A directed factor model graph is a directed
generalized Poisson random dot product graph. The edges
in this graph are assumpted to be independent and Poisson
distributed. The graph is parameterized by its expected
adjacency matrix, with is E[A] = X S Y'. We do not recommend
that causal users use this function, see instead directed_dcsbm()
and related functions, which will formulate common variants
of the stochastic blockmodels as undirected factor models
with lots of helpful input validation.
directed_factor_model(
X,
S,
Y,
...,
expected_in_degree = NULL,
expected_out_degree = NULL,
expected_density = NULL,
poisson_edges = TRUE,
allow_self_loops = TRUE
)A directed_factor_model S3 class based on a list
with the following elements:
X: The incoming latent positions as a Matrix() object.
S: The mixing matrix as a Matrix() object.
Y: The outgoing latent positions as a Matrix() object.
n: The number of nodes with incoming edges in the network.
k1: The dimension of the latent node position vectors
encoding incoming latent communities (i.e. in X).
d: The number of nodes with outgoing edges in the network.
Does not need to match n -- rectangular adjacency matrices
are supported.
k2: The dimension of the latent node position vectors
encoding outgoing latent communities (i.e. in Y).
poisson_edges: Whether or not the graph is taken to be have
Poisson or Bernoulli edges, as indicated by a logical vector
of length 1.
allow_self_loops: Whether or not self loops are allowed.
A matrix() or Matrix() representing real-valued
latent node positions encoding community structure of
incoming edges. Entries must be positive.
A matrix() or Matrix() mixing matrix. Entries
must be positive.
A matrix() or Matrix() representing real-valued
latent node positions encoding community structure of
outgoing edges. Entries must be positive.
Ignored. For internal developer use only.
If specified, the desired expected in degree
of the graph. Specifying expected_in_degree simply rescales S
to achieve this. Defaults to NULL. Specify only one of
expected_in_degree, expected_out_degree, and expected_density.
If specified, the desired expected out degree
of the graph. Specifying expected_out_degree simply rescales S
to achieve this. Defaults to NULL. Specify only one of
expected_in_degree, expected_out_degree, and expected_density.
If specified, the desired expected density
of the graph. Specifying expected_density simply rescales S
to achieve this. Defaults to NULL. Specify only one of
expected_in_degree, expected_out_degree, and expected_density.
Logical indicating whether or not
multiple edges are allowed to form between a pair of
nodes. Defaults to TRUE. When FALSE, sampling proceeds
as usual, and duplicate edges are removed afterwards. Further,
when FALSE, we assume that S specifies a desired between-factor
connection probability, and back-transform this S to the
appropriate Poisson intensity parameter to approximate Bernoulli
factor connection probabilities. See Section 2.3 of Rohe et al. (2017)
for some additional details.
Logical indicating whether or not
nodes should be allowed to form edges with themselves.
Defaults to TRUE. When FALSE, sampling proceeds allowing
self-loops, and these are then removed after the fact.
n <- 10000
k1 <- 5
k2 <- 3
d <- 5000
X <- matrix(rpois(n = n * k1, 1), nrow = n)
S <- matrix(runif(n = k1 * k2, 0, .1), nrow = k1, ncol = k2)
Y <- matrix(rexp(n = k2 * d, 1), nrow = d)
fm <- directed_factor_model(X, S, Y)
fm
fm2 <- directed_factor_model(X, S, Y, expected_in_degree = 50)
fm2
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