The Multi-category Parallel Model-design, Analysis And Applications

In the past few years, some non-randomized techniques were introduced to assist sample surveys containing sensitive questions. However, these existing non-randomized models, such as crosswise model, triangular model, hidden sensitive (HS) model and the multi-category triangular model, have some limitations in practise, especially for all these models ask for one of the outcomes of the sensitive variable Y is non-sensitive. In this disertation, we extend the newly introduced parallel model to the multi-category case. In this case, all categories of the sensitive variable can be sensitive or one of them is totally non-sensitive. The maximum likelihood estimators (MLEs) of parameters which we are interested in and the corresponding covariