The logistic regression model with response variables subject to randomized response

Abstract

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.

The statistical analysis of cheating paradigms

“…and can be estimated by standard maximization routines (for details, see Scheers & Dayton, 1988;van den Hout, van der Heijden, & Gilchrist, 2007). The resulting regression coefficients can be interpreted as usual-that is, as the change in the logit of dishonesty given a unit change in the predictor.…”

Innovative Techniques for Estimating Illegal Activities in a Human-Wildlife-Management Conflict

“…By using a customized link function [35], [48] the logistic regression model was adapted in order to investigate the relationship of indirect measures of behaviour (PQ estimates and BIAT D-scores) with our ‘best-measure’ of farmers' involvement in illegal badger killing captured by RRT. In our first fitted model PQ estimates were positively related to RRT response; as farmers' estimates of their peers' badger killing behaviour increased, as too did the probability that they themselves admitted to killing badgers.…”

“…The GLM used a customized link function incorporating the known probabilities of the forced RRT responses [35], [48]. To investigate the effectiveness of PQ estimates and BIAT D-scores at predicting badger killing behaviour GLMs incorporating either PQ estimates or BIAT D-scores were statistically compared (likelihood ratio test) to a null model.…”

New scrambled response models for estimating the mean of a sensitive quantitative character

“…This information can be used at the design stage of a survey or directly at the estimation stage or at both phases. Many authors have dealt with the problem of the efficient use of auxiliary variables but works relating auxiliary information to RR methods are still scarce and mainly concerned with the logistic model [27]. Besides these, we mention the works by Chaudhuri and Mukerjee [3], Allen and Singh [1] and Grewal et al [11], which treated randomized models in the Downloaded by [New York University] at 21:45 14 May 2015 context of sampling with unequal probabilities, and Diana and Perri [4,5], who discussed the use of a single auxiliary variable for quantitative and qualitative sensitive data by introducing classes of estimators.…”