Bayesian Framework for Computational Modeling

Derived from the work of Kruschke (2015, ), the present package aims to provide a framework for conducting Bayesian analysis using Markov chain Monte Carlo (MCMC) sampling utilizing the Just Another Gibbs Sampler ('JAGS', Plummer, 2003, < http://mcmc-jags.sourceforge.net/>). The initial version includes several modules for conducting Bayesian equivalents of chi-squared tests, analysis of variance (ANOVA), multiple (hierarchical) regression, softmax regression, and for fitting data (e.g., structural equation modeling).

bfw: Bayesian Framework for Computational Modeling

What is bfw?

The purpose of bfw is to establish a framework for conducting Bayesian analysis in R, using MCMC and JAGS (Plummer, 2003). The framework provides several modules to conduct linear and non-linear (hierarchical) analyses, and allows the use of custom functions and complex JAGS models.

Derived from the excellent work of Kruschke (2015), the goal of the framework is to easily estimate parameter values and the stability of estimates from the highest density interval (HDI), make null value assessment through region of practical equivalence testing (ROPE) and conduct convergence diagnostics (e.g., Gelman & Rubin, 1992).

Users are encouraged to apply justified priors by modifying existing JAGS models found in extdata/models or by adding custom models. Similarly, one might modify models to conduct posterior predictive checks (see Kruschke, 2013). The purpose of the framework is not to provide generic modules suitable for all circumstances, but rather act as a platform for modifying or developing models for a given project.

List of current modules

• Bernoulli trials
• Covariate estimations (including correlation and Cronbach’s alpha)
• Fit observed and latent data (e.g., SEM, CFA, mediation models)
• Bayesian equivalent of Cohen’s kappa
• Mean and standard deviation estimations
• Predict metric values (cf., ANOVA)
• Predict nominal values (cf., chi-square test)
• Simple, multiple and hierarchical regression
• Softmax regression (i.e., multinomial logistic regression)

List of current visualizations

• Plot density of parameter values (including ROPE)
• Plot mean data (including repeated measures)
• Plot nominal data (e.g., expected and observed values)
• Plot circlize data (e.g., multiple response categories)

Prerequisites

• JAGS (>=4.3.0): http://mcmc-jags.sourceforge.net/
• Java JDK (>=1.4): https://www.java.com/en/download/manual.jsp

Dependencies

Dependencies are automatically installed from CRAN. By default, outdated dependencies are automatically upgraded.

Installing

You can install bfw from GitHub. If you already have a previous version of bfw installed, using the command below will update to the latest development version.

devtools::install_github("oeysan/bfw")

Please note that stable versions are hosted at CRAN, whereas GitHub versions are in active development.

Stable version (CRAN)

utils::install.packages("bfw")

Issues

Please report any bugs/issues here

Example 1: Normal distributed data

Compute mean and standard deviation estimates.
Please see manual for more examples.

# Apply MASS to create normal distributed data with mean = 0 and standard deviation = 1
set.seed(99)
data <- data.frame(y =
                     MASS::mvrnorm(n=100,
                                   mu=0,
                                   Sigma=matrix(1, 1),
                                   empirical=TRUE) )

# Run normal distribution analysis on data
## Use 50 000 iterations, set seed for replication.
### Null value assessment is set at ROPE = -0.5 - 0.5 for mean
mcmc <- bfw(project.data = data,
            y = "y",
            saved.steps = 50000,
            jags.model = "mean",
            jags.seed = 100,
            ROPE = c(-0.5,0.5),
            silent = TRUE)

# Run t-distribution analysis on data
mcmc.robust <- bfw(project.data = data,
                   y = "y",
                   saved.steps = 50000,
                   jags.model = "mean",
                   jags.seed = 101,
                   ROPE = c(-0.5,0.5),
                   run.robust = TRUE,
                   silent = TRUE)

# Use psych to describe the normally distributed data
psych::describe(data)[,c(2:12)]
#>      n mean sd median trimmed  mad   min  max range  skew kurtosis
#> X1 100    0  1   0.17    0.04 0.81 -3.26 2.19  5.45 -0.57     0.53

# Print summary of normal distribution analysis
## Only the most relevant information is shown here
round(mcmc$summary.MCMC[,c(3:6,9:12)],3)
#>               Mode   ESS  HDIlo HDIhi ROPElo ROPEhi ROPEin   n
#> mu[1]: Y    -0.003 49830 -0.201 0.196      0      0    100 100
#> sigma[1]: Y  0.995 48890  0.869 1.150      0    100      0 100

# Print summary of t-distribution analysis
round(mcmc.robust$summary.MCMC[,c(3:6,9:12)],3)
#>              Mode   ESS  HDIlo HDIhi ROPElo ROPEhi ROPEin   n
#> mu[1]: Y    0.027 25887 -0.167 0.229      0      0    100 100
#> sigma[1]: Y 0.933 10275  0.749 1.115      0    100      0 100

