Item count technique with a continuous or count control variable for analyzing sensitive questions in surveys

The paper introduces a new item count technique (ICT) for dealing with sensitive features. One of the aims of the proposed method is to eliminate both the "ceiling" and "floor" effects that can occur in the original ICT. In the new model, in contrast to the classical one and recently proposed models, the two groups into which the sample is split are treated similarly. Therefore, there is no traditional distinction between the control and treatment groups. The control variable can be either a qualitative count variable or a continuous variable. To our knowledge, ICT methods with continuous control have not been proposed before. Although our new model differs substantially in the approach, it requires only a slight modification of the questionnaire design, which in no way leaks respondents' privacy. Substantial gain in statistical efficiency is achieved as compared to the earlier proposed Poisson and negative binomial ICTs. The new method also reduces the bias of maximum likelihood estimators and allows to obtain bootstrap confidence intervals with a substantially smaller width. The statistical properties of the method are investigated theoretically and by simulations.