Simulate Data from a Social Influence Regression Model

Generates synthetic network data from a known SIR data-generating process. Useful for testing, benchmarking, and pedagogical demonstrations. The function simulates Y[i,j,t] from the specified family using influence covariates W, lagged network state X, and optional exogenous covariates Z.

Usage

sim_sir(
  m,
  T_len,
  p = 2,
  q = 1,
  family = "poisson",
  alpha = NULL,
  beta = NULL,
  theta = NULL,
  W = NULL,
  sigma = 1,
  seed = NULL
)

Arguments

m

Integer. Number of nodes in the network.

T_len

Integer. Number of time periods.

p

Integer. Number of influence covariates in W. Default is 2.

q

Integer. Number of exogenous covariates in Z. Default is 1. Set to 0 for no exogenous covariates.

family

Character string: "poisson" (default), "normal", or "binomial".

alpha

Numeric vector of length p for sender influence weights. The first element (alpha_1) is fixed at 1 for identifiability; only alpha_2:p are free. If NULL (default), drawn from N(0, 0.3).

beta

Numeric vector of length p for receiver influence weights. If NULL (default), drawn from N(0, 0.3).

theta

Numeric vector of length q for exogenous covariate effects. If NULL (default), drawn from U(-0.5, 0.5).

W

Optional 3D array (m x m x p) of influence covariates. If NULL (default), generated with standard normal entries.

sigma

Numeric. Standard deviation for the normal family. Default 1.

seed

Optional integer for reproducibility.

Value

A list with components:

Y

3D array (m x m x T_len) of simulated outcomes.

W

3D array (m x m x p) of influence covariates.

X

3D array (m x m x T_len) of lagged network state. For Poisson family, X is log(Y + 1) to prevent explosive dynamics.

Z

4D array (m x m x q x T_len) of exogenous covariates, or NULL if q = 0.

alpha

True alpha vector (length p, with alpha_1 = 1).

beta

True beta vector (length p).

theta

True theta vector (length q).

A

True sender influence matrix (m x m).

B

True receiver influence matrix (m x m).

family

The distribution family used.

Examples

if (FALSE) { # \dontrun{
# Simulate Poisson network
dat <- sim_sir(m = 15, T_len = 10, p = 2, q = 1, family = "poisson", seed = 42)

# Fit model to recover parameters
fit <- sir(dat$Y, dat$W, dat$X, dat$Z, family = "poisson")
cbind(true = c(dat$theta, dat$alpha[-1], dat$beta), estimated = coef(fit))
} # }