Optimal Allocation of the Sample in the Poisson Item Count Technique
DOI:
https://doi.org/10.18778/0208-6018.335.03Keywords:
optimal allocation, latent variable, EM algorithm, sensitive question, indirect questioning, Poisson item count techniqueAbstract
Indirect methods of questioning are of utmost importance when dealing with sensitive questions. This paper refers to the new indirect method introduced by Tian et al. (2014) and examines the optimal allocation of the sample to control and treatment groups. If determining the optimal allocation is based on the variance formula for the method of moments (difference in means) estimator of the sensitive proportion, the solution is quite straightforward and was given in Tian et al. (2014). However, maximum likelihood (ML) estimation is known from much better properties, therefore determining the optimal allocation based on ML estimators has more practical importance. This problem is nontrivial because in the Poisson item count technique the study sensitive variable is a latent one and is not directly observable. Thus ML estimation is carried out by using the expectation‑maximisation (EM) algorithm and therefore an explicit analytical formula for the variance of the ML estimator of the sensitive proportion is not obtained. To determine the optimal allocation of the sample based on ML estimation, comprehensive Monte Carlo simulations and the EM algorithm have been employed.
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Additional Files
- Relationship between size n_2 and rank of estimator regarding its RMSE for moment (left) and ML (right) estimators and different set of model parameters.
- Comparison of the root mean square error (RMSE) of estimators for moment estimation (dotted line) and ML estimation (solid line) for λ=2 and π=0,2.
- The fragment of the root mean square error of ML estimators for λ=2 and π=0,2.
- Exemplary quadratic interpolation (dotted line) on the fragment of the root mean square error of ML estimators (solid line) for λ=2 and π=0,2 based on the results corresponding to the treatment group sizes: 96, 112 and 128 (black dots).
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