Abstract
In this paper, we extended Yennum et al.’s model, in which geometric distribution is used as a randomization device for a population that consists of different-sized clusters, and clusters are obtained by probability proportional to size (PPS) sampling. Estimators of a sensitive parameter, their variances, and their variance estimators are derived under PPS sampling and equal probability two-stage sampling, respectively. We also applied these sampling schemes to Yennum et al.’s generalized model. Numerical studies were carried out to compare the efficiencies of the proposed sampling methods for each case of Yennum et al.’s model and Yennum et al.’s generalized model.
Highlights
The randomized response model (RRM) was suggested by [1] to estimate the true population proportion of sensitive characteristics, such as illegal gambling, drug-abuse, tax evasion, the extent of illegal income, and the experience of abortion, among others [2,3,4].Since Warner’s work, many scholars have developed the RRM in various ways
Yennum et al.’s model via proportional sampling by considering the primary sampling unit as the school and the secondary sampling unit as the students. From this point of view, we extend Yennum et al.’s model, in which geometric distribution is used as a randomization device based on a population that consists of different-sized clusters, and the clusters are selected by proportional to size (PPS) sampling
We consider Yennum et al.’s generalized model, in which generalized geometric distribution is used as a randomization device when n clusters are sampled by PPS sampling or equal probability sampling from the population, which consists of N clusters with size Mi (i = 1, 2, · · ·, N ), and mi (i = 1, 2, · · ·, n) units are drawn by simple random sampling from each sampled cluster
Summary
The randomized response model (RRM) was suggested by [1] to estimate the true population proportion of sensitive characteristics, such as illegal gambling, drug-abuse, tax evasion, the extent of illegal income, and the experience of abortion, among others [2,3,4]. Yennum et al.’s model via proportional sampling by considering the primary sampling unit as the school and the secondary sampling unit as the students From this point of view, we extend Yennum et al.’s model, in which geometric distribution is used as a randomization device based on a population that consists of different-sized clusters, and the clusters are selected by PPS sampling.
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