pcorSimulatorJointPaired creates two similar positive definite precision matrices with three possible
graph structures: hubs-based, power-law and random. Moreover, it allows for three types of
differential graph structures: random differences, clustered differences or a mixture of the two. Then, it
generates (dependent) datasets from a multivariate normal distribution defined by the inverse of such precision matrices.
pcorSimulatorJoint(nobs, nclusters, nnodesxcluster, pattern = "hubs",
diffType = "cluster", dataDepend = "ind", low.strength = 0.5,
sup.strength = 0.9, pdiff = 0, nhubs = 5, degree.hubs = 20,
nOtherEdges = 30, alpha = 2.3, plus = 0, prob = 0.05,
perturb.clust = 0, mu = 0, diagCCtype = "dicot",
diagNZ.strength = .5, mixProb = 0.5, probSign = 0.5,
exactZeroTh = 0.05, seed = sample(10000,nclusters+2))number of observations.
number of clusters or blocks of variables.
number of nodes/variables per cluster.
graph structure pattern: name that uniquely identifies "hubs", "power" and "random".
pattern in differential edges: name that uniquely identifies "random", "cluster" or "mixed".
model used to describe the dependent structure for the data: name that uniquely identifies "ind" (no dependence), "diagOmega", "mult" or "add".
minimum magnitude for nonzero partial correlation elements before regularization.
maximum magnitude for nonzero partial correlation elements before regularization.
proportion of differential edges from the total number edges in each graph.
number of hubs per cluster (if pattern = "hubs").
degree of hubs (if pattern = "hubs").
number of edges for non-hub nodes (if pattern = "hubs").
positive coefficient for the Riemman function in power-law distributions.
power-law distribution added complexity (zero by default).
probability of edge existence for random networks (if pattern="random").
proportion of the total number of edges that are connecting two different clusters.
expected values vector to generate data (zero by default).
way to generate diagonal values of either cross partial correlation matrix (if dataDepend = "diagOmega") or cross correlation matrix (if dataDepend = "mult" or dataDepend = "add"): name that uniquely identifies "dicot" or "beta13" (see details).
magnitude for the non-zero elements in the diagonal of the cross (partial) correlation when diagCCtype = "dicot".
proportion of random differential connections if diffType = "mixed". The remaining
connections are given by a cluster type.
probability of positive sign for non-zero partial correlation coefficients. Thus, negative signs
are obtained with probability 1-probSign.
partial correlation coefficients smaller than exactZeroTh are considered exact zeros.
vector with seeds for each cluster.
An object of class pcorSimJoint containing the following components:
dataset for first population.
dataset for second population.
precision matrix for first population.
precision matrix for second population.
total number of variables.
differential edges.
generated values for the dependent structure.
joint covariance matrix used to generate the data.
adjacency matrix corresponding to the non-zero structure of omega1.
adjacency matrix corresponding to the non-zero structure of omega2.
First, pcorSimulator is used to create a common precision matrix among the two populations.
Then, differential edges are added based on the next two patterns: Cluster - a graph cluster is zero in one condition and non-zero in the other
condition; Random - differential connections are given randomly in the graph.
Paired structure is defined by arguments dataDepend and diagCCtype.
Additive (dataDepend = "add") and multiplicative (dataDepend = "mult") models are used on the cross-covariance matrix
such that \(\Sigma_{XY} = \Delta \Sigma_X \Delta^t\), with diagonal matrix \(\Delta\), \(0\leq\Delta_{ii}<1\) and \(\Sigma_{XY} = \Delta\Sigma_X^{1/2}\Sigma_Y^{1/2} \Delta^t\) respectively where diagonal coefficients in \(\Delta\) are defined by diagCCtype.
A simplification is also considered by assuming that variables in one data set are only
conditionally dependent to the same variables of the other data set, hence assuming
a diagonal structure in the cross joint partial correlation matrix that can also be defined by \(\Delta\). For the three models,
In case diagCCtype = "dicot" the diagonal elements in \(\Delta\) have zero/non-zero structure (with non-zero coefficients given in the parameter \(\Delta\)). In case diagCCtype = "beta13" the diagonal elements are generated by a beta distribution with shape parameter equal to 1 and scale parameter equal to 3.
Cai, T., W. Liu, and X. Luo (2011). A Constrained L1 Minimization Approach to Sparse Precision Matrix Estimation. Journal of the American Statistical Association 106(494), 594-607.
Newman, M. (2003). The structure and function of complex networks. SIAM REVIEW 45, 167-256.
Wit, E. and A. Abbruzzo (2015, feb). Factorial graphical models for dynamic networks. Network Science 3(01), 37-57.
Caballe, A., N. Bochkina, and C. Mayer (2016). Selection of the Regularization Parameter in Graphical Models using network charactaristics. eprint arXiv:1509.05326, 1-25.
pcorSimulator for precision matrix generator.
plot.pcorSimJoint for plotting joint partial correlation matrices.
# NOT RUN {
# example to use pcorSimulatorJoint function
EX1 <- pcorSimulatorJoint(nobs = 50, nclusters = 2, nnodesxcluster = c(30, 40),
pattern = "pow", diffType = "cluster", dataDepend = "ind",
pdiff = 0.2, diagCCtype = "dicot", diagNZ.strength = .5)
print(EX1)
EX2 <- pcorSimulatorJoint(nobs = 50, nclusters = 2, nnodesxcluster = c(30, 40),
pattern = "pow", diffType = "rand", dataDepend = "diag",
pdiff = 0.05, diagCCtype = "beta")
print(EX2)
# }
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