# Causal Paths Analysis `paths` estimates path-specific causal effects in the presence of $K(\geq 1)$ causally ordered mediators. It implements the pure imputation estimator and the imputation-based weighting estimator (when a propensity score model is provided) as detailed in Zhou and Yamamoto (2020). The user supplies the names of the treatment, outcome, mediator variables, $K+1$ fitted models characterizing the conditional mean of the outcome given treatment, pretreatment confounders, and varying sets of mediators, and a data frame containing all the variables. The function returns $K+1$ path-specific causal effects that together constitute the total treatment effect. When $K=1$, the path-specific causal effects are identical to the natural direct and indirect effects in standard causal mediation analysis. ```r paths( a, y, m, models, ps_model = NULL, data, nboot = 500, conf_level = 0.95, ... ) ## S3 method for class 'paths' print(x, digits = 3, ...) ``` ## Arguments - `a`: a character string indicating the name of the treatment variable. The treatment should be a binary variable taking either 0 or 1. - `y`: a character string indicating the name of the outcome variable. - `m`: a list of $K$ character vectors indicating the names of $K$ causally ordered mediators $M_1,\ldots, M_K$. - `models`: a list of $K+1$ fitted model objects describing how the outcome depends on treatment, pretreatment confounders, and varying sets of mediators, where $K$ is the number of mediators. * the first element is a baseline model of the outcome conditional on treatment and pretreatment confounders. * the $k$th element is an outcome model conditional on treatment, pretreatment confounders, and mediators $M_1,\ldots, M_{k-1}$. * the last element is an outcome model conditional on treatment, pretreatment confounders, and all of the mediators, i.e., $M_1,\ldots, M_K$. The fitted model objects can be of type `lm`, `glm`, `gbm`, `wbart`, or `pbart`. - `ps_model`: an optional propensity score model for treatment. It can be of type `glm`, `gbm`, `ps`, or `pbart`. When it is provided, the imputation-based weighting estimator is also used to compute path-specific causal effects. - `data`: a data frame containing all variables. - `nboot`: number of bootstrap iterations for estimating confidence intervals. Default is 500. - `conf_level`: the confidence level of the returned two-sided confidence intervals. Default is `0.95`. - `...`: additional arguments to be passed to `boot::boot`, e.g. `parallel` and `ncpus`. For the `print` method, additional arguments to be passed to `print.default` - `x`: a fitted model object returned by the `paths` function. - `digits`: minimal number of significant digits printed. ## Returns An object of class `paths`, which is a list containing the following elements - **pure**: estimates of direct and path-specific effects via $M_1, \ldots, M_K$ based on the pure imputation estimator. - **hybrid**: estimates of direct and path-specific effects via $M_1, \ldots, M_K$ based on the imputation-based weighting estimator. - **varnames**: a list of character strings indicating the names of the pretreatment confounders ($X$), treatment($A$), mediators ($M_1, \ldots, M_K$), and outcome ($Y$). - **formulas**: formulas for the outcome models. - **classes**: classes of the outcome models. - **families**: model families of the outcome models. - **args**: a list containing arguments of the outcome models. - **ps_formula**: formula for the propensity score model. - **ps_class**: class of the propensity score model. - **ps_family**: model family of the propensity score model. - **ps_args**: arguments of the propensity score model. - **data**: the original data. - **nboot**: number of bootstrap iterations. - **conf_level**: confidence level for confidence intervals. - **boot_out**: output matrix from the bootstrap iterations. - **call**: the matched call to the `paths` function. ## Examples ```r data(tatar) m1 <- c("trust_g1", "victim_g1", "fear_g1") m2 <- c("trust_g2", "victim_g2", "fear_g2") m3 <- c("trust_g3", "victim_g3", "fear_g3") mediators <- list(m1, m2, m3) formula_m0 <- annex ~ kulak + prosoviet_pre + religiosity_pre + land_pre + orchard_pre + animals_pre + carriage_pre + otherprop_pre + violence formula_m1 <- update(formula_m0, ~ . + trust_g1 + victim_g1 + fear_g1) formula_m2 <- update(formula_m1, ~ . + trust_g2 + victim_g2 + fear_g2) formula_m3 <- update(formula_m2, ~ . + trust_g3 + victim_g3 + fear_g3) formula_ps <- violence ~ kulak + prosoviet_pre + religiosity_pre + land_pre + orchard_pre + animals_pre + carriage_pre + otherprop_pre #################################################### using GLM #################################################### # outcome models glm_m0 <- glm(formula_m0, family = binomial("logit"), data = tatar) glm_m1 <- glm(formula_m1, family = binomial("logit"), data = tatar) glm_m2 <- glm(formula_m2, family = binomial("logit"), data = tatar) glm_m3 <- glm(formula_m3, family = binomial("logit"), data = tatar) glm_ymodels <- list(glm_m0, glm_m1, glm_m2, glm_m3) # propensity score model glm_ps <- glm(formula_ps, family = binomial("logit"), data = tatar) # causal paths analysis using glm # note: For illustration purposes only a small number of bootstrap replicates are used paths_glm <- paths(a = "violence", y = "annex", m = mediators, glm_ymodels, ps_model = glm_ps, data = tatar, nboot = 3) #################################################### using GBM #################################################### require(gbm) # outcome models gbm_m0 <- gbm(formula_m0, data = tatar, distribution = "bernoulli", interaction.depth = 3) gbm_m1 <- gbm(formula_m1, data = tatar, distribution = "bernoulli", interaction.depth = 3) gbm_m2 <- gbm(formula_m2, data = tatar, distribution = "bernoulli", interaction.depth = 3) gbm_m3 <- gbm(formula_m3, data = tatar, distribution = "bernoulli", interaction.depth = 3) gbm_ymodels <- list(gbm_m0, gbm_m1, gbm_m2, gbm_m3) # propensity score model via gbm gbm_ps <- gbm(formula_ps, data = tatar, distribution = "bernoulli", interaction.depth = 3) # causal paths analysis using gbm # note: For illustration purposes only a small number of bootstrap replicates are used paths_gbm <- paths(a = "violence", y = "annex", m = mediators, gbm_ymodels, ps_model = gbm_ps, data = tatar, nboot = 3) ``` ## References Zhou, Xiang and Teppei Yamamoto. 2020. "[Tracing Causal Paths from Experimental and Observational Data](https://osf.io/2rx6p)". ## See Also `summary.paths`, `plot.paths`, `sens`

paths function