, Volume 29, Issue 1, pp 76-90

A Property of the CHAID Partitioning Method for Dichotomous Randomized Response Data and Categorical Predictors

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In this paper, we present empirical and theoretical results on classification trees for randomized response data. We considered a dichotomous sensitive response variable with the true status intentionally misclassified by the respondents using rules prescribed by a randomized response method. We assumed that classification trees are grown using the Pearson chi-square test as a splitting criterion, and that the randomized response data are analyzed using classification trees as if they were not perturbed. We proved that classification trees analyzing observed randomized response data and estimated true data have a one-to-one correspondence in terms of ranking the splitting variables. This is illustrated using two real data sets.

Most of the research of Pier Francesco Perri was done during his stay at the Department of Methodology and Statistics, University of Utrecht (The Netherlands). His work was partly supported by the research voucher awarded by Regione Calabria, Italy.