bcf: Fit Bayesian Causal Forests

In bcf: Causal Inference for a Binary Treatment and Continuous Outcome using Bayesian Causal Forests

Description

Fit Bayesian Causal Forests

Usage

bcf(y, z, x_control, x_moderate = x_control, pihat, nburn, nsim, nthin = 1,
  update_interval = 100, ntree_control = 200, sd_control = 2 * sd(y),
  base_control = 0.95, power_control = 2, ntree_moderate = 50,
  sd_moderate = sd(y), base_moderate = 0.25, power_moderate = 3, nu = 3,
  lambda = NULL, sigq = 0.9, sighat = NULL, include_pi = "control",
  use_muscale = TRUE, use_tauscale = TRUE)

Arguments

y	Response variable
z	Treatment variable
x_control	Design matrix for the "prognostic" function mu(x)
x_moderate	Design matrix for the covariate-dependent treatment effects tau(x)
pihat	Length n estimates of
nburn	Number of burn-in MCMC iterations
nsim	Number of MCMC iterations to save after burn-in
nthin	Save every nthin'th MCMC iterate. The total number of MCMC iterations will be nsim*nthin + nburn.
update_interval	Print status every update_interval MCMC iterations
ntree_control	Number of trees in mu(x)
sd_control	SD(mu(x)) marginally at any covariate value (or its prior median if use_muscale=TRUE)
base_control	Base for tree prior on mu(x) trees (see details)
power_control	Power for the tree prior on mu(x) trees
ntree_moderate	Number of trees in tau(x)
sd_moderate	SD(tau(x)) marginally at any covariate value (or its prior median if use_tauscale=TRUE)
base_moderate	Base for tree prior on tau(x) trees (see details)
power_moderate	Power for the tree prior on tau(x) trees (see details)
nu	Degrees of freedom in the chisq prior on sigma^2
lambda	Scale parameter in the chisq prior on sigma^2
sigq	Calibration quantile for the chisq prior on sigma^2
sighat	Calibration estimate for the chisq prior on sigma^2
include_pi	Takes values "control", "moderate", "both" or "none". Whether to include pihat in mu(x) ("control"), tau(x) ("moderate"), both or none. Values of "control" or "both" are HIGHLY recommended with observational data.
use_muscale	Use a half-Cauchy hyperprior on the scale of mu.
use_tauscale	Use a half-Normal prior on the scale of tau.

Details

Fits the Bayesian Causal Forest model (Hahn et. al. 2018): For a response variable y, binary treatment z, and covariates x,

y_i = μ(x_i, π_i) + τ(x_i, π_i)z_i + ε_i

where π_i is an (optional) estimate of the propensity score \Pr(Z_i=1 | X_i=x_i) and ε_i \sim N(0,σ^2)

Some notes:

• x_control and x_moderate must be numeric matrices. See e.g. the makeModelMatrix function in the dbarts package for appropriately constructing a design matrix from a data.frame

• sd_control and sd_moderate are the prior SD(mu(x)) and SD(tau(x)) at a given value of x (respectively). If use_muscale = FALSE, then this is the parameter σ_μ from the original BART paper, where the leaf parameters have prior distribution N(0, σ_μ/m), where m is the number of trees. If use_muscale=TRUE then sd_control is the prior median of a half Cauchy prior for SD(mu(x)). If use_tauscale = TRUE, then sd_moderate is the prior median of a half Normal prior for SD(tau(x)).

• By default the prior on σ^2 is calibrated as in Chipman, George and McCulloch (2008).

Value

A list with elements

tau	nsim by n matrix of posterior samples of individual treatment effects
mu	nsim by n matrix of posterior samples of individual treatment effects
sigma	Length nsim vector of posterior samples of sigma

References

Hahn, Murray, and Carvalho(2017). Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects. https://arxiv.org/abs/1706.09523. (Call citation("bcf") from the command line for citation information in Bibtex format.)

Examples

# data generating process
p = 3 #two control variables and one moderator
n = 250
#
set.seed(1)

x = matrix(rnorm(n*p), nrow=n)

# create targeted selection
q = -1*(x[,1]>(x[,2])) + 1*(x[,1]<(x[,2]))

# generate treatment variable
pi = pnorm(q)
z = rbinom(n,1,pi)

# tau is the true (homogeneous) treatment effect
tau = (0.5*(x[,3] > -3/4) + 0.25*(x[,3] > 0) + 0.25*(x[,3]>3/4))

# generate the response using q, tau and z
mu = (q + tau*z)

# set the noise level relative to the expected mean function of Y
sigma = diff(range(q + tau*pi))/8

# draw the response variable with additive error
y = mu + sigma*rnorm(n)

# If you didn't know pi, you would estimate it here
pihat = pnorm(q)

bcf_fit = bcf(y, z, x, x, pihat, nburn=2000, nsim=2000)

# Get posterior of treatment effects
tau_post = bcf_fit$tau
tauhat = colMeans(tau_post)
plot(tau, tauhat); abline(0,1)

bcf documentation built on Jan. 19, 2022, 1:08 a.m.