New improved poisson and negative binomial item count techniques for eliciting truthful answers to sensitive questions

Item count techniques (ICTs) are indirect survey questioning methods designed to deal with sensitive features. These techniques have gained the support of many applied researchers and undergone further theoretical development. Latterly in the literature, two new item count methods, called Poisson and negative binomial ICTs, have been proposed. However, if the population parameters of the control variable are not provided by the outside source, the methods are not very efficient. Efficiency is an important issue in indirect methods of questioning due to the fact that the protection of respondents' privacy is usually achieved at the expense of the efficiency of the estimation. In the present paper we propose new improved Poisson and negative binomial ICTs, in which two control variables are used in both groups, although in a different manner. In the paper we analyse best linear unbiased and maximum likelihood estimators of the proportion of the sensitive attribute in the population in the introduced new models. The theoretical findings presented in the paper are supported by a comprehensive simulation study. The improved procedure allowed the increase of the efficiency of the estimation compared to the original Poisson and negative binomial ICTs.