Logistic regression analysis of non-randomized response data collected by the parallel model in sensitive surveys

To study the relationship between a sensitive binary response variable and a set of non-sensitive covariates, this paper develops a hidden logistic regression to analyse non-randomized response data collected via the parallel model originally proposed by Tian (2014). This is the first paper to employ the logistic regression analysis in the field of non-randomized response techniques. Both the Newton-Raphson algorithm and a monotone quadratic lower bound algorithm are developed to derive the maximum likelihood estimates of the parameters of interest. In particular, the proposed logistic parallel model can be used to study the association between a sensitive binary variable and another non-sensitive binary variable via the measure of odds ratio. Simulations are performed and a study on people's sexual practice data in the United States is used to illustrate the proposed methods.