sim_pte: Simulations for Personalized Treatment Effects
In uplift: Uplift Modeling

Description Usage Arguments Details Value Author(s) References Examples

Numerical simulation for treatment effect heterogeneity estimation as described in Tian et al. (2012)

1	sim_pte(n = 1000, p = 20, rho = 0, sigma = sqrt(2), beta.den = 4)

`n`	number of observations.
`p`	number of predictors.
`rho`	covariance between predictors.
`sigma`	multiplier of error term.
`beta.den`	size of main effects relative to interaction effects. See details.

sim_pte simulates data according to the following specification:

Y = I(∑_{j=1}^p β_{j}X_{j} + ∑_{j=1}^p γ_{j}X_{j}T +σ_{0}ε > 0)

where γ=(1/2,-1/2,1/2,-1/2, 0,...,0), β=(-1)^{j+1}I(3 ≤q j ≤q 10) / \code{beta.den}, (X_{1}, …, X_{p}) follows a mean zero multivariate normal distribution with a compound symmetric variance-covariance matrix, (1-ρ)\mathbf{I}_{p} +ρ \mathbf{1}^{T}\mathbf{1}, T=[-1,1] is the treatment indicator and ε is N(0,1).

In this case, the "true" treatment effect score (Prob(Y=1|T=1) - Prob(Y=1|T=-1)) is given by

Φ (\frac{∑_{j=1}^p (β_{j} + γ_{j})X_{j}}{σ_{0}}) - Φ (\frac{∑_{j=1}^p (β_{j} - γ_{j})X_{j}}{σ_{0}})

A data frame including the response variable (Y), the treatment (treat=1) and control (treat=-1) assignment, the predictor variables (X) and the "true" treatment effect score (ts)

Leo Guelman <leo.guelman@gmail.com>

Tian, L., Alizadeh, A., Gentles, A. and Tibshirani, R. 2012. A simple method for detecting interactions between a treatment and a large number of covariates. Submitted on Dec 2012. arXiv:1212.2995 [stat.ME].

Guelman, L., Guillen, M., and Perez-Marin A.M. (2013). Optimal personalized treatment rules for marketing interventions: A review of methods, a new proposal, and an insurance case study. Submitted.

library(uplift)
### Simulate train data

set.seed(12345)
dd <- sim_pte(n = 1000, p = 10, rho = 0, sigma =  sqrt(2), beta.den = 4)
dd$treat <- ifelse(dd$treat == 1, 1, 0) # required coding for upliftRF

### Fit model

form <- as.formula(paste('y ~', 'trt(treat) +', paste('X', 1:10, sep = '', collapse = "+"))) 

fit1 <- upliftRF(formula = form,
                 data = dd, 
                 ntree = 100, 
                 split_method = "Int",
                 interaction.depth = 3,
                 minsplit = 100, 
                 minbucket_ct0 = 50, 
                 minbucket_ct1 = 50,
                 verbose = TRUE)
summary(fit1)