Description Usage Arguments Details Value Author(s) References See Also Examples
View source: R/pcorSimulator.R
pcorSimulator
creates a block diagonal positive definite precision matrix with three possible
graph structures: hubs-based, power-law and random. Then, it generates samples from a multivariate normal
distribution with covariance matrix given by the inverse of such precision matrix.
1 2 3 4 5 | pcorSimulator(nobs, nclusters, nnodesxcluster, pattern = "powerLaw",
low.strength = 0.5, sup.strength = 0.9, nhubs = 5,
degree.hubs = 20, nOtherEdges = 30, alpha = 2.3, plus = 0,
prob = 0.05, perturb.clust = 0, mu = 0,
probSign = 0.5, seed = sample(10000, nclusters))
|
nobs |
number of observations. |
nclusters |
number of clusters or blocks of variables. |
nnodesxcluster |
number of nodes/variables per cluster. |
pattern |
graph structure pattern: name that uniquely identifies |
low.strength |
minimum magnitude for nonzero partial correlation elements before regularization. |
sup.strength |
maximum magnitude for nonzero partial correlation elements before regularization. |
nhubs |
number of hubs per cluster (if |
degree.hubs |
degree of hubs (if |
nOtherEdges |
number of edges for non-hub nodes (if |
alpha |
positive coefficient for the Riemman function in power-law distributions. |
plus |
power-law distribution added complexity (zero by default). |
prob |
probability of edge presence for random networks (if |
perturb.clust |
proportion of the total number of edges that are connecting two different clusters. |
mu |
expected values vector to generate data (zero by default). |
probSign |
probability of positive sign for non-zero partial correlation coefficients. Thus, negative signs
are obtained with probability |
seed |
vector with seeds for each cluster. |
Hubs-based networks are graphs where only few nodes have a much higher degree (or connectivity) than the rest. Power-law networks assume that the variable p_k, which denotes the fraction of nodes in the network that has degree k, is given by a power-law distribution
p_k = \frac{k^{-α}}{\varsigma(α)},
for k ≥q 1, a constant α>0 and the normalizing function \varsigma(α) which is the Riemann zeta function. Finally, random networks are also defined by the distribution in the proportion p_k. In this case, p_k follows a binomial distribution
p_k = {p\choose k} θ^k (1-θ)^{p-k},
where the parameter θ determines the proportion of edges (or sparsity) in the graph.
The regularization is given by Ω^{(1)} = Ω^{(0)} + δ I, with δ such that the condition number of Ω^{(1)} is less than the number of nodes.
An object of class pcorSim
containing the following components:
y |
generated data set. |
hubs |
hub nodes position. |
edgesInGraph |
edges given by the non-zero elements in the precision matrix. |
omega |
precision matrix used to generate the data. |
covMat |
covariance matrix used to generate the data. |
path |
adjacency matrix corresponding to the non-zero structure of |
Caballe, Adria <a.caballe@sms.ed.ac.uk>, Natalia Bochkina and Claus Mayer.
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.
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.
plot.pcorSim
for graphical representation of the generated partial correlation matrix.
pcorSimulatorJoint
for joint partial correlation matrix generation.
1 2 3 4 5 6 7 8 9 10 | # example to use pcorSimulator function
EX1 <- pcorSimulator(nobs = 50, nclusters=3, nnodesxcluster=c(100,30,50),
pattern="powerLaw", plus=0)
print(EX1)
EX2 <- pcorSimulator(nobs = 25, nclusters=2, nnodesxcluster=c(60,40),
pattern="powerLaw", plus=1)
print(EX2)
|
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