# Conduct Randomization Inference This function makes it easy to conduct three kinds of randomization inference. ```r conduct_ri( formula = NULL, model_1 = NULL, model_2 = NULL, test_function = NULL, assignment = "Z", outcome = NULL, declaration = NULL, sharp_hypothesis = 0, studentize = FALSE, IPW = TRUE, IPW_weights = NULL, sampling_weights = NULL, permutation_matrix = NULL, data, sims = 1000, progress_bar = FALSE, p = "two-tailed" ) ``` ## Arguments - `formula`: an object of class formula, as in `lm`. Use formula when conducting significance tests of an Average Treatment Effect estimate under a sharp null hypothesis. For the difference-in-means estimate, do not include covariates. For the OLS covariate-adjusted estimate, include covariates. - `model_1`: an object of class formula, as in `lm`. Models 1 and 2 must be "nested." model_1 should be the "restricted" model and model_2 should be the "unrestricted" model. - `model_2`: an object of class formula, as in `lm`. Models 1 and 2 must be "nested." model_1 should be the "restricted" model and model_2 should be the "unrestricted" model. - `test_function`: A function that takes data and returns a scalar test statistic. - `assignment`: a character string that indicates which variable is randomly assigned. Defaults to "Z". - `outcome`: a character string that indicates which variable is the outcome variable. Defaults to NULL. - `declaration`: A random assignment declaration, created by `declare_ra`. - `sharp_hypothesis`: either a numeric scalar or a numeric vector of length k - 1, where k is the number of treatment conditions. In a two-arm trial, this number is the *hypothesized* difference between the treated and untreated potential potential outcomes for each unit.. In a multi-arm trial, each number in the vector is the hypothesized difference in potential outcomes between the baseline condition and each successive treatment condition. - `studentize`: logical, defaults to FALSE. Should the test statistic be the t-ratio rather than the estimated ATE? T-ratios will be calculated using HC2 robust standard errors or their clustered equivalent. CLUSTERING NOT YET IMPLEMENTED. - `IPW`: logical, defaults to TRUE. Should inverse probability weights be calculated? - `IPW_weights`: a character string that indicates which variable is the existing inverse probability weights vector. Usually unnecessary, as IPW weights will be incorporated automatically if IPW = TRUE. Defaults to NULL. - `sampling_weights`: a character string that indicates which variable is the sampling weights vector. Optional, defaults to NULL. NOT YET IMPLEMENTED - `permutation_matrix`: An optional matrix of random assignments, typically created by `obtain_permutation_matrix`. - `data`: A data.frame. - `sims`: the number of simulations. Defaults to 1000. - `progress_bar`: logical, defaults to FALSE. Should a progress bar be displayed in the console? - `p`: Should "two-tailed", "upper", or "lower" p-values be reported? Defaults to "two-tailed". For two-tailed p-values, whether or not a simulated value is as large or larger than the observed value is determined with respect to the distance to the sharp null. ## Details 1. Conduct hypothesis tests under the sharp null when the test statistic is the difference-in-means or covariate-adjusted average treatment effect estimate. 2. Conduct "ANOVA" style hypothesis tests, where the f-statistic from two nested models is the test statistic. This procedure is especially helpful when testing interaction terms under null of constant effects. 3. Arbitrary (scalar) test statistics ## Examples ```r # Data from Gerber and Green Table 2.2 # Randomization Inference for the Average Treatment Effect table_2.2 <- data.frame(d = c(1, 0, 0, 0, 0, 0, 1), y = c(15, 15, 20, 20, 10, 15, 30)) ## Declare randomization procedure declaration <- declare_ra(N = 7, m = 2) # out <- conduct_ri(y ~ d, declaration = declaration, assignment = "d", sharp_hypothesis = 0, data = table_2.2) summary(out) plot(out) tidy(out) # Using a custom permutation matrix permutation_matrix <- matrix(c(0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0), ncol = 7) conduct_ri(y ~d, assignment = "d", data = table_2.2, permutation_matrix = permutation_matrix) # Randomization Inference for an Interaction N <- 100 declaration <- randomizr::declare_ra(N = N, m = 50) Z <- randomizr::conduct_ra(declaration) X <- rnorm(N) Y <- .9 * X + .2 * Z + 1 * X * Z + rnorm(N) dat <- data.frame(Y, X, Z) ate_obs <- coef(lm(Y ~ Z, data = dat))[2] out <- conduct_ri( model_1 = Y ~ Z + X, model_2 = Y ~ Z + X + Z * X, declaration = declaration, assignment = "Z", sharp_hypothesis = ate_obs, data = dat, sims = 100 ) plot(out) summary(out) summary(out, p = "two-tailed") summary(out, p = "upper") summary(out, p = "lower") tidy(out) # Randomization Inference for arbitrary test statistics ## In this example we're conducting a randomization check (in this case, a balance test). N <- 100 declaration <- randomizr::declare_ra(N = N, m = 50) Z <- randomizr::conduct_ra(declaration) X <- rnorm(N) Y <- .9 * X + .2 * Z + rnorm(N) dat <- data.frame(Y, X, Z) balance_fun <- function(data) { f_stat <- summary(lm(Z ~ X, data = data))$f[1] names(f_stat) <- NULL return(f_stat) } ## confirm function works as expected balance_fun(dat) ## conduct randomization inference out <- conduct_ri( test_function = balance_fun, declaration = declaration, assignment = "Z", sharp_hypothesis = 0, data = dat, sims = 100 ) plot(out) summary(out) tidy(out) ```

conduct_ri function