A Three-Stage randomized response model is proposed to estimate the proportions of the individuals having two related sensitive characteristics. The first-stage is constructed to include the first device to estimate the proportion of the individuals having the first sensitive characteristic. The second-stage is designed to include the second device to estimate the proportion of the individuals having the second sensitive characteristic. The third-stage is sketched to include the third device to estimate the proportion of the individuals having both related sensitive characteristics at the same time. Estimates of the parameters of the suggested model are obtained by using Maximum Likelihood method and Non-Linear programming with Newton-Raphson methods. Since the Maximum Likelihood method may give inadmissible estimates of the parameters of randomized response models, so the Non-Linear programming with Newton-Raphson methods are used to manipulate this problem. The conditional proportions , i.e. the proportions of the individuals having the second sensitive characteristic among those having or not having the first sensitive characteristic, their biases and variances are derived. MathCAD program is used to solve equations of the Non- Linear programming and to apply Newton-Raphson method. An application to the informal marriage and induced abortion among the female students in the University level is given. The Bootstrap technique is used to calculate the estimated expected values of the estimators of all parameters of the suggested models. SPSS program is used to draw the Bootstrapped samples from the original sample. The study showed that the Maximum Likelihood method and Non-Linear programming with Newton-Raphson methods gave the same estimates of the parameters of the first and second devices. Maximum Likelihood method gave inadmissible estimates of the parameters of the third device |
