The logistic regression model with response variables subject to randomized response

The univariate and multivariate logistic regression model is discussed where response variables are subject to randomized response (RR). RR is an interview technique that can be used when sensitive questions have to be asked and respondents are reluctant to answer directly. RR variables may be described as misclassified categorical variables where conditional misclassification probabilities are known. The univariate model is revisited and is presented as a generalized linear model. Standard software can be easily adjusted to take into account the RR design. The multivariate model does not appear to have been considered elsewhere in an RR setting; it is shown how a Fisher scoring algorithm can be used to take the RR aspect into account. The approach is illustrated by analyzing RR data taken from a study in regulatory non-compliance regarding unemployment benefit.