propensityForest {causalTree} | R Documentation

## Propensity Forest for Causal Effect Regression and Estimation (Modified Causal Tree Ensembles)

### Description

Fit and evaluate a user selected number of `causalTree` models to get an ensemble of `rpart` objects Trees are split using covariates and the treatment vector instead of the outcome variable, and evaluated using the complete data covariates and the actual outcome variable.

### Usage

    propensityForest(formula, data, treatment,
                             na.action,
                             split.Rule, split.Honest, split.Bucket, bucketNum,
                             bucketMax, cv.option, cv.Honest, minsize,
                             propensity, control, split.alpha, cv.alpha,

                             sample.size.total, sample.size.train.frac = 1,
                             mtry, nodesize, num.trees,ncolx,ncov_sample)

### Arguments

`formula` | a formula, with a response and features but no interaction terms. If this a a data frome, that is taken as the model frame (see `model.frame).`
`data` | an optional data frame that includes the variables named in the formula.
`weights` | optional case weights.
`treatment` | a vector that indicates the treatment status of each observation. 1 represents treated and 0 represents control. Only binary treatment supported in this version.
`na.action` | the default action deletes all observations for which `y` is missing, but keeps those in which one or more predictors are missing.
`split.Rule` | causalTree splitting options, one of `"TOT"`, `"CT"`, `"fit"`, `"tstats"`, four splitting rules in causalTree. Note that the `"tstats"` alternative does not have an associated cross-validation method `cv.option`; see Athey and Imbens (2016) for a discussion. Note further that `split.Rule` and `cv.option` can mix and match.
`split.Honest` | boolean option, `TRUE` or `FALSE`, used for `split.Rule` as `"CT"` or `"fit"`. If set as `TRUE`, do honest splitting, with default `split.alpha` = 0.5; if set as `FALSE`, do adaptive splitting with `split.alpha` = 1. The user choice of `split.alpha` will be ignored if `split.Honest` is set as `FALSE`, but will be respected if set to `TRUE`. For `split.Rule`=`"TOT"`, there is no honest splitting option and the parameter `split.alpha` does not matter. For `split.Rule`=`"tstats"`, a value of `TRUE` enables use of `split.alpha` in calculating the risk function, which determines the order of pruning in cross-validation. Note also that causalTree function returns the estimates from the training data, no matter what the value of `split.Honest` is; the tree must be re-estimated to get the honest estimates using `estimate.causalTree`. The wrapper function `honest.CausalTree` does honest estimation in one step and returns a tree.
`split.Bucket` | boolean option, `TRUE` or `FALSE`, used to specify whether to apply the discrete method in splitting the tree. If set as `TRUE`, in splitting a node, the observations in a leaf will be be partitioned into buckets, with each bucket containing `bucketNum` treated and `bucketNum` control units, and where observations are ordered prior to partitioning. Splitting will take place by bucket.
`bucketNum` | number of observations in each bucket when set `split.Bucket` = `TRUE`. However, the code will override this choice in order to guarantee that there are at least `minsize` and at most `bucketMax` buckets.
`bucketMax` | Option to choose maximum number of buckets to use in splitting when set `split.Bucket` = `TRUE`, `bucketNum` can change by choice of `bucketMax`.
`cv.option` | cross validation options, one of `"TOT"`, `"matching"`, `"CT"`, `"fit"`, four cross validation methods in causalTree. There is no `cv.option` for the `split.Rule` `"tstats"`; see Athey and Imbens (2016) for discussion.
`cv.Honest` | boolean option, `TRUE` or `FALSE`, only used for `cv.option` as `"CT"` or `"fit"`, to specify whether to apply honest risk evalation function in cross validation. If set `TRUE`, use honest risk function, otherwise use adaptive risk function in cross validation. If set `FALSE`, the user choice of `cv.alpha` will be set to 1. If set `TRUE`, `cv.alpha` will default to 0.5, but the user choice of `cv.alpha` will be respected. Note that honest cv estimates within-leaf variances and may perform better with larger leaf sizes and/or small number of cross-validation sets.
`minsize` | in order to split, each leaf must have at least `minsize` treated cases and `minsize` control cases. The default value is set as 2.
`propensity` | propensity score used in `"TOT"` splitting and `"TOT"`, honest `"CT"` cross validation methods. The default value is the proportion of treated cases in all observations. In this implementation, the propensity score is a constant for the whole dataset. Unit-specific propensity scores are not supported; however, the user may use inverse propensity scores as case weights if desired.
`control` | a list of options that control details of the `rpart` algorithm. See `rpart.control`.
`split.alpha` | scale parameter between 0 and 1, used in splitting risk evaluation function for `"CT"`. When `split.Honest = FALSE`, `split.alpha` will be set as 1. For `split.Rule`=`"tstats"`, if `split.Honest`=`TRUE`, `split.alpha` is used in calculating the risk function, which determines the order of pruning in cross-validation.
`cv.alpha` | scale paramter between 0 and 1, used in cross validation risk evaluation function for `"CT"` and `"fit"`. When `cv.Honest = FALSE`, `cv.alpha` will be set as 1.
`cost` | a vector of non-negative costs, one for each variable in the model. Defaults to one for all variables. These are scalings to be applied when considering splits, so the improvement on splitting on a variable is divided by its cost in deciding which split to choose.
`sample.size.total` | Sample size used to build each tree in the forest (sampled randomly with replacement)
`sample.size.train.frac` | Fraction of the sample size used for building each tree (training)
`mtry` | Number of data features used to build a tree (This variable is not used presently)
`nodesize` | Minimum number of observations for treated and control cases in one leaf node
`num.trees` | Number of trees to be built in the causal forest
`ncolx` | Total number of covariates
`ncov_sample` | Number of covariates randomly sampled to build each tree in the forest
`...` | arguments to `rpart.control` may also be specified in the call to `causalForest`. They are checked against the list of valid arguments. An example of a commonly set parameter would be `xval`, which sets the number of cross-validation samples. The parameter `minsize` is implemented differently in `causalTree` than in rpart; we require a minimum of `minsize` treated observations and a minimum of `minsize` control observations in each leaf.

