# Marginal Effects for Count Data Models and Tobit Models with Social Interactions `meffects` computes marginal effects for count data and Tobit models with social interactions. It is a generic function which means that new printing methods can be easily added for new classes. ```r meffects(model, ...) ## S3 method for class 'cdnet' meffects( model, Glist, cont.var, bin.var, type.var, Glist.contextual, data, tol = 1e-10, maxit = 500, boot = 1000, progress = TRUE, ncores = 1, ... ) ## S3 method for class 'summary.cdnet' meffects( model, Glist, cont.var, bin.var, type.var, Glist.contextual, data, tol = 1e-10, maxit = 500, boot = 1000, progress = TRUE, ncores = 1, ... ) ## S3 method for class 'sart' meffects( model, Glist, cont.var, bin.var, type.var, Glist.contextual, data, tol = 1e-10, maxit = 500, boot = 1000, progress = TRUE, ncores = 1, ... ) ## S3 method for class 'summary.sart' meffects( model, Glist, cont.var, bin.var, type.var, Glist.contextual, data, tol = 1e-10, maxit = 500, boot = 1000, progress = TRUE, ncores = 1, ... ) ``` ## Arguments - `model`: an object of class `cdnet` (`summary.cdnet`) or `sart` (`summary.sart`), output of the function `cdnet` or `sart`, respectively. - `...`: Additional arguments passed to methods. - `Glist`: The network matrix used to obtain `model`. Typically, this is the `Glist` argument supplied to the function `cdnet` or `sart`. - `cont.var`: A character vector of continuous variable names for which the marginal effects should be computed. - `bin.var`: A character vector of binary variable names for which the marginal effects should be computed. - `type.var`: A list indicating "own" and contextual variables that appear in the `cont.var` and `bin.var` arguments. The list contains pairs of variable names, with the first element being the "own" variable and the second being the contextual variable. When a variable has no associated contextual variable, only the variable name is included. For example, `type.var = list(c("x1", "gx1"), c("x2", "gx2"), "x3")` means that `gx1` is the contextual variable for `x1`, `gx2` is the contextual variable for `x2`, and `x3` has no contextual variable. This information is used to compute the indirect and total marginal effects for `x1`, `x2`, and `x3`. - `Glist.contextual`: The network matrix used to compute contextual variables, if any are specified in the `type.var` argument. For networks consisting of multiple subnets, `Glist` can be a list of subnets, where the `m`-th element is an `ns*ns` adjacency matrix, with `ns` denoting the number of nodes in the `m`-th subnet. - `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(model)`, typically the environment from which `meffects` is called. - `tol`: The tolerance value used in the fixed-point iteration method to compute `y`. The process stops if the $\ell_1$-distance between two consecutive values of `y` is less than `tol`. - `maxit`: The maximum number of iterations in the fixed-point iteration method. - `boot`: The number of bootstrap simulations to compute standard errors and confidence intervals. - `progress`: A logical value indicating whether the progress of the bootstrap simulations should be printed to the console. - `ncores`: Number of CPU cores (threads) used to run the bootstrap process in parallel. ## Returns A list containing: - **`info`**: General information about the model. - **`estimate`**: The Maximum Likelihood (ML) estimates of the parameters. - **`Ey`**: $E(y)$, the expected values of the endogenous variable. - **`GEy`**: The average of $E(y)$ among peers. - **`cov`**: A list containing covariance matrices (if `cov = TRUE`). - **`details`**: Additional outputs returned by the optimizer. - **`meffects`**: A list containing the marginal effects. ## Examples ```r #' set.seed(123) M <- 5 # Number of sub-groups nvec <- round(runif(M, 100, 200)) n <- sum(nvec) # Adjacency matrix A <- list() for (m in 1:M) { nm <- nvec[m] Am <- matrix(0, nm, nm) max_d <- 30 #maximum number of friends for (i in 1:nm) { tmp <- sample((1:nm)[-i], sample(0:max_d, 1)) Am[i, tmp] <- 1 } A[[m]] <- Am } Anorm <- norm.network(A) #Row-normalization # X X <- cbind(rnorm(n, 1, 3), rexp(n, 0.4)) # Two group: group <- 1*(X[,1] > 0.95) # Networks # length(group) = 2 and unique(sort(group)) = c(0, 1) # The networks must be defined as to capture: # peer effects of `0` on `0`, peer effects of `1` on `0` # peer effects of `0` on `1`, and peer effects of `1` on `1` G <- list() cums <- c(0, cumsum(nvec)) for (m in 1:M) { tp <- group[(cums[m] + 1):(cums[m + 1])] Am <- A[[m]] G[[m]] <- norm.network(list(Am * ((1 - tp) %*% t(1 - tp)), Am * ((1 - tp) %*% t(tp)), Am * (tp %*% t(1 - tp)), Am * (tp %*% t(tp)))) } # Parameters lambda <- c(0.2, 0.3, -0.15, 0.25) Gamma <- c(4.5, 2.2, -0.9, 1.5, -1.2) delta <- rep(c(2.6, 1.47, 0.85, 0.7, 0.5), 2) # Data data <- data.frame(X, peer.avg(Anorm, cbind(x1 = X[,1], x2 = X[,2]))) colnames(data) = c("x1", "x2", "gx1", "gx2") ytmp <- simcdnet(formula = ~ x1 + x2 + gx1 + gx2, Glist = G, Rbar = rep(5, 2), lambda = lambda, Gamma = Gamma, delta = delta, group = group, data = data) y <- ytmp$y hist(y, breaks = max(y) + 1) table(y) # Estimation est <- cdnet(formula = y ~ x1 + x2 + gx1 + gx2, Glist = G, Rbar = rep(5, 2), group = group, optimizer = "fastlbfgs", data = data, opt.ctr = list(maxit = 5e3, eps_f = 1e-11, eps_g = 1e-11)) meffects(est, Glist = G, data = data, cont.var = c("x1", "x2", "gx1", "gx2"), type.var = list(c("x1", "gx1"), c("x2", "gx2")), Glist.contextual = Anorm, boot = 100, ncores = 2) ```

meffects function