syn.ctree, syn.cart: Synthesis with classification and regression trees (CART)

Description

Generates univariate synthetic data using classification and regression trees (without or with bootstrap).

Usage

syn.ctree(y, x, xp, smoothing, proper = FALSE, minbucket = 5, ...)
syn.cart(y, x, xp, smoothing, proper = FALSE, minbucket = 5, cp = 1e-04, ...)

Arguments

an original data vector of length n.

a matrix (n x p) of original covariates.

a matrix (k x p) of synthesised covariates.

smoothing

smoothing method for continuous variables.

proper

for proper synthesis (proper = TRUE) a CART model is fitted to a bootstrapped sample of the original data.

minbucket

the minimum number of observations in any terminal node. See rpart.control and ctree_control for details.

complexity parameter. Any split that does not decrease the overall lack of fit by a factor of cp is not attempted. See rpart.control for details.

...

additional parameters passed to ctree_control for syn.ctree and rpart.control for syn.cart.

Value

k with synthetic values of y.

Details

The procedure for synthesis by a CART model is as follows:

Fit a classification or regression tree by binary recursive partitioning.
For each xp find the terminal node.
Randomly draw a donor from the members of the node and take the observed value of y from that draw as the synthetic value.

syn.ctree uses ctree function from the party package and syn.cart uses rpart function from the rpart package. They differ, among others, in a selection of a splitting variable and a stopping rule for the splitting process. A Guassian kernel smoothing can be applied to continuous variables by setting smoothing parameter to "density". It is recommended as a tool to decrease the disclosure risk. Increasing minbucket is another means of data protection. CART models were suggested for generation of synthetic data by Reiter (2005) and then evaluated by Drechsler and Reiter (2011).

References

Reiter, J.P. (2005). Using CART to Generate Partially Synthetic, Public Use Microdata. Journal of Official Statistics, 21(3), 441--462. Drechsler, J. and Reiter, J.P. (2011). An empirical evaluation of easily implemented, nonparametric methods for generating synthetic datasets. Computational Statistics and Data Analysis, 55(12), 3232--3243.