uplift (version 0.3.5)

ccif: Causal Conditional Inference Forest

Description

ccif implements recursive partitioning in a causal conditional inference framework.

Usage

"ccif"(formula, data, ...)
"ccif"(
x, 
y, 
ct, 
mtry = floor(sqrt(ncol(x))), 
ntree = 100, 
split_method = c("ED", "Chisq", "KL", "L1", "Int"), 
interaction.depth = NULL, 
pvalue = 0.05, 
bonferroni = FALSE, 
minsplit = 20, 
minbucket_ct0 = round(minsplit/4),
minbucket_ct1 = round(minsplit/4), 
keep.inbag = FALSE, 
verbose = FALSE, 
...)
"print"(x, ...)

Arguments

data

A data frame containing the variables in the model. It should include a variable reflecting the binary treatment assignment of each observation (coded as 0/1).

x, formula

a data frame of predictors or a formula describing the model to be fitted. A special term of the form trt() must be used in the model equation to identify the binary treatment variable. For example, if the treatment is represented by a variable named treat, then the right hand side of the formula must include the term +trt(treat).

y

a binary response (numeric) vector.

ct

a binary (numeric) vector representing the treatment assignment (coded as 0/1).

mtry

the number of variables to be tested in each node; the default is floor(sqrt(ncol(x))).

ntree

the number of trees to generate in the forest; default is ntree = 100.

split_method

the split criteria used at each node of each tree; Possible values are: "ED" (Euclidean distance), "Chisq" (Chi-squared divergence), "KL" (Kullback-Leibler divergence), "Int" (Interaction method).

interaction.depth

The maximum depth of variable interactions. 1 implies an additive model, 2 implies a model with up to 2-way interactions, etc.

pvalue

the maximum acceptable pvalue required in order to make a split.

bonferroni

apply a bonferroni adjustment to pvalue.

minsplit

the minimum number of observations that must exist in a node in order for a split to be attempted.

minbucket_ct0

the minimum number of control observations in any terminal node.

minbucket_ct1

the minimum number of treatment observations in any terminal node.

keep.inbag

if set to TRUE, an nrow(x) by ntree matrix is returned, whose entries are the "in-bag" samples in each tree.

verbose

print status messages?

...

Additional arguments passed to independence_test{coin}. See details.

Value

An object of class ccif, which is a list with the following components:

call

the original call to ccif

trees

the tree structure that was learned

split_method

the split criteria used at each node of each tree

ntree

the number of trees used

mtry

the number of variables tested at each node

var.names

a character vector with the name of the predictors

var.class

a character vector containing the class of each predictor variable

inbag

an nrow(x) by ntree matrix showing the in-bag samples used by each tree

Details

Causal conditional inference trees estimate personalized treatment effects (a.k.a. uplift) by binary recursive partitioning in a conditional inference framework. Roughly, the algorithm works as follows: 1) For each terminal node in the tree we test the global null hypothesis of no interaction effect between the treatment $T$ and any of the $n$ covariates selected at random from the set of $p$ covariates ($n \leq p$). Stop if this hypothesis cannot be rejected. Otherwise select the input variable with strongest interaction effect. The interaction effect is measured by a p-value corresponding to a permutation test (Strasser and Weber, 1999) for the partial null hypothesis of independence between each input variable and a transformed response. Specifically, the response is transformed so the impact of the input variable on the response has a causal interpretation for the treatment effect (see details in Guelman et al. 2013) 2) Implement a binary split in the selected input variable. 3) Recursively repeate steps 1) and 2).

The independence test between each input and the transformed response is performed by calling independence_test{coin}. Additional arguments may be passed to this function via `$\ldots$'.

All split methods are described in Guelman et al. (2013a, 2013b).

This function is very slow at the moment. It was built as a prototype in R. A future version of this package will provide an interface to C++ for this function, which is expected to significantly improve speed.

References

Guelman, L., Guillen, M., and Perez-Marin A.M. (2013a). Uplift random forests. Cybernetics & Systems, forthcoming.

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

Hothorn, T., Hornik, K. and Zeileis, A. (2006).Unbiased recursive partitioning: A conditional inference framework. Journal of Computational and Graphical Statistics, 15(3): 651-674.

Strasser, H. and Weber, C. (1999). On the asymptotic theory of permutation statistics. Mathematical Methods of Statistics, 8: 220-250.

Examples

library(uplift)

### Simulate train data

set.seed(12345)
dd <- sim_pte(n = 100, p = 6, rho = 0, sigma =  sqrt(2), beta.den = 4)

dd$treat <- ifelse(dd$treat == 1, 1, 0) 

### Fit model

form <- as.formula(paste('y ~', 'trt(treat) +', paste('X', 1:6, sep = '', collapse = "+"))) 

fit1 <- ccif(formula = form,
             data = dd, 
             ntree = 50, 
             split_method = "Int",
             distribution = approximate (B=999),
             pvalue = 0.05,
             verbose = TRUE)
print(fit1)
summary(fit1)