bartc {bartCause}R Documentation

Causal Inference using Bayesian Additive Regression Trees


Fits a collection of treatment and response models using the Bayesian Additive Regression Trees (BART) algorithm, producing estimates of treatment effects.


bartc(response, treatment, confounders, parametric, data, subset, weights,
      method.rsp = c("bart", "tmle", "p.weight"),
      method.trt = c("bart", "glm", "none"),
      estimand   = c("ate", "att", "atc"), = NULL,
      commonSup.rule = c("none", "sd", "chisq"),
      commonSup.cut  = c(NA_real_, 1, 0.05),
      args.rsp = list(), args.trt = list(),
      p.scoreAsCovariate = TRUE, use.ranef = TRUE, group.effects = FALSE,
      crossvalidate = FALSE,
      keepCall = TRUE, verbose = TRUE,
      seed = NA_integer_,



A vector of the outcome variable, or a reference to such in the data argument. Can be continuous or binary.


A vector of the binary treatment variable, or a reference to data.


A matrix or data frame of covariates to be used in estimating the treatment and response model. Can also be the right-hand-side of a formula (e.g. x1 + x2 + ...). The data argument will be searched if supplied.


The right-hand-side of a formula (e.g. x1 + x2 + (1 | g) ...) giving the equation of a parametric form to be used for estimating the mean structure. See the details section below.


An optional data frame or named list containing the response, treatment, and confounders.


An optional vector using to subset the data. Can refer to data if provided.


An optional vector of population weights used in model fitting and estimating the treatment effect. Can refer to data if provided.


A character string specifying which method to use when fitting the response surface and estimating the treatment effect. Options are: "bart" - fit the response surface with BART and take the average of the individual treatment effect estimates, "p.weight" - fit the response surface with BART but compute the treatment effect estimate by using a propensity score weighted sum of individual effects, and "tmle" - as above, but further adjust the individual estimates using the Targeted Minimum Loss based Estimation (TMLE) adjustment.


A character string specifying which method to use when fitting the treatment assignment mechanism, or a vector/matrix of propensity scores. Character string options are: "bart" - fit BART directly to the treatment variable, "glm" - fit a generalized linear model with a binomial response and all confounders added linearly, and "none" - do no propensity score estimation. Cannot be "none" if the response model requires propensity scores. When supplied as a matrix, it should be of dimensions equal to the number of observations times the number of samples used in any response model.


A character string specifying which causal effect to target. Options are "ate" - average treatment effect, "att" - average treatment effect on the treated, and "atc" - average treatment effect on the controls.

An optional factor that, when present, causes the treatment effect estimate to be calculated within each group.


Rule for exclusion of observations lacking in common support. Options are "none" - no suppression, "sd" - exclude units whose predicted counterfactual standard deviation is extreme compared to the maximum standard deviation under those units' observed treatment condition, where extreme refers to the distribution of all standard deviations of observed treatment conditions, "chisq" - exclude observations according to ratio of the variance of posterior predicted counterfactual to the posterior variance of the observed condition, having a Chi Squared distribution with one degree of freedom under the null hypothesis of have equal distributions.


Cutoffs for commonSup.rule. Ignored for "none", when commonSup.rule is "sd", refers to how many standard deviations of the distribution of posterior variance for counterfactuals an observation can be above the maximum of posterior variances for that treatment condition. When commonSup.rule is "chisq", is the p value used for rejection of the hypothesis of equal variances.


A logical such that when TRUE, the propensity score is added to the response model as a covariate. When used, this is equivalent to the 'ps-BART' method described by described by Hahn, Murray, and Carvalho.


Logical specifying if variable - when present - should be included as a "random" or "fixed" effect. If true, rbart will be used for BART models. Using random effects for treatment assignment mechanisms of type "glm" require that the lme4 package be available.


Logical specifying if effects should be calculated within groups if the variable is provided. Response methods of "tmle" and "p.weight" are such that if group effects are calculated, then the population effect is not provided.


A logical such that when FALSE, the call to bartc is not kept. This can reduce the amount of information printed by summary when passing in data as literals.


One of TRUE, FALSE, "trt", or "rsp". Enables code to attempt to estimate the optimal end-node sensitivity parameter. This uses a rudimentary Bayesian optimization routine and can be extremely slow.


A logical that when TRUE prints information as the model is fit.


Optional integer specifying the desired pRNG seed. It should not be needed when running single-threaded - set.seed will suffice, and can be used to obtain reproducible results when multi-threaded. See Reproducibility section of bart2.

args.rsp, args.trt, ...

Further arguments to the treatment and response model fitting algorithms. Arguments passed to the main function as ... will be used in both models. args.rsp and args.trt can be used to set parameters in a single fit, and will override other values. See glm and bart2 for reference.


bartc represents a collection of methods that primarily use the Bayesian Additive Regression Trees (BART) algorithm to estimate causal treatment effects with binary treatment variables and continuous or binary outcomes. This requires models to be fit to the response surface (distribution of the response as a function of treatment and confounders, p(Y(1), Y(0) | X) and optionally for treatment assignment mechanism (probability of receiving treatment, i.e. propensity score, Pr(Z = 1 | X)). The response surface model is used to impute counterfactuals, which may then be adjusted together with the propensity score to produce estimates of effects.

