bayesANOVA-package: Bayesian ANOVA

In bayesanova: Bayesian Inference in the Analysis of Variance via Markov Chain Monte Carlo in Gaussian Mixture Models

Description

Provides a Bayesian version of the analysis of variance (ANOVA) based on a three-component Gaussian mixture, for which a Gibbs sampler produces the posteriors of the means and standard deviation of each component. Also, model assumptions can be checked and results visualised.

Details

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The core function is bayes.anova which provides the Bayesian version of the ANOVA. Also, assumptions can be checked via assumption.check, and anovaplot produces visualizations of the results.

Author(s)

Riko Kelter

Maintainer: 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)
assumption.check(x1,x2,x3,conf.level = 0.95)
result=bayes.anova(n=1000,first=x1,second=x2,third=x3)
anovaplot(result)

Example output

Model assumptions checked. No significant deviations from normality detected. Bayesian ANOVA can be run safely.
Bayesian ANOVA output:
Details: Gaussian-mixture model with three components


|Parameter     |LQ    |Mean  |UQ    |Std.Err |
|:-------------|:-----|:-----|:-----|:-------|
|mu1           |-0.01 |0.02  |0.06  |0.02    |
|mu2           |0.89  |0.92  |0.94  |0.01    |
|mu3           |1.91  |1.94  |1.96  |0.01    |
|sigma1        |0.99  |1.16  |1.37  |0.09    |
|sigma2        |0.86  |1     |1.16  |0.08    |
|sigma3        |0.86  |1.01  |1.19  |0.08    |
|mu2-mu1       |0.85  |0.9   |0.94  |0.02    |
|mu3-mu1       |1.87  |1.91  |1.97  |0.02    |
|mu3-mu2       |0.98  |1.02  |1.06  |0.02    |
|sigma2-sigma1 |-0.44 |-0.16 |0.1   |0.13    |
|sigma3-sigma1 |-0.38 |-0.15 |0.12  |0.12    |
|sigma3-sigma2 |-0.23 |0.01  |0.26  |0.12    |
|delta12       |-0.93 |-0.86 |-0.79 |0.03    |
|delta13       |-1.96 |-1.84 |-1.74 |0.06    |
|delta23       |-1.08 |-1.02 |-0.95 |0.03    |
dev.new(): using pdf(file="Rplots1.pdf")

bayesanova documentation built on Oct. 28, 2021, 5:09 p.m.