mDAG {mDAG}

Inferring Causal Network from Mixed Observational Data Using a Directed Acyclic Graph

Description

This function learns a mixed directed acyclic graph based on both continuous and categorical data.

Usage

mDAG(data, type, level, SNP = rep(0, ncol(data)), lambdaGam = 0.25,
  ruleReg = "OR", threshold = "LW", weights = rep(1, nrow(data)),
  alpha = 0.05, nperm = 10000)

Arguments

data

A n x p matrix. Each row is a sample; each column is a variable.

type

A string vector of length p, indicating the type of variable for each column in data. 'g' for Gaussian, 'c' for categorical.

level

A vector of length p, indicating the number of categories of each variable. For continuous variables, set it to 1.

SNP

A vector of length p, indicating which variable is a SNP.

lambdaGam

Hyperparameter \gamma in the EBIC if lambdaSel = 'EBIC'. Defaults is lambdaGam = 0.25.

ruleReg

Default is 'OR'. Rule used to combine two estimates from nodewise regression (one from regressing A on B and the other from B on A). ruleReg = 'AND' requires both estimates to be nonzero in order to set the edge to be present. ruleReg = 'OR' requires at least one estiamte to be nonzero in order to set the edge to be present.

threshold

Default is 'LW'. A threshold below which the combined estimates from nodewise regression are put to zero. threshold = 'LW' refers to the threshold in Loh and Wainwright (2012). threshold = 'HW' refers to the threshold in Haslbeck and Waldorp (2016). If threshold = 'none' no thresholding is applied.

weights

A vector of length n, indicating weights for observations.

alpha

Significance level for permutation test of conditional independece. Default is 0.05.

nperm

The number of permutations in the permutation test of conditional independece. Default is 10000.

Value

A list of the following components:

• arcs: A two-column matrix, indicating arcs of the DAG.

• nodes: A list. Each element is named after a node and contains the following elements.

  • nbr: a string vector indicating the neighbourhood of the node.

  • parents: a string vector indicating the parents of the node.

  • children: a string vector indicating the children of the node.

• skeleton: A p x p adjacency matrix. If there is an edge from node i to node j, its (i,j) th entry = 1; otherwise = 0.

Author(s)

Wujuan Zhong, Li Dong, Quefeng Li, Xiaojing Zheng

References

Jonas M. B. Haslbeck, Lourens J. Waldorp (2016). mgm: Structure Estimation for Time-Varying Mixed Graphical Models in high-dimensional Data arXiv preprint:1510.06871v2

Markus Kalisch, Martin Maechler, Diego Colombo, Marloes H. Maathuis, Peter Buehlmann (2012). Causal Inference Using Graphical Models with the R Package pcalg. Journal of Statistical Software, 47(11), 1-26.

Loh, P. L., & Wainwright, M. J. (2012, December). Structure estimation for discrete graphical models: Generalized covariance matrices and their inverses. In NIPS (pp. 2096-2104).

Haslbeck, J., & Waldorp, L. J. (2016). mgm: Structure Estimation for time-varying Mixed Graphical Models in high-dimensional Data. arXiv preprint arXiv:1510.06871.

Marco Scutari (2010). Learning Bayesian Networks with the bnlearn R Package. Journal of Statistical Software, 35(3), 1-22.

Venables, W. N. & Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth Edition. Springer, New York. ISBN 0-387-95457-0

Georg Heinze and Meinhard Ploner (2018). logistf: Firth's Bias-Reduced Logistic Regression. R package version 1.23.

Min Jin Ha (2013). PenPC: A Two-step Approach to Estimate the Skeletons of High Dimensional Directed Acyclic Graphs. R package version 0.99.1.

Examples

# load package
library(mDAG)
type=c("g","g","g","g","c")
level=c(1,1,1,1,2)
# To save time for running example, we set nperm as 150. 
# Use default nperm=10000 to generate a more reliable DAG for your own data.
dag=mDAG(data=example_data, type=type, level=level, nperm=150)
print(dag$skeleton)
# draw the DAG
# library(bnlearn)
# bnlearn:::graphviz.backend(nodes=names(dag$nodes),arcs=dag$arcs,shape="rectangle")