bayes.anova {bayesanova}

bayes.anova

Description

This function runs a Bayesian analysis of variance (ANOVA) on the data. The Bayesian ANOVA model assumes normally distributed data in all three groups, and conducts inference based on a Gibbs sampler in a three-component Gaussian-mixture with unknown parameters.

Usage

bayes.anova(n=10000,first,second,third,fourth=NULL,fifth=NULL,sixth=NULL,
hyperpars="custom",burnin=n/2,sd="sd",q=0.1,ci=0.95)

Arguments

n

Number of posterior draws the Gibbs sampler produces. The default is n=10000.

first

Numerical vector containing the values of the first group

second

Numerical vector containing the values of the second group

third

Numerical vector containing the values of the third group

fourth

Numerical vector containing the values of the fourth group. Default value is NULL.

fifth

Numerical vector containing the values of the fifth group. Default value is NULL.

sixth

Numerical vector containing the values of the sixth group. Default value is NULL.

hyperpars

Sets the hyperparameters on the prior distributions. Two options are provided. The default is "custom", and the other is "rafterys". For details, see the references.

burnin

Burn-in samples for the Gibbs sampler

sd

Selects if posterior draws should be produced for the standard deviation (default) or the variance. The two options are "sd" and "var" respectively.

q

Tuning parameter for the hyperparameters. The default is q=0.1 and it is recommended not to change this.

ci

The credible level for the credible intervals produced. Default is ci=0.95.

Details

The Gibbs sampler is run with four Markov chains to run convergence diagnostics.

Value

Returns a dataframe which includes four columns for each parameter of interest. Each column corresponds to the posterior draws of a single Markov chain obtained by the Gibbs sampling algorithm.

Author(s)

Riko Kelter

References

For details, see: https://arxiv.org/abs/1906.07524v1

Examples

set.seed(42)
x1=rnorm(75,0,1)
x2=rnorm(75,1,1)
x3=rnorm(75,2,1)
x4=rnorm(75,-1,1)
result=bayes.anova(first=x1,second=x2,third=x3)
result=bayes.anova(n=1000,first=x1,second=x2,third=x3,
hyperpars="custom",burnin=750,ci=0.99,sd="sd")
result2=bayes.anova(n=1000,first=x1,second=x2,third=x3,
fourth=x4)