Simulates data with with independent groups of variables.
SimulateComponents(
n = 100,
pk = c(10, 10),
adjacency = NULL,
nu_within = 1,
v_within = c(0.5, 1),
v_sign = -1,
continuous = TRUE,
pd_strategy = "min_eigenvalue",
ev_xx = 0.1,
scale_ev = TRUE,
u_list = c(1e-10, 1),
tol = .Machine$double.eps^0.25,
scale = TRUE,
output_matrices = FALSE
)A list with:
simulated data with n observation and
sum(pk) variables.
loadings coefficients of the orthogonal latent variables (principal components).
support of the loadings coefficients.
proportion of explained variance by each of the orthogonal latent variables.
adjacency matrix of the simulated graph.
simulated (true) precision
matrix. Only returned if output_matrices=TRUE.
simulated
(true) partial correlation matrix. Only returned if
output_matrices=TRUE.
simulated (true) correlation
matrix. Only returned if output_matrices=TRUE.
number of observations in the simulated dataset.
vector of the number of variables per group in the simulated
dataset. The number of nodes in the simulated graph is sum(pk). With
multiple groups, the simulated (partial) correlation matrix has a block
structure, where blocks arise from the integration of the length(pk)
groups. This argument is only used if theta is not provided.
optional binary and symmetric adjacency matrix encoding the
conditional graph structure between observations. The clusters encoded in
this argument must be in line with those indicated in pk. Edges in
off-diagonal blocks are not allowed to ensure that the simulated orthogonal
components are sparse. Corresponding entries in the precision matrix will
be set to zero.
probability of having an edge between two nodes belonging to
the same group, as defined in pk. If length(pk)=1, this is
the expected density of the graph. If implementation=HugeAdjacency,
this argument is only used for topology="random" or
topology="cluster" (see argument prob in
huge.generator). Only used if nu_mat is not
provided.
vector defining the (range of) nonzero entries in the
diagonal blocks of the precision matrix. These values must be between -1
and 1 if pd_strategy="min_eigenvalue". If continuous=FALSE,
v_within is the set of possible precision values. If
continuous=TRUE, v_within is the range of possible precision
values.
vector of possible signs for precision matrix entries. Possible
inputs are: -1 for positive partial correlations, 1 for
negative partial correlations, or c(-1, 1) for both positive and
negative partial correlations.
logical indicating whether to sample precision values from
a uniform distribution between the minimum and maximum values in
v_within (diagonal blocks) or v_between (off-diagonal blocks)
(if continuous=TRUE) or from proposed values in v_within
(diagonal blocks) or v_between (off-diagonal blocks) (if
continuous=FALSE).
method to ensure that the generated precision matrix is
positive definite (and hence can be a covariance matrix). If
pd_strategy="diagonally_dominant", the precision matrix is made
diagonally dominant by setting the diagonal entries to the sum of absolute
values on the corresponding row and a constant u. If
pd_strategy="min_eigenvalue", diagonal entries are set to the sum of
the absolute value of the smallest eigenvalue of the precision matrix with
zeros on the diagonal and a constant u.
expected proportion of explained variance by the first Principal
Component (PC1) of a Principal Component Analysis. This is the largest
eigenvalue of the correlation (if scale_ev=TRUE) or covariance (if
scale_ev=FALSE) matrix divided by the sum of eigenvalues. If
ev_xx=NULL (the default), the constant u is chosen by maximising the
contrast of the correlation matrix.
logical indicating if the proportion of explained variance by
PC1 should be computed from the correlation (scale_ev=TRUE) or
covariance (scale_ev=FALSE) matrix. If scale_ev=TRUE, the
correlation matrix is used as parameter of the multivariate normal
distribution.
vector with two numeric values defining the range of values to explore for constant u.
accuracy for the search of parameter u as defined in
optimise.
logical indicating if the true mean is zero and true variance is one for all simulated variables. The observed mean and variance may be slightly off by chance.
logical indicating if the true precision and (partial) correlation matrices should be included in the output.
The data is simulated from a centered multivariate Normal distribution with a block-diagonal covariance matrix. Independence between variables from the different blocks ensures that sparse orthogonal components can be generated.
The block-diagonal partial correlation matrix is obtained using a graph structure encoding the conditional independence between variables. The orthogonal latent variables are obtained from eigendecomposition of the true correlation matrix. The sparse eigenvectors contain the weights of the linear combination of variables to construct the latent variable (loadings coefficients). The proportion of explained variance by each of the latent variable is computed from eigenvalues.
As latent variables are defined from the true correlation matrix, the
number of sparse orthogonal components is not limited by the number of
observations and is equal to sum(pk).
ourstabilityselectionfake
MakePositiveDefinite
Other simulation functions:
SimulateAdjacency(),
SimulateClustering(),
SimulateCorrelation(),
SimulateGraphical(),
SimulateRegression(),
SimulateStructural()
# \donttest{
# Simulation of 3 components with high e.v.
set.seed(1)
simul <- SimulateComponents(pk = c(5, 3, 4), ev_xx = 0.4)
print(simul)
plot(simul)
plot(cumsum(simul$ev), ylim = c(0, 1), las = 1)
# Simulation of 3 components with moderate e.v.
set.seed(1)
simul <- SimulateComponents(pk = c(5, 3, 4), ev_xx = 0.25)
print(simul)
plot(simul)
plot(cumsum(simul$ev), ylim = c(0, 1), las = 1)
# Simulation of multiple components with low e.v.
pk <- sample(3:10, size = 5, replace = TRUE)
simul <- SimulateComponents(
pk = pk,
nu_within = 0.3, v_within = c(0.8, 0.5), v_sign = -1, ev_xx = 0.1
)
plot(simul)
plot(cumsum(simul$ev), ylim = c(0, 1), las = 1)
# }
Run the code above in your browser using DataLab