CDatanet (version 2.2.1)

simsart: Simulating Data from Tobit Models with Social Interactions

Description

simsart simulates censored data with social interactions (see Xu and Lee, 2015).

Usage

simsart(formula, Glist, theta, tol = 1e-15, maxit = 500, cinfo = TRUE, data)

Value

A list consisting of:

yst

\(y^{\ast}\), the latent variable.

y

The observed censored variable.

Ey

\(E(y)\), the expected value of \(y\).

Gy

The average of \(y\) among peers.

GEy

The average of \(E(y)\) among peers.

meff

A list including average and individual marginal effects.

iteration

The number of iterations performed per sub-network in the fixed-point iteration method.

Arguments

formula

a class object formula: a symbolic description of the model. formula must be, for example, y ~ x1 + x2 + gx1 + gx2, where y is the endogenous vector, and x1, x2, gx1, and gx2 are control variables. These 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 the details).

tol

the tolerance value used in the fixed-point iteration method to compute y. The process stops if the \(\ell_1\)-distance between two consecutive values of y is less than tol.

maxit

the maximum number of iterations in the fixed-point iteration method.

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 simsart is called.

Details

For a complete information model, the outcome \(y_i\) is defined as: $$\begin{cases} y_i^{\ast} = \lambda \bar{y}_i + \mathbf{z}_i'\Gamma + \epsilon_i, \\ y_i = \max(0, y_i^{\ast}), \end{cases}$$ 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: $$\begin{cases} y_i^{\ast} = \lambda E(\bar{y}_i) + \mathbf{z}_i'\Gamma + \epsilon_i, \\ y_i = \max(0, y_i^{\ast}). \end{cases}$$

References

Xu, X., & Lee, L. F. (2015). Maximum likelihood estimation of a spatial autoregressive Tobit model. Journal of Econometrics, 188(1), 264-280, tools:::Rd_expr_doi("10.1016/j.jeconom.2015.05.004").

See Also

sart, simsar, simcdnet.

Examples

# \donttest{
# Define group sizes
set.seed(123)
M      <- 5 # Number of sub-groups
nvec   <- round(runif(M, 100, 200)) # Number of nodes per sub-group
n      <- sum(nvec) # Total number of nodes

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

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

# Construct network adjacency matrices
G      <- list()
for (m in 1:M) {
  nm           <- nvec[m] # Nodes in sub-group m
  Gm           <- matrix(0, nm, nm) # Initialize adjacency matrix
  max_d        <- 30 # Maximum degree
  for (i in 1:nm) {
    tmp        <- sample((1:nm)[-i], sample(0:max_d, 1)) # Random connections
    Gm[i, tmp] <- 1
  }
  rs           <- rowSums(Gm) # Normalize rows
  rs[rs == 0]  <- 1
  Gm           <- Gm / rs
  G[[m]]       <- Gm
}

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

# Complete information game simulation
ytmp    <- simsart(formula = ~ x1 + x2 + gx1 + gx2, 
                   Glist = G, theta = theta, 
                   data = data, cinfo = TRUE)
data$yc <- ytmp$y # Add simulated outcome to the dataset

# Incomplete information game simulation
ytmp    <- simsart(formula = ~ x1 + x2 + gx1 + gx2, 
                   Glist = G, theta = theta, 
                   data = data, cinfo = FALSE)
data$yi <- ytmp$y # Add simulated outcome to the dataset
# }