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A property of the CHAID partitioning method for dichotomous randomized response data and categorical predictors

A property of the CHAID partitioning method for dichotomous randomized response data and categorical predictors
A property of the CHAID partitioning method for dichotomous randomized response data and categorical predictors
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
0176-4268
76-90
Perri, Pier Francesco
47d34ceb-e064-4704-a4c4-f16c1862e939
van der Heijden, Peter G.M.
85157917-3b33-4683-81be-713f987fd612
Perri, Pier Francesco
47d34ceb-e064-4704-a4c4-f16c1862e939
van der Heijden, Peter G.M.
85157917-3b33-4683-81be-713f987fd612

Perri, Pier Francesco and van der Heijden, Peter G.M. (2012) A property of the CHAID partitioning method for dichotomous randomized response data and categorical predictors. Journal of Classification, 29 (1), 76-90. (doi:10.1007/s00357-011-9094-8).

Record type: Article

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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Published date: 2012
Organisations: Statistical Sciences Research Institute

Identifiers

Local EPrints ID: 344645
URI: http://eprints.soton.ac.uk/id/eprint/344645
ISSN: 0176-4268
PURE UUID: de674c54-e1d7-4b53-8621-186deb941ca1
ORCID for Peter G.M. van der Heijden: ORCID iD orcid.org/0000-0002-3345-096X

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Date deposited: 07 Nov 2012 15:06
Last modified: 15 Mar 2024 03:46

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Author: Pier Francesco Perri

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