TobitBART

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The goal of TobitBART is to provide implementations of type 1 and type 2 Tobit models with Bayesian Additive Regression Trees (Chipman et al. 2010) instead of linear combinations of covariates. Sums-of-trees are sampled using the dbarts package.

The Type 1 Tobit implementaiton is based on Chib (1992). The Type 2 Tobit implementaiton is based on Omori (2007), van Hasselt (2011), and Ding (2014).

The tbart1 function runs Type 1 TOBART.

The tbart1np function runs Type 1 TOBART with a Dirichlet Process mixture distribution for the error (George et al. 2019).

The softtbart1 function runs Type 1 TOBART with soft trees and a hyperprior on splitting variables for sparse data generating processes (Linero and Yang 2018).

The softtbart1np function runs Type 1 TOBART with with soft trees, a hyperprior on splitting variables for sparse data generating processes (Linero and Yang 2018), and a Dirichlet Process mixture distribution for the error (George et al. 2019).

The tbart2c function runs Type 2 TOBART with bivariate normal errors in the selection and outcome equations. [Not tested yet]

The tbart2np function runs nonparametric Type 2 TOBART. The errors in the selection and outcome equations are jointly distributed as a Dirichlet Process mixture of bivariate normal distributions. [Not tested yet]

The softtbart2 function runs Type 2 TOBART with bivariate normal errors in the selection and outcome equations, soft trees, and a hyperprior on splitting variables for sparse data generating processes (Linero and Yang 2018) . [Not tested yet]

The softtbart2np function runs nonparametric Type 2 TOBART with soft trees, and a hyperprior on splitting variables for sparse data generating processes (Linero and Yang 2018). The errors in the selection and outcome equations are jointly distributed as a Dirichlet Process mixture of bivariate normal distributions. [Not tested yet]

Chib, S. (1992). Bayes inference in the Tobit censored regression model. Journal of Econometrics, 51(1-2), 79-99.

Ding, P. (2014). Bayesian robust inference of sample selection using selection-t models. Journal of Multivariate Analysis, 124, 451-464.

George, E., Laud, P., Logan, B., McCulloch, R., & Sparapani, R. (2019). Fully nonparametric Bayesian additive regression trees. In Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part B (Vol. 40, pp. 89-110). Emerald Publishing Limited.

Linero, A. R., & Yang, Y. (2018). Bayesian regression tree ensembles that adapt to smoothness and sparsity. Journal of the Royal Statistical Society Series B: Statistical Methodology, 80(5), 1087-1110.

Omori, Y. (2007). Efficient Gibbs sampler for Bayesian analysis of a sample selection model. Statistics & probability letters, 77(12), 1300-1311.

Van Hasselt, M. (2011). Bayesian inference in a sample selection model. Journal of Econometrics, 165(2), 221-232.

Installation

You can install the development version of TobitBART like so:

library(devtools)

install.packages("dbarts")
install.packages("GIGrvg")
install.packages("Rfast")
install.packages("censReg")
install.packages("accelerometry")
install.packages("wrswoR")
install.packages("dqrng")
install_github("boennecd/fastncdf")
install_github("EoghanONeill/TobitBART")

Example

This is a basic example:

library(TobitBART)
## basic example code

#example taken from https://stats.idre.ucla.edu/r/dae/tobit-models/

dat <- read.csv("https://stats.idre.ucla.edu/stat/data/tobit.csv")

train_inds <- sample(1:200,190)
test_inds <- (1:200)[-train_inds]

ytrain <- dat$apt[train_inds]
ytest <- dat$apt[test_inds]

xtrain <- cbind(dat$read, dat$math)[train_inds,]
xtest <- cbind(dat$read, dat$math)[test_inds,]

tobart_res <- tbart1(xtrain,xtest,ytrain,
                     below_cens = -Inf,
                     above_cens = 800,
                     n.iter = 400,
                     n.burnin = 100)