Example 2: Same data but with outliers

# Add 10 outliers, each with a value of 10.
biased.data <- rbind(data,data.frame(y = rep(10,10)))

# Run normal distribution analyis on biased data
biased.mcmc <- bfw(project.data = biased.data,
                   y = "y",
                   saved.steps = 50000,
                   jags.model = "mean",
                   jags.seed = 102,
                   ROPE = c(-0.5,0.5),
                   silent = TRUE)

# Run t-distribution analysis on biased data
biased.mcmc.robust <- bfw(project.data = biased.data,
                          y = "y",
                          saved.steps = 50000,
                          jags.model = "mean",
                          jags.seed = 103,
                          ROPE = c(-0.5,0.5),
                          run.robust =TRUE,
                          silent = TRUE)

# Use psych to describe the biased data
psych::describe(biased.data)[,c(2:12)]
#>      n mean   sd median trimmed  mad   min max range skew kurtosis
#> X1 110 0.91 3.04   0.25    0.21 0.92 -3.26  10  13.3  2.3     4.38

# Print summary of normal distribution analysis on biased data
## Only the most relevant information is shown here
round(biased.mcmc$summary.MCMC[,c(3:6,9:12)],3)
#>              Mode   ESS HDIlo HDIhi ROPElo ROPEhi ROPEin   n
#> mu[1]: Y    0.922 50000 0.346  1.50      0     92   8.05 110
#> sigma[1]: Y 2.995 49069 2.662  3.48      0    100   0.00 110

# # Print summary of t-distribution analysis on biased data
round(biased.mcmc.robust$summary.MCMC[,c(3:6,9:12)],3)
#>              Mode   ESS  HDIlo HDIhi ROPElo ROPEhi  ROPEin   n
#> mu[1]: Y    0.168 29405 -0.015 0.355      0  0.008  99.992 110
#> sigma[1]: Y 0.679 17597  0.512 0.903      0 99.128   0.872 110

Example 3: Custom function and model

Shamelessly adapted from here (credits to James Curran).

# Create a function for left-censored data
custom.function <- function(DF, ...) {

  x <- as.vector(unlist(DF))
  x[x < log(29)] = NA
  n <- length(x)
  LOD <- rep(log(29), n)
  is.above.LOD <- ifelse(!is.na(x), 1, 0)
  lambda <- 0.5
  initial.x = rep(NA, length(x))
  n.missing <- sum(!is.above.LOD)
  initial.x[!is.above.LOD] <- runif(n.missing, 0, log(29))

  initial.list <- list(lambda = lambda,
                       x = initial.x
  )

  data.list <- list(n = n,
                    x = x,
                    LOD = LOD,
                    is.above.LOD = is.above.LOD
  )

  # Return data list
  return (
    list (
      params = "lambda",
      initial.list = initial.list,
      data.list = data.list,
      n.data = as.matrix(n)
      )
    )
}

# Create a model
custom.model = "
  model{
    for(i in 1:n){
      is.above.LOD[i] ~ dinterval(x[i], LOD[i])
      x[i] ~ dexp(lambda)
    }
    lambda ~ dgamma(0.001, 0.001)
  }
"

# Simulate some data
set.seed(35202)
project.data <- as.matrix(rexp(10000, rate = 1.05))

# Run analysis
custom.mcmc <- bfw(project.data = project.data,
                   custom.function = custom.function,
                   custom.model = custom.model,
                   saved.steps = 50000,
                   jags.seed = 100,
                   ROPE = c(1.01,1.05),
                   silent = TRUE)

# Print analysis
round(custom.mcmc$summary.MCMC[,c(3,5,6,9:12)],3)
#>     Mode    HDIlo    HDIhi   ROPElo   ROPEhi   ROPEin        n 
#>     1.03     1.00     1.06     7.64    14.33    78.03 10000.00

The cost of conducting robust estimates

# Running time for normal distribution analyis
biased.mcmc$run.time[2] - biased.mcmc$run.time[1]
#> Time difference of 7.35 secs

# Running time for t-distribution analysis
biased.mcmc.robust$run.time[2] - biased.mcmc.robust$run.time[1]
#> Time difference of 31.3 secs

License

This project is licensed under the MIT License - see LICENSE.md for details

Acknowledgments

• John Kruschke for his overall amazing work, and especially for his workshop at ICPSR 2016. It opened my eyes to Bayesian statistics.
• Martyn Plummer for his work on JAGS. Cheers!

References

• Gelman, A., & Rubin, D. B. (1992). Inference from Iterative Simulation Using Multiple Sequences. Statistical Science, 7(4), 457-472. https://doi.org/10.1214/ss/1177011136
• Kruschke, J. K. (2013). Posterior predictive checks can and should be Bayesian: Comment on Gelman and Shalizi, ‘Philosophy and the practice of Bayesian statistics’. British Journal of Mathematical and Statistical Psychology, 66(1), 4556. https://doi.org/10.1111/j.2044-8317.2012.02063.x
• Kruschke, J. K. (2015). Doing Bayesian data analysis: a tutorial with R, JAGS, and Stan. Academic Press: Boston.
• Plummer, M. (2003). JAGS A program for analysis of Bayesian graphical models using Gibbs sampling (Version 4.3.0). Retrieved from http://mcmc-jags.sourceforge.net/