The Generalized Logistic Regression Estimator in a Finite Population Sampling without Replacement Setting with Randomized Response

The randomized response technique (RR), introduced by Warner (1965) was designed to avoid non-answers to questions about sensitive issues and protect the privacy of the interviewee. Sonic other randomized response techniques have been developed as the Mortons technique which was developed based on a finite population sampling without replacement. In this paper we are presenting an estimation of the population (total of individuals N) based on Mortons technique assisted for a logistic regression model and considering a specific sensitive characteristic A, with an auxiliary variable associated to the sensitive variable. Analyses were conducted assuming finite population sampling and based on the p-estimators theory through a model assisted estimator. In addition, we propose an estimator of the variance of the estimator, as well as the results of simulations showing that the model assisted estimator of the variance decreases compared with an estimator which depends of the sampling design.