View source: R/homophily.fixed.R
homophily.FE | R Documentation |
homophily.FE
is used to estimate a network formation model with homophily. The model includes degree heterogeneity as fixed effects (see details).
homophily.FE(
network,
formula,
data,
init = NULL,
opt.ctr = list(maxit = 300, eps_f = 1e-06, eps_g = 1e-05),
print = TRUE
)
network |
matrix or list of sub-matrix of social interactions containing 0 and 1, where links are represented by 1 |
formula |
an object of class formula: a symbolic description of the model. The |
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 |
init |
(optional) either a list of starting values containing |
opt.ctr |
(optional) is a list of |
print |
Boolean indicating if the estimation progression should be printed. |
Let p_{ij}
be a probability for a link to go from the individual i
to the individual j
.
This probability is specified as
p_{ij} = F(\mathbf{x}_{ij}'\beta + \mu_j + \nu_j)
where F
is the cumulative of the standard normal distribution. Unobserved degree heterogeneity is captured by
\mu_i
and \nu_j
. The latter are treated as fixed effects. As shown by Yan et al. (2019), the estimator of
the parameter \beta
is biased. A bias correction is then necessary and is not implemented in this version. However
the estimator of \mu_i
and \nu_j
are consistent.
A list consisting of:
n |
number of individuals in each network. |
n.obs |
number of observations. |
n.links |
number of links. |
K |
number of explanatory variables. |
estimate |
maximizer of the log-likelihood. |
loglike |
maximized log-likelihood. |
optim |
returned value of the optimization solver, which contains details of the optimization. The solver used is |
init |
returned list of starting value. |
loglike(init) |
log-likelihood at the starting value. |
Yan, T., Jiang, B., Fienberg, S. E., & Leng, C. (2019). Statistical inference in a directed network model with covariates. Journal of the American Statistical Association, 114(526), 857-868, \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.1080/01621459.2018.1448829")}.
homophily
.
set.seed(1234)
M <- 2 # Number of sub-groups
nvec <- round(runif(M, 20, 50))
beta <- c(.1, -.1)
Glist <- list()
dX <- matrix(0, 0, 2)
mu <- list()
nu <- list()
Emunu <- runif(M, -1.5, 0) #expectation of mu + nu
smu2 <- 0.2
snu2 <- 0.2
for (m in 1:M) {
n <- nvec[m]
mum <- rnorm(n, 0.7*Emunu[m], smu2)
num <- rnorm(n, 0.3*Emunu[m], snu2)
X1 <- rnorm(n, 0, 1)
X2 <- rbinom(n, 1, 0.2)
Z1 <- matrix(0, n, n)
Z2 <- matrix(0, n, n)
for (i in 1:n) {
for (j in 1:n) {
Z1[i, j] <- abs(X1[i] - X1[j])
Z2[i, j] <- 1*(X2[i] == X2[j])
}
}
Gm <- 1*((Z1*beta[1] + Z2*beta[2] +
kronecker(mum, t(num), "+") + rlogis(n^2)) > 0)
diag(Gm) <- 0
diag(Z1) <- NA
diag(Z2) <- NA
Z1 <- Z1[!is.na(Z1)]
Z2 <- Z2[!is.na(Z2)]
dX <- rbind(dX, cbind(Z1, Z2))
Glist[[m]] <- Gm
mu[[m]] <- mum
nu[[m]] <- num
}
mu <- unlist(mu)
nu <- unlist(nu)
out <- homophily.FE(network = Glist, formula = ~ -1 + dX)
muhat <- out$estimate$mu
nuhat <- out$estimate$nu
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