direct function

Inference on Average Direct Effect Parameters

Inference on the average direct effect of the IV on the outcome, that on the treatment receipt, and the local average direct effect in the presence of network spillover of unknown form

direct(
  Y,
  D,
  Z,
  IEM = NULL,
  S,
  A,
  K = 1,
  t = NULL,
  bw = NULL,
  B = NULL,
  alp = 0.05
)

Arguments

• Y: An n-dimensional outcome vector
• D: An n-dimensional binary treatment vector
• Z: An n-dimensional binary instrumental vector
• IEM: An n-dimensional instrumental exposure vector. If IEM = NULL or t = NULL, the constant IEM is used. Default is NULL.
• S: An n-dimensional logical vector to indicate whether each unit belongs to the sub-population S
• A: An n times n symmetric binary adjacency matrix
• K: A scalar to indicate the range of neighborhood used for constructing the interference set. Default is 1. In the direct() function, K is used only for computing the bandwidth.
• t: A scalar of the evaluation point of IEM. Default is NULL.
• bw: A scalar of the bandwidth used for the HAC estimation and the wild bootstrap. If bw = NULL, the rule-of-thumb bandwidth proposed by Leung (2022) is used. Default is NULL.
• B: The number of bootstrap repetitions. If B = NULL, the wild bootstrap is skipped. Default is NULL.
• alp: The significance level. Default is 0.05.

Returns

A data.frame containing the following elements: - est: The parameter estimate

• HAC_SE: The standard error computed by the network HAC estimation

• HAC_CI_L: The lower bound of the confidence interval computed by the network HAC estimation

• HAC_CI_U: The upper bound of the confidence interval computed by the network HAC estimation

• wild_SE: The standard error computed by the wild bootstrap

• wild_CI_L: The lower bound of the confidence interval computed by the wild bootstrap

• wild_CI_U: The upper bound of the confidence interval computed by the wild bootstrap

• bw: The bandwidth used for the HAC estimation and the wild bootstrap

• size: The size of the subpopulation S

Details

The direct() function estimates the average direct effect of the IV on the outcome, that on the treatment receipt, and the local average direct effect via inverse probability weighting in the approximate neighborhood interference framework. The function also computes the standard errors and the confidence intervals for the target parameters based on the network HAC estimation and the wild bootstrap. For more details, see Hoshino and Yanagi (2023). The lengths of Y, D, Z, S and of the row and column of A must be the same. IEM must be NULL or a vector of the same length as Y. t must be NULL or a value in the support of IEM. K must be a positive integer. bw must be NULL or a non-negative integer. B must be NULL or a positive number. alp must be a positive number between 0 and 0.5.

Examples

# Generate artificial data
set.seed(1)
n <- 2000
data <- latenetwork::datageneration(n = n)

# Arguments
Y   <- data$Y
D   <- data$D
Z   <- data$Z
IEM <- data$IEM
S   <- rep(TRUE, n)
A   <- data$A
K   <- 1
t   <- 0
bw  <- NULL
B   <- NULL
alp <- 0.05

# Estimation
latenetwork::direct(Y = Y,
                    D = D,
                    Z = Z,
                    IEM = IEM,
                    S = S,
                    A = A,
                    K = K,
                    t = t,
                    bw = bw,
                    B = B,
                    alp = alp)

References

Hoshino, T., & Yanagi, T. (2023). Causal inference with noncompliance and unknown interference. arXiv preprint arXiv:2108.07455.

Leung, M.P. (2022). Causal inference under approximate neighborhood interference. Econometrica, 90(1), pp.267-293.