An Alternating Parallel Non-Randomized Response Model

A new non-randomized response model is proposed. The proposed model, referred to as the alternating parallel non-randomized response model, is built on relaxing one of the assumptions of the parallel non-randomized response model. The proposed model considers the case where the probability of one of the non-sensitive questions in the parallel model is unknown. An estimator of the proportion of the sensitive attribute is derived based on the proposed model using the maximum likelihood estimation method. An efficiency comparison between the proposed model and a variant of the parallel model is then carried out and the combinations of the parameters for which the proposed model is more efficient are determined. A main advantage of the alternating parallel model is that it outperforms the variant of the parallel model when the probability of belonging to the sensitive group is small.