simsar: Simulating data from linear-in-mean models with social...

In CDatanet: Econometrics of Network Data

Simulating data from linear-in-mean models with social interactions

Description

simsar simulates continuous variables with social interactions (see Lee, 2004 and Lee et al., 2010).

Usage

simsar(formula, Glist, theta, cinfo = TRUE, data)

Arguments

formula	a class object formula: a symbolic description of the model. formula must be as, for example, y ~ x1 + x2 + gx1 + gx2 where y is the endogenous vector and x1, x2, gx1 and gx2 are control variables, which can include contextual variables, i.e. averages among the peers. Peer averages can be computed using the function peer.avg.
Glist	The network matrix. For networks consisting of multiple subnets, Glist can be a list of subnets with the m-th element being an ns*ns adjacency matrix, where ns is the number of nodes in the m-th subnet.
theta	a vector defining the true value of \theta = (\lambda, \Gamma, \sigma) (see the model specification in details).
cinfo	a Boolean indicating whether information is complete (cinfo = TRUE) or incomplete (cinfo = FALSE). In the case of incomplete information, the model is defined under rational expectations.
data	an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which simsar is called.

Details

For a complete information model, the outcome y_i is defined as:

y_i = \lambda \bar{y}_i + \mathbf{z}_i'\Gamma + \epsilon_i,

where \bar{y}_i is the average of y among peers, \mathbf{z}_i is a vector of control variables, and \epsilon_i \sim N(0, \sigma^2). In the case of incomplete information models with rational expectations, y_i is defined as:

y_i = \lambda E(\bar{y}_i) + \mathbf{z}_i'\Gamma + \epsilon_i.

Value

A list consisting of:

y	the observed count data.
Gy	the average of y among friends.

References

Lee, L. F. (2004). Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models. Econometrica, 72(6), 1899-1925, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/j.1468-0262.2004.00558.x")}.

Lee, L. F., Liu, X., & Lin, X. (2010). Specification and estimation of social interaction models with network structures. The Econometrics Journal, 13(2), 145-176, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/j.1368-423X.2010.00310.x")}

See Also

sar, simsart, simcdnet.

Examples

# Groups' size
set.seed(123)
M      <- 5 # Number of sub-groups
nvec   <- round(runif(M, 100, 1000))
n      <- sum(nvec)

# Parameters
lambda <- 0.4
Gamma  <- c(2, -1.9, 0.8, 1.5, -1.2)
sigma  <- 1.5
theta  <- c(lambda, Gamma, sigma)

# X
X      <- cbind(rnorm(n, 1, 1), rexp(n, 0.4))

# Network
G      <- list()

for (m in 1:M) {
  nm           <- nvec[m]
  Gm           <- matrix(0, nm, nm)
  max_d        <- 30
  for (i in 1:nm) {
    tmp        <- sample((1:nm)[-i], sample(0:max_d, 1))
    Gm[i, tmp] <- 1
  }
  rs           <- rowSums(Gm); rs[rs == 0] <- 1
  Gm           <- Gm/rs
  G[[m]]       <- Gm
}

# data
data   <- data.frame(X, peer.avg(G, cbind(x1 = X[,1], x2 =  X[,2])))
colnames(data) <- c("x1", "x2", "gx1", "gx2")

ytmp    <- simsar(formula = ~ x1 + x2 + gx1 + gx2, Glist = G, 
                  theta = theta, data = data) 
y       <- ytmp$y

CDatanet documentation built on June 22, 2024, 11:14 a.m.