Triangular Model and Two of Its Variants Under Stratified Sampling
Keywords:
Estimation of proportion, maximum likelihood estimation, non-randomized response technique, triangular modelAbstract
The non-randomized response (NRR) technique is a procedure that can be used in surveys with sensitive questions, and it has many advantages over the randomized response (RR) technique such as the ease of implementation and the ability to be used in self-administrated surveys as no random device is required. Many NRR models were developed to increase the efficiency and/or increase the respondents’ cooperation such as the triangular model and the alternating triangular model. In this paper, we extended the triangular model and two of its variants; the alternating triangular model and the triangular model under non-compliance; to stratified random sampling. The maximum likelihood estimation method was employed to estimate the population proportion possessing the sensitive attribute under each of the three extended models. Unbiased estimators of the sensitive proportion were derived and their sampling variances were obtained. In addition, the optimal allocation of the sample size for the three extended models was derived.
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