Description Usage Arguments Details Value Author(s) References See Also Examples
View source: R/pcorSimulatorJointPaired.r
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.
1 2 3 4 5 6 7 8 | 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))
|
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 |
diffType |
pattern in differential edges: name that uniquely identifies |
dataDepend |
model used to describe the dependent structure for the data: 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. |
pdiff |
proportion of differential edges from the total number edges in each graph. |
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 existence 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). |
diagCCtype |
way to generate diagonal values of either cross partial correlation matrix (if |
diagNZ.strength |
magnitude for the non-zero elements in the diagonal of the cross (partial) correlation when |
mixProb |
proportion of random differential connections if |
probSign |
probability of positive sign for non-zero partial correlation coefficients. Thus, negative signs
are obtained with probability |
exactZeroTh |
partial correlation coefficients smaller than exactZeroTh are considered exact zeros. |
seed |
vector with seeds for each cluster. |
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 Σ_{XY} = Δ Σ_X Δ^t, with diagonal matrix Δ, 0≤qΔ_{ii}<1 and Σ_{XY} = ΔΣ_X^{1/2}Σ_Y^{1/2} Δ^t respectively where diagonal coefficients in Δ 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 Δ. For the three models,
In case diagCCtype = "dicot"
the diagonal elements in Δ have zero/non-zero structure (with non-zero coefficients given in the parameter Δ). 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.
An object of class pcorSimJoint
containing the following components:
D1 |
dataset for first population. |
D2 |
dataset for second population. |
omega1 |
precision matrix for first population. |
omega2 |
precision matrix for second population. |
P |
total number of variables. |
diffs |
differential edges. |
delta |
generated values for the dependent structure. |
covJ |
joint covariance matrix used to generate the data. |
path1 |
adjacency matrix corresponding to the non-zero structure of |
path2 |
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.
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.
1 2 3 4 5 6 7 8 9 10 | # 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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