Example 1: Gaussian Graphical Models

Here is a simple example to see the performance of the package for the Gaussian graphical models. First, by using the function bdgraph.sim(), we simulate 200 observations (n = 200) from a multivariate Gaussian distribution with 15 variables (p = 15) and “scale-free” graph structure, as follows

set.seed( 20 )

data.sim = bdgraph.sim( n = 200, p = 15, graph = "scale-free", vis = TRUE )

Since the generated data are Gaussian, we run the bdgraph() function by choosing method = "ggm", as follows

bdgraph.obj = bdgraph( data = data.sim, method = "ggm", iter = 5000, verbose = FALSE )

To report confusion matrix with cutoff point 0.5:

conf.mat( actual = data.sim, pred = bdgraph.obj, cutoff = 0.5 )
            Actual
  Prediction  0  1
           0 91  4
           1  0 10

conf.mat.plot( actual = data.sim, pred = bdgraph.obj, cutoff = 0.5 )

To compare the result with the true graph

compare( data.sim, bdgraph.obj, main = c( "Target", "BDgraph" ), vis = TRUE )

                 Target BDgraph
  True Positive      10  10.000
  True Negative      95  91.000
  False Positive      0   4.000
  False Negative      0   0.000
  F1-score            1   0.833
  Specificity         1   0.958
  Sensitivity         1   1.000
  MCC                 1   0.827

Now, as an alternative, we run the bdgraph.mpl() function which is based on the GGMs and marginal pseudo-likelihood, as follows

bdgraph.mpl.obj = bdgraph.mpl( data = data.sim, method = "ggm", iter = 5000, verbose = FALSE )

conf.mat( actual = data.sim, pred = bdgraph.mpl.obj )
            Actual
  Prediction  0  1
           0 91  4
           1  0 10
conf.mat.plot( actual = data.sim, pred = bdgraph.mpl.obj )

We could compare the results of both algorithms with the true graph as follows

compare( list( bdgraph.obj, bdgraph.mpl.obj ), data.sim, 
         main = c( "Target", "BDgraph", "BDgraph.mpl" ), vis = TRUE )

                 Target BDgraph BDgraph.mpl
  True Positive      14  10.000      10.000
  True Negative      91  91.000      91.000
  False Positive      0   0.000       0.000
  False Negative      0   4.000       4.000
  F1-score            1   0.833       0.833
  Specificity         1   1.000       1.000
  Sensitivity         1   0.714       0.714
  MCC                 1   0.827       0.827

To see the performance of the BDMCMC algorithm we could plot the ROC curve as follows

plotroc( list( bdgraph.obj, bdgraph.mpl.obj ), data.sim, cut = 200,
         labels = c( "BDgraph", "BDgraph.mpl" ), color = c( "blue", "red" ) )

Example 2: Gaussian Copula Graphical Models

Here is a simple example to see the performance of the package for the mixed data using Gaussian copula graphical models. First, by using the function bdgraph.sim(), we simulate 300 observations (n = 300) from mixed data (type = "mixed") with 10 variables (p = 10) and “random” graph structure, as follows

set.seed( 2 )

data.sim = bdgraph.sim( n = 300, p = 10, type = "mixed", graph = "random", vis = TRUE )

Since the generated data are mixed data, we are using run the bdgraph() function by choosing method = "gcgm", as follows:

bdgraph.obj = bdgraph( data = data.sim, method = "gcgm", iter = 5000, verbose = FALSE )

To compare the result with the true graph, we could run

compare( bdgraph.obj, data.sim, main = c( "Target", "BDgraph" ), vis = TRUE )

                 Target BDgraph
  True Positive      12   9.000
  True Negative      33  31.000
  False Positive      0   2.000
  False Negative      0   3.000
  F1-score            1   0.783
  Specificity         1   0.939
  Sensitivity         1   0.750
  MCC                 1   0.709

plotroc( bdgraph.obj, data.sim, labels = "BDgraph", color = "blue" )

For more examples see Mohammadi and Wit (2019).