Similar to lm, models can be specified symbolically. When the data term is present, it will be added to the search path for the response, treatment, and confounders variables. The confounders must be specified devoid of any "left hand side", as they appear in both of the models.

Response Surface

The response surface methods included are:

Treatment Assignment

The treatment assignment models are:


bartc uses the stan4bart package, when available, to fit semi- parametric surfaces. Equations can be given as to lm. Grouping structures are also permitted, and use the syntax of lmer.


For a fitted model, the easiest way to analyze the resulting fit is to use the generics fitted, extract, and predict to analyze specific quantities and summary to aggregate those values into targets (e.g. ATE, ATT, or ATC).

Common Support Rules

Common support, or that the probability of receiving all treatment conditions is non-zero within every area of the covariate space (P(Z = 1 | X = x) > 0 for all x in the inferential sample), can be enforced by excluding observations with high posterior uncertainty. bartc supports two common support rules through commonSup.rule argument:

Special Arguments

Some default arguments are unconventional or are passed in a unique fashion.

Missing Data

Missingness is allowed only in the response. If some response values are NA, the BART models will be trained just for where data are available and those values will be used to make predictions for the missing observations. Missing observations are not used when calculating statistics for assessing common support, although they may still be excluded on those grounds. Further, missing observations may not be compatible with response method "tmle".


bartc returns an object of class bartcFit. Information about the object can be derived by using methods summary, plot_sigma, plot_est, plot_indiv, and plot_support. Numerical quantities are recovered with the fitted and extract generics. Predictions for new observations are obtained with predict.

Objects of class bartcFit are lists containing items:


character string specifying the method used to fit the response surface


character string specifying the method used to fit the treatment assignment mechanism


character string specifying the targeted causal effect


object containing the fitted response model


dbartsData object used when fitting the response model


object containing the fitted treatment model

optional factor vector containing the groups in which treatment effects are estimated


matrix or array of posterior samples of the treatment effect estimate


the vector of propensity scores used as a covariate in the response model, when applicable


matrix or array of posterior samples of the propensity score, when applicable


samples from the posterior of the expected value for individual responses under the observed treatment regime

samples from the posterior of the expected value for individual responses under the counterfactual treatment


character string giving the name of the treatment variable in the data of fit.rsp


vector of treatment assignments


how bartc was called


number of independent posterior sampler chains in response model


common support rule used for suppressing observations


common support parameter used to set cutoff when suppressing observations


vector of standard deviations of individual posterior predictors for observed treatment conditions

vector of standard deviations of individual posterior predictors for counterfactuals


logical vector expressing which observations are used when estimating treatment effects


logical for whether ranef models were used; only added when true


logical for whether group-level estimates are made; only added when true


a random seed for use when drawing from the posterior predictive distribution


Vincent Dorie:


Chipman, H., George, E. and McCulloch R. (2010) BART: Bayesian additive regression trees. The Annals of Applied Statistics 4(1), 266–298. The Institute of Mathematical Statistics. doi:10.1214/09-AOAS285.

Hill, J. L. (2011) Bayesian Nonparametric Modeling for Causal Inference. Journal of Computational and Graphical Statistics 20(1), 217–240. Taylor & Francis. doi:10.1198/jcgs.2010.08162.

Hill, J. L. and Su Y. S. (2013) Assessing Lack of Common Support in Causal Inference Using Bayesian Nonparametrics: Implications for Evaluating the Effect of Breastfeeding on Children's Cognitive Outcomes The Annals of Applied Statistics 7(3), 1386–1420. The Institute of Mathematical Statistics. doi:10.1214/13-AOAS630.

Carnegie, N. B. (2019) Comment: Contributions of Model Features to BART Causal Inference Performance Using ACIC 2016 Competition Data Statistical Science 34(1), 90–93. The Institute of Mathematical Statistics. doi:10.1214/18-STS682

Hahn, P. R., Murray, J. S., and Carvalho, C. M. (2020) Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects (with Discussion). Bayesian Analysis 15(3), 965–1056. International Society for Bayesian Analysis. doi:10.1214/19-BA1195.

See Also



## fit a simple linear model
n <- 100L
beta.z <- c(.75, -0.5,  0.25)
beta.y <- c(.5,   1.0, -1.5)
sigma <- 2

x <- matrix(rnorm(3 * n), n, 3)
tau <- rgamma(1L, 0.25 * 16 * rgamma(1L, 1 * 32, 32), 16)

p.score <- pnorm(x %*% beta.z)
z <- rbinom(n, 1, p.score)

mu.0 <- x %*% beta.y
mu.1 <- x %*% beta.y + tau

y <- mu.0 * (1 - z) + mu.1 * z + rnorm(n, 0, sigma)

# low parameters only for example
fit <- bartc(y, z, x, n.samples = 100L, n.burn = 15L, n.chains = 2L)

## example to show refitting under the common support rule
fit2 <- refit(fit, commonSup.rule = "sd")
fit3 <- bartc(y, z, x, subset = fit2$commonSup.sub,
              n.samples = 100L, n.burn = 15L, n.chains = 2L)

[Package bartCause version 1.0-6 Index]