sar {CDatanet} | R Documentation |

## Estimating linear-in-mean models with social interactions

### Description

`sar`

computes quasi-maximum likelihood estimators for linear-in-mean models with social interactions (see Lee, 2004 and Lee et al., 2010).

### Usage

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

### Arguments

`formula` |
a class object formula: a symbolic description of the model. |

`Glist` |
The network matrix. For networks consisting of multiple subnets, |

`lambda0` |
an optional starting value of |

`fixed.effects` |
a Boolean indicating whether group heterogeneity must be included as fixed effects. |

`optimizer` |
is either |

`opt.ctr` |
list of arguments of nlm or optim (the one set in |

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

`cov` |
a Boolean indicating if the covariance should be computed. |

`cinfo` |
a Boolean indicating whether information is complete ( |

`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 |

### 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:

`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.

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, doi:10.1111/j.1368-423X.2010.00310.x

### See Also

### 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)
data$y <- ytmp$y
out <- sar(formula = y ~ x1 + x2 + + gx1 + gx2, Glist = G,
optimizer = "optim", data = data)
summary(out)
```

*CDatanet*version 2.2.0 Index]