Statistical Modelling 10 (2010), 57–67
The randomized response log linear model as a composite link model
Ardo van den Hout
MRC Biostatistics Unit
Institute of Public Health
Cambridge
UK
eMail: ardo.vandenhout@mrc-bsu.cam.ac.uk
Robert Gilchrist
STORM Research Centre
London Metropolitan University
London
UK
Peter GM van der Heijden
Department of Methodology and Statistics
Utrecht University
Utrecht
The Netherlands
Abstract:
In randomized response (RR) designs, misclassification is used to
protect the privacy of respondents when sensitive questions are asked.
A generalized linear model with a composite link function is presented
to formulate log linear models that take the RR design into account.
The approach is extended to model the situation where some respondents
do not follow the instructions of the RR design. For example, if there
are three binary RR variables with regard to practicing fraud, the
2 x 2 x 2 cross-classification of the true answers is latent due to
the misclassification. Using composite link functions, log linear
models can be specified for the latent table to investigate possible
association between the variables. Fast iteratively re-weighted least
squares algorithms are presented.
Keywords:
iteratively re-weighted least squares;
misclassification; sensitive questions
back