--- title: "Getting Started with the latenetwork Package" output: rmarkdown::html_vignette vignette: > %\VignetteIndexEntry{Getting Started with the latenetwork Package} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- ```{r, include = FALSE} knitr::opts_chunk$set( collapse = TRUE, comment = "#>" ) options(rmarkdown.html_vignette.check_title = FALSE) ``` ```{r setup, include = FALSE} library(latenetwork) ``` ## Introduction The **latenetwork** package provides tools for causal inference under noncompliance with treatment assignment and network interference of unknown form. The package enables to implement the instrumental variables (IV) estimation for the local average treatment effect (LATE) type parameters via inverse probability weighting (IPW) using the concept of instrumental exposure mapping (IEM) and the framework of approximate neighborhood interference (ANI). The parameters of interest are as follows. - The average direct effect (ADE) parameters: - The ADE of the IV on the outcome. - The ADE of the IV on the treatment receipt. - The local average direct effect (LADE). - The average indirect effect (AIE) parameters: - The AIE of the IV on the outcome. - The AIE of the IV on the treatment receipt. - The local average indirect effect (LAIE). - The average overall effect (AOE) parameters: - The AOE of the IV on the outcome. - The AOE of the IV on the treatment receipt. - The local average overall effect (LAOE). - The average spillover effect (ASE) parameters: - The ASE of the IV on the outcome. - The ASE of the IV on the treatment receipt. - The local average spillover effect (LASE). For more details on the identification and estimation methods, see the "Review of Causal Inference with Noncompliance and Unknown Interference" vignette with: `vignette("review", package = "latenetwork")`. ## Installation Get the package from CRAN: ```{r, eval = F, echo = T} install.packages("latenetwork") ``` or from GitHub: ```{r, eval = F, echo = T} # install.packages("devtools") # if needed devtools::install_github("tkhdyanagi/latenetwork", build_vignettes = TRUE) ``` ## Functions The **latenetwork** package provides the following functions: - `direct()`: Estimation and statistical inference for the ADE parameters. - `indirect()`: Estimation and statistical inference for the AIE parameters. - `overall()`: Estimation and statistical inference for the AOE parameters. - `spillover()`: Estimation and statistical inference for the ASE parameters. #### Arguments All package functions have the following arguments: - `Y`: An n-dimensional outcome vector. - `D`: An n-dimensional binary treatment vector. Set `D` to the same argument as `Z` if you would like to perform the intention-to-treat analysis only. - `Z`: An n-dimensional binary instrumental vector. - `S`: An n-dimensional logical vector of indicating whether each unit belongs to the sub-population on which the parameters of interest are defined. - `A`: An n times n symmetric binary adjacency matrix whose diagonal elements are 0. - `K`: A scalar of indicating the range of neighborhood used for constructing interference sets. Default is 1. - `bw`: A scalar of 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. The `direct()` function has the following additional arguments: - `IEM`: An n-dimensional instrumental exposure vector. If `t = NULL`, the constant IEM is used. Default is NULL. - `t`: A scalar of the evaluation point of the IEM. If `t = NULL`, the constant IEM is used. Default is NULL. The `spillover()` function has the following additional arguments: - `IEM`: An n-dimensional instrumental exposure vector. - `z`: A scalar of the evaluation point of the IV. - `t0`: A scalar of the evaluation point of the IEM (from). - `t1`: A scalar of the evaluation point of the IEM (to). #### Returns Each function returns a data.frame with the following elements: - `est`: The estimate of each parameter. - `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`: ## Example To run the following example, install the **igraph** package if needed. ```{r, eval = F, echo = T} # if needed -------------------------------------------------------------------- install.packages("igraph") ``` Generate artificial data from the `datageneration()` function. ```{r, eval = T, echo = T} # Generate artificial data from a ring network---------------------------------- set.seed(1) n <- 2000 data <- latenetwork::datageneration(n = n) ``` Perform the causal inference with: ```{r, eval = T, echo = T} # Arguments -------------------------------------------------------------------- Y <- data$Y D <- data$D Z <- data$Z A <- data$A IEM <- ifelse(A %*% Z > 0, 1, 0) S <- rep(TRUE, n) K <- 1 z <- 1 t <- 0 t0 <- 0 t1 <- 1 bw <- NULL B <- NULL alp <- 0.05 # Causal inference ------------------------------------------------------------- # The ADE parameters defined by IEM = (A %*% Z > 0) result_direct1 <- latenetwork::direct(Y = Y, D = D, Z = Z, IEM = IEM, S = S, A = A, K = K, t = t, bw = bw, B = B, alp = alp) # The ADE parameters defined by the constant IEM result_direct2 <- latenetwork::direct(Y = Y, D = D, Z = Z, IEM = NULL, S = S, A = A, K = K, t = NULL, bw = bw, B = B, alp = alp) # The AIE parameters defined by K = 1 result_indirect <- latenetwork::indirect(Y = Y, D = D, Z = Z, S = S, A = A, K = K, bw = bw, B = B, alp = alp) # The AOE parameters defined by K = 1 result_overall <- latenetwork::overall(Y = Y, D = D, Z = Z, S = S, A = A, K = K, bw = bw, B = B, alp = alp) # The ASE parameters defined by IEM = (A %*% Z > 0) result_spillover <- latenetwork::spillover(Y = Y, D = D, Z = Z, IEM = IEM, S = S, A = A, K = K, z = z, t0 = t0, t1 = t1, bw = bw, B = B, alp = alp) ``` You can see the estimation results with: ```{r, eval = T, echo = T} result_direct1 result_direct2 result_indirect result_overall result_spillover ``` ## References Hoshino, T. and Yanagi, T., 2023. Causal inference with noncompliance and unknown interference. arXiv preprint arXiv:2108.07455. [Link](https://doi.org/10.48550/arXiv.2108.07455) Leung, M.P. (2022). Causal inference under approximate neighborhood interference. Econometrica, 90(1), pp.267-293. [Link](https://doi.org/10.3982/ECTA17841)