simsart: Simulate data from the Tobit Model with Social Interactions

In CDatanet: Modeling Count Data with Peer Effects

Simulate data from the Tobit Model with Social Interactions

Description

simsart is used to simulate censored data with social interactions (see details). The model is presented in Xu and Lee(2015).

Usage

simsart(
  formula,
  contextual,
  Glist,
  theta,
  tol = 1e-15,
  maxit = 500,
  RE = FALSE,
  data
)

Arguments

formula	an object of class formula: a symbolic description of the model. The formula should be as for example y ~ x1 + x2 | x1 + x2 where y is the endogenous vector, the listed variables before the pipe, x1, x2 are the individual exogenous variables and the listed variables after the pipe, x1, x2 are the contextual observable variables. Other formulas may be y ~ x1 + x2 for the model without contextual effects, y ~ -1 + x1 + x2 | x1 + x2 for the model without intercept or y ~ x1 + x2 | x2 + x3 to allow the contextual variable to be different from the individual variables.
contextual	(optional) logical; if true, this means that all individual variables will be set as contextual variables. Set the formula as y ~ x1 + x2 and contextual as TRUE is equivalent to set the formula as y ~ x1 + x2 | x1 + x2.
Glist	the adjacency matrix or list sub-adjacency matrix.
theta	the parameter value as \theta = (\lambda, \beta, \gamma, \sigma). The parameter \gamma should be removed if the model does not contain contextual effects (see details).
tol	the tolerance value used in the Fixed Point Iteration Method to compute y. The process stops if the L_1 distance between two consecutive values of y is less than tol.
maxit	the maximal number of iterations in the Fixed Point Iteration Method.
RE	a Boolean which indicates if the model if under rational expectation of not.
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 mcmcARD is called.

Details

The left-censored variable \mathbf{y} is generated from a latent variable \mathbf{y}^*. The latent variable is given for all i as

y_i^* = \lambda \mathbf{g}_i y + \mathbf{x}_i'\beta + \mathbf{g}_i\mathbf{X}\gamma + \epsilon_i,

where \epsilon_i \sim N(0, \sigma^2).
The censored variable y_i is then define that is y_i = 0 if y_i^* \leq 0 and y_i = y_i^* otherwise.

Value

A list consisting of:

yst	ys (see details), the latent variable.
y	the censored variable.
yb	expectation of y under rational expectation.
Gy	the average of y among friends.
Gyb	Average of expectation of y among friends under rational expectation.
marg.effects	the marginal effects.
iteration	number of iterations performed by sub-network in the Fixed Point Iteration Method.

References

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

See Also

sart, simsar, simcdnet.

Examples

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

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

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

# Network
Glist  <- 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
  Glist[[m]]   <- Gm
}


# data
data    <- data.frame(x1 = X[,1], x2 =  X[,2])

rm(list = ls()[!(ls() %in% c("Glist", "data", "theta"))])

ytmp    <- simsart(formula = ~ x1 + x2 | x1 + x2, Glist = Glist,
                   theta = theta, data = data)

y       <- ytmp$y

# plot histogram
hist(y)

CDatanet documentation built on Aug. 12, 2023, 1:06 a.m.