COMPARISON OF SOME METHODS OF IMPROVING THE EFFICIENCY OF RANDOMIZED RESPONSE DESIGNS

Abstract

This work compares different randomized response designs by their measures of efficiency using the concept of Jeopardy Function. A population is divided into two sensitive groups, 𝐴 𝑎𝑛𝑑 𝐴𝐶 with unknown proportion 𝜋 𝑎𝑛𝑑 (1 − 𝜋), respectively. Considering a dichotomous response model where a typical response R is yes (say, y) or no (say, n). The conditional probabilities that a person R comes from individual of groups, 𝐴 𝑎𝑛𝑑 𝐴𝐶 , are 𝑃(𝑅|𝐴) 𝑎𝑛𝑑 𝑃(𝑅|𝐴𝐶 ), respectively. These probabilities are at the researcher’s disposal and are called Design probabilities. Taking into consideration these design probabilities, a natural measure was proposed and it was carried by 𝑅 𝑎𝑏𝑜𝑢𝑡 𝐴 𝑎𝑛𝑑 𝐴𝐶 , respectively. These measure are as follows: 𝑔(𝑅|𝐴) = 𝑃(𝑅|𝐴) 𝑃(𝑅|𝐴𝐶 ) ; 𝑔(𝑅|𝐴𝐶 ) = 1 𝑔(𝑅|𝐴) . Considering the Percentage Relative Efficiency of Mangat et al. (1995) and Bhargava and Singh (2002), defined by; 𝑃𝑅𝐸 = 𝑉(𝜋̂𝐵𝑆) 𝑉(𝜋̂𝑀) × 100, It is found that the Bhargava and Singh model is better than Mangat et al.’s model when 𝜋 > 1 2 , and when 𝜋 < 1 2 , Mangat et al.’s model is better than Bhargava and Singh’s model.