Maximum Likelihood (ML) estimates of the parameters of the three-stage randomized response model, suggested by Guirguis (2011), are presented. Since the Maximum Likelihood method may give inadmissible estimates of the parameters of the randomized response models, So Guirguis (2011) used the methods of Non-Linear programming with Newton-Raphson to estimate the parameters of the suggested model by him. Estimating the parameters of the model, using Lagrange Multipliers with Newton-Raphson methods, is very difficult, especially, when the number of parameters of a sensitive characteristic, or the number of sensitive characteristics, is more than one. So application of the EM algorithm is presented to find the Maximum Likelihood estimates of the parameters of the model. It is shown that one can apply the EM algorithm by viewing the observations from the model as incomplete data. A general formulation of EM algorithm is sketched for the model. An application to the EM algorithm procedures, to the same case study in Guirguis (2011), of the informal marriage and induced abortion among the female students in the University level is given. Comparison between the Maximum Likelihood estimates of the parameters and their estimated variances of the model, using Maximum Likelihood, Lagrange Multipliers with Newton-Raphson and EM algorithm techniques, is given |
