A Property of the CHAID Partitioning Method for Dichotomous Randomized Response Data and Categorical Predictors |
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Authors: | Pier Francesco Perri Peter GM van der Heijden |
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Institution: | (1) Department of Mathematics, Washington University in Saint Louis, Campus Box 1146, One Brookings Drive, 63130 St. Louis, MO, USA;(2) Department of Statistics, University of Illinois at Urbana-Champaign, 725 S. Wright St., 61820 Champaign, IL, USA;(3) Department of Statistics, University of Illinois at Urbana-Champaign, 725 S. Wright Street, 61820 Champaign, IL, USA |
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Abstract: | 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. |
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