### Details

Propensity forest is similar to a causal forest, with some important differences as discussed below. The causalForest builds an ensemble of CausalTrees, by repeated random sampling of the data with replacement. For prediction, the average value over all tree predictions is used. Propensity forest differs from a causal forest in the following way: The tree building phase is done by using the covariates and treatment vector as the dummy output/outcomes variable (instead of the actual outcomes variable) During the tree evaluation phase, the reestimation error is calculated on the actual outcomes variable to evaluate the tree performance. Note that the propensity forest will always build an adaptive (non honest) ensemble of trees.

CausalTree differs from `rpart` function from rpart package in splitting rules and cross validation methods. Please check Athey and Imbens, Recursive Partitioning for Heterogeneous Causal Effects (2016) and Stefan Wager and Susan Athey, Estimation and Inference of Heterogeneous Treatment Effects using Random Forests for more details.

### Value

An object of class `rpart`. See `rpart.object`.

### References

Breiman L., Friedman J. H., Olshen R. A., and Stone, C. J. (1984) Classification and Regression Trees. Wadsworth.

Athey, S and G Imbens (2016) Recursive Partitioning for Heterogeneous Causal Effects. http://arxiv.org/abs/1504.01132

Wager,S and Athey, S (2015) Estimation and Inference of Heterogeneous Treatment Effects using Random Forests http://arxiv.org/abs/1510.04342

### See Also

`honest.causalTree`, `rpart.control`, `rpart.object`, `summary.rpart`, `rpart.plot`

### Examples

    pf <- propensityForest(as.formula(paste("y~",f)), data=dataTrain, treatment=dataTrain$w,
                       split.Bucket=F,
                       sample.size.total = floor(nrow(dataTrain) / 2),
                       mtry = ceiling(ncol(dataTrain)/3), nodesize = 25, num.trees=num.trees.temp,ncolx=ncolx,ncov_sample=ncov_sample)

    pfpredtest <- predict(pf, newdata=dataTest, type="vector")
    plot(dataTest$tau_true,pfpredtest)

    pfpredtrainall <- predict(pf, newdata=dataTrain, predict.all = TRUE, type="vector")

[Package causalTree version 0.0 Index]