R: Graph data simulation

bdgraph.sim {BDgraph}

R Documentation

Graph data simulation

Description

Simulating multivariate distributions with different types of underlying graph structures, including "random", "cluster", "smallworld", "scale-free", "lattice", "hub", "star", "circle", "AR(1)", and "AR(2)". Based on the underlying graph structure, the function generates different types of multivariate data, including "Gaussian", "non-Gaussian", "categorical", "pois" (Poisson), "nbinom" (negative binomial), "dweibull" (discrete Weibull), "binary", or "mixed" data. This function can be used also for simulating only graphs by setting the option n=0 (default).

Usage

bdgraph.sim( p = 10, graph = "random", n = 0, type = "Gaussian", prob = 0.2, 
             size = NULL, mean = 0, class = NULL, cut = 4, b = 3,
             D = diag( p ), K = NULL, sigma = NULL, 
             q = exp(-1), beta = 1, vis = FALSE, rewire = 0.05,
             range.mu = c( 3, 5 ), range.dispersion = c( 0.01, 0.1 ) )

Arguments

`p`	number of variables (nodes).
`graph`	graph structure with options "`random`", "`cluster`", "`smallworld`", "`scale-free`", "`lattice`", "`hub`", "`star`", "`circle`", "`AR(1)`", and "`AR(2)`". It could also be an adjacency matrix corresponding to a graph structure (an upper triangular matrix in which g_{ij}=1 if there is a link between nodes i and j, otherwise g_{ij}=0).
`n`	number of samples required. Note that for the case `n = 0`, only the graph is generated.
`type`	type of data with options "`Gaussian`" (default), "`non-Gaussian`", "`categorical`", "`pois`", "`nbinom`", "`dweibull`", "`binary`", and "`mixed`". For the option "`Gaussian`", data are generated from a multivariate normal distribution. For the option "`non-Gaussian`", data are transfered from a multivariate normal distribution to a continuous multivariate non-Gaussian distribution via Exponential marginals. For the option "`categorical`", data are transfered from a multivariate normal distribution to multivariate 'categorical' data. For the option "`pois`", data are transfered from a multivariate normal distribution to a multivariate Poisson distribution. For the option "`nbinom`", data are transfered from a multivariate normal distribution to a multivariate Negative Binomial distribution. For the option "`dweibull`", data are transfered from a multivariate normal distribution to a multivariate discrete Weibull distribution with parameters `q` and `beta`. For the option "`binary`", data are generated directly from the joint distribution, in this case p must be less than 17. For the option "`mixed`", data are transfered from a multivariate normal distribution to a mixture of 'categorical', 'non-Gaussian', 'binary' and 'Gaussian', respectively.
`prob`	if `graph` = "`random`", it is the probability that a pair of nodes has a link.
`size`	number of links in the true graph (graph size).
`mean`	vector specifying the mean of the variables.
`class`	if `graph` = "`cluster`", it is the number of classes.
`cut`	if `type` = "`categorical`", it is the number of categories for simulating 'categorical' data.
`b`	degree of freedom for G-Wishart distribution, W_G(b, D).
`D`	positive definite (p \times p) "scale" matrix for G-Wishart distribution, W_G(b, D). The default is an identity matrix.
`K`	if `graph` = "`fixed`", it is a positive-definite symmetric matrix, corresponding to the true precision matrix.
`sigma`	if `graph` = "`fixed`", it is a positive-definite symmetric matrix corresponding to the true covariance matrix.
`q, beta`	if `type` = "`dweibull`", they are the parameters of the discrete Weibull distribution with density p( x, q, β ) = q^{x^{β}}-q^{(x+1)^{β}}, \quad \forall x = \{ 0, 1, 2, … \}. They can be given either as a vector of length p or as an (n x p) matrix, e.g. if covariates are available and a regression model is used.
`vis`	visualize the true graph structure.
`rewire`	rewiring probability for smallworld network. Must be between 0 and 1.
`range.mu, range.dispersion`	if `type` = "`nbinom`", vector with two elements specifying the range of parameters for the Negative Binomial distribution.

Value

An object with S3 class "sim" is returned:

`data`	generated data as an (n x p) matrix.
`sigma`	covariance matrix of the generated data.
`K`	precision matrix of the generated data.
`G`	adjacency matrix corresponding to the true graph structure.

Author(s)

Reza Mohammadi a.mohammadi@uva.nl, Pariya Behrouzi, Veronica Vinciotti, Ernst Wit, and Alexander Christensen

References

Mohammadi, R. and Wit, E. C. (2019). BDgraph: An R Package for Bayesian Structure Learning in Graphical Models, Journal of Statistical Software, 89(3):1-30, doi: 10.18637/jss.v089.i03

Mohammadi, A. and Wit, E. C. (2015). Bayesian Structure Learning in Sparse Gaussian Graphical Models, Bayesian Analysis, 10(1):109-138, doi: 10.1214/14-BA889

Mohammadi, R., Massam, H. and Letac, G. (2021). Accelerating Bayesian Structure Learning in Sparse Gaussian Graphical Models, Journal of the American Statistical Association, doi: 10.1080/01621459.2021.1996377

Mohammadi, A. et al (2017). Bayesian modelling of Dupuytren disease by using Gaussian copula graphical models, Journal of the Royal Statistical Society: Series C, 66(3):629-645, doi: 10.1111/rssc.12171

Dobra, A. and Mohammadi, R. (2018). Loglinear Model Selection and Human Mobility, Annals of Applied Statistics, 12(2):815-845, doi: 10.1214/18-AOAS1164

Pensar, J. et al (2017) Marginal pseudo-likelihood learning of discrete Markov network structures, Bayesian Analysis, 12(4):1195-215, doi: 10.1214/16-BA1032

Examples

## Not run: 
# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( p = 10, n = 50, prob = 0.3, vis = TRUE )

print( data.sim )
     
# Generating multivariate normal data from a 'hub' graph
data.sim <- bdgraph.sim( p = 6, n = 3, graph = "hub", vis = FALSE )

round( data.sim $ data, 2 )
     
# Generating mixed data from a 'hub' graph 
data.sim <- bdgraph.sim( p = 8, n = 10, graph = "hub", type = "mixed" )

round( data.sim $ data, 2 )

# Generating only a 'scale-free' graph (with no data) 
graph.sim <- bdgraph.sim( p = 8, graph = "scale-free" )

plot( graph.sim )

graph.sim $ G

## End(Not run)

[Package BDgraph version 2.65 Index]