generate_blin: Generate data from the continuous BLIN model

Description

This function generates data from the bipartite logitudinal influence network (BLIN) model \(Y_t = A^T \sum_{k=1}^{lag} Y_{t-k} + \sum_{k=1}^{lag} Y_{t-k} B + X_t \beta + \tau E_t\).

Usage

generate_blin(S, L, tmax, lag = 1, tau = 1, sigmaY = 1, muAB = 0,
  sigmaAB = 1, rankA = S, rankB = L, use_cov = TRUE, seed = NA,
  sparse = NA)

Arguments

Dimension of A.

Dimension of B.

tmax

Number of observations of relational data.

lag

Autoregressive lag in model, defaults to 1.

tau

Optional error standard deviatiom, defaults to 1.

sigmaY

Optional standard deviation of entries in \(Y_t\), defaults to 1.

muAB

Optional mean of entries in decomposition of matrices \(A = UV^T\) and \(B = WZ^T\), defaults to 0.

sigmaAB

Optional standard deviation of entries in decomposition matrices of \(A = UV^T\) and \(B = WZ^T\), defaults to 1.

rankA

Rank of influence network matrix \(A\), defaults to full rank.

rankB

Optional rank of influence network matrix \(B\), defaults to full rank.

use_cov

Optional logical used to indicate whether to include \(X_t \beta\) in the model (TRUE) or not (FALSE), defaults to TRUE.

seed

Optional numeric to set seed before generating, defaults to NA (no seed set).

sparse

Optional degree of sparsity in A and B, i.e. sparsity=.9 means 10% of the entries in A and B are set to zero at random. Defaults to NA (no entries set to zero).

Value

fit

An blin object containing summary information.

Details

This function generates a continuous bipartite longitudinal relational data set from the BLIN model, \(Y_t = A^T \sum_{k=1}^{lag} Y_{t-k} + \sum_{k=1}^{lag} Y_{t-k} B + X_t \beta + \tau E_t\), where \( \{ Y_t \}_t \) is a set of \(S \times L\) matrices representing the bipartite relational data at each observation \(t\). The set \(\{X_t \}_t\) is a set of \(S \times L \times p\) arrays describing the influence of the coefficient vector \(beta\). Finally, each matrix \(E_t\) consists of iid standard normal random variables.

The matrices \(A\) and \(B\) are square matrices respesenting the influence networks among \(S\) senders and \(L\) receivers, respectively. The matrix \(A\) has decomposition \(A = UV^T\), where each of \(U\) and \(V\) is an \(S \times {rankA}\) matrix of iid standard normal random variables with mean muAB and standard deviation sigmaAB. Similarly, the matrix \(B\) has decomposition \(B = WZ^T\), where each of \(W\) and \(Z\) is an \(L \times {rankB}\) matrix of iid standard normal random variables with standard deviation sigmaAB and mean muAB for \(W\) and mean -muAB for \(Z\). Lastly, the covariate array \(X_t\) has 3 covariates: the first is an intercept, the second consists of iid Bernoulli random variables, and the third consists of iid standard normal random variables. All coefficients are \(\beta_i = 0\) for \(i = 1,2,3\).

Examples

Run this code

# NOT RUN {
S <- 5
L <- 4
tmax <- 10
data <- generate_blin(S,L,tmax, lag=2, sparse=.8)
names(data)
dim(data$X)
data$A

# }