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Data Simulation

In this vignette, we will simulate data from an additive Bayesian network and compare it to the original data.

Fit a model to the original data

First, we will fit a model to the original data that we will use to simulate new data from. We will use the ex1.dag.data data set and fit a model to it.

# Load example data
mydat <- ex1.dag.data

# Set the distribution of each node
mydists <- list(b1="binomial",
                p1="poisson",
                g1="gaussian",
                b2="binomial",
                p2="poisson",
                b3="binomial",
                g2="gaussian",
                b4="binomial",
                b5="binomial",
                g3="gaussian")

# Build the score cache
mycache <- buildScoreCache(data.df = mydat,
                           data.dists = mydists,
                           method = "bayes",
                           max.parents = 4)

# Structure learning
mp.dag <- mostProbable(score.cache = mycache)
#> Step1. completed max alpha_i(S) for all i and S
#> Total sets g(S) to be evaluated over: 1024

# Estimate the parameters
myfit <- fitAbn(object = mp.dag)

# Plot the DAG
plot(myfit)

plot of chunk fit_model

Simulate new data

Based on the abnFit object, we can simulate new data. By default simulateAbn() synthesizes 1000 new data points.

mydat_sim <- simulateAbn(object = myfit)
str(mydat_sim)
#> 'data.frame':    1000 obs. of  10 variables:
#>  $ b1: Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
#>  $ b2: Factor w/ 2 levels "0","1": 1 1 1 1 2 1 1 2 2 2 ...
#>  $ b3: Factor w/ 2 levels "0","1": 2 1 2 1 1 1 2 1 2 2 ...
#>  $ b4: Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
#>  $ b5: Factor w/ 2 levels "0","1": 2 2 2 2 2 2 1 2 2 2 ...
#>  $ g1: num  0.796 -0.92 0.167 -2.602 -0.432 ...
#>  $ g2: num  0.112 -0.708 -1.621 0.115 1.504 ...
#>  $ g3: num  0.703 -0.891 0.206 -0.55 -1.458 ...
#>  $ p1: num  0 1 1 0 0 0 1 0 1 0 ...
#>  $ p2: num  17 7 6 16 9 12 7 9 5 9 ...

In the background, the simulateAbn() function translates the abnFit object into a BUGS model and calls the rjags package to simulate new data.

Especially for debugging purposes, it can be usefull to manually inspect the BUGS file that is generated by simulateAbn(). This can be done by not running the simulation with run.simulation = FALSE and print the BUGS file to console with verbose = TRUE.

# Simulate new data and print the BUGS file to the console
simulateAbn(object = myfit,
            run.simulation = FALSE,
            verbose = TRUE)

To store the BUGS file for reproducibility or manual inspection, we can set the bugsfile argument to a file name to save the BUGS file to disk.

Compare the original and simulated data

We can compare the original and simulated data by plotting the distributions of the variables.

# order the columns of mydat equal to mydat_sim
mydat <- mydat[, colnames(mydat_sim)]

library(ggplot2)
library(gridExtra)

# Create a list of variables
variables <- names(mydat)

# Initialize an empty list to store plots
plots <- list()

# For each variable
for (i in seq_along(variables)) {
  # Check if the variable is numeric
  if (is.numeric(mydat[[variables[i]]])) {
    # Create a histogram for the variable in mydat
    p1 <- ggplot(mydat, aes(!!as.name(variables[i]))) +
      geom_histogram(binwidth = 0.5, fill = "skyblue", color = "black") +
      labs(title = paste("mydat", variables[i]), x = variables[i], y = "Count") +
      theme_minimal()

    # Create a histogram for the variable in mydat_sim
    p2 <- ggplot(mydat_sim, aes(!!as.name(variables[i]))) +
      geom_histogram(binwidth = 0.5, fill = "skyblue", color = "black") +
      labs(title = paste("mydat_sim", variables[i]), x = variables[i], y = "Count") +
      theme_minimal()
  } else {
    # Create a bar plot for the variable in mydat
    p1 <- ggplot(mydat, aes(!!as.name(variables[i]))) +
      geom_bar(fill = "skyblue", color = "black") +
      labs(title = paste("mydat", variables[i]), x = variables[i], y = "Count") +
      theme_minimal()

    # Create a bar plot for the variable in mydat_sim
    p2 <- ggplot(mydat_sim, aes(!!as.name(variables[i]))) +
      geom_bar(fill = "skyblue", color = "black") +
      labs(title = paste("mydat_sim", variables[i]), x = variables[i], y = "Count") +
      theme_minimal()
  }

  # Combine the plots into a grid
  plots[[i]] <- arrangeGrob(p1, p2, ncol = 2)
}

# Print all plots
do.call(grid.arrange, c(plots, ncol = 1))

plot of chunk unnamed-chunk-3

The plots show that the distributions of the original and simulated data are similar.

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