sar {CDatanet}R Documentation

Estimate SAR model

Description

sar is used to estimate peer effects continuous variables (see details). The model is presented in Lee(2004).

Usage

sar(
  formula,
  contextual,
  Glist,
  lambda0 = NULL,
  fixed.effects = FALSE,
  optimizer = "optim",
  opt.ctr = list(),
  print = TRUE,
  cov = TRUE,
  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.

lambda0

(optional) starting value of \lambda. The parameter \gamma should be removed if the model does not contain contextual effects (see details).

fixed.effects

logical; if true, group heterogeneity is included as fixed effects.

optimizer

is either nlm (referring to the function nlm) or optim (referring to the function optim). Other arguments of these functions such as, the control values and the method can be defined through the argument opt.ctr.

opt.ctr

list of arguments of nlm or optim (the one set in optimizer) such as control, method, ...

print

a Boolean indicating if the estimate should be printed at each step.

cov

a Boolean indicating if the covariance should be computed.

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

Model

The variable \mathbf{y} 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).

Value

A list consisting of:

info

list of general information on the model.

estimate

Maximum Likelihood (ML) estimator.

cov

covariance matrix of the estimate.

details

outputs as returned by the optimizer.

References

Lee, L. F. (2004). Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models. Econometrica, 72(6), 1899-1925, doi:10.1111/j.1468-0262.2004.00558.x.

See Also

sart, cdnet, simsar.

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

y       <- ytmp$y

# plot histogram
hist(y, breaks = max(y))

data    <- data.frame(yt = y, x1 = data$x1, x2 = data$x2)
rm(list = ls()[!(ls() %in% c("Glist", "data"))])

out     <- sar(formula = yt ~ x1 + x2, contextual = TRUE, 
                 Glist = Glist, optimizer = "optim", data = data)
summary(out)


[Package CDatanet version 2.1.2 Index]