters for each random effect variance (as many vectors as the number of specified random effects variances).

par_sigma

Vector containing the tiplet of hyperparameters for the prior of the data variance.

var_pri_beta

Prior variance for the model coefficients.

inits

List of object for initializing the chains. Objects with compatible dimensions must be named with beta, sigma2 and tau2.

verbose

Logical. If FALSE, the messages from the Gibbs sampler are not shown.

burnin

Number of iterations to consider as burn-in.

n_thin

Number of thinning observations.

Details

The function allows to estimate a log-normal linear mixed model through a Gibbs sampler. The model equation is specified as in lmer model and the target functionals to estimate need to be declared. A weakly informative prior setting is automatically assumed, always keeping the finiteness of the posterior moments of the target functionals.

Value

The output list provided is composed of three parts. The object $par_prior contains the parameters fixed for the variance components priors. The object $samples contains the posterior samples for all the paramters. They are returned as a mcmc object and they can be analysed trough the functions contained in the coda package in order to check for the convergence of the algorithm. Finally, in $summaries an overview of the posteriors of the model parameters and of the target functionals is provided.

Examples

library(BayesLN)
# Load the dataset included in the package
data("laminators")
data_pred_new <- data.frame(Worker = unique(laminators$Worker))
Mod_est<-LN_hierarchical(formula_lme = log_Y~(1|Worker),
                         data_lme = laminators,
                         data_pred = data_pred_new,
                         functional = c("Subject","Marginal"),
                         order_moment = 2, nsamp = 50000, burnin = 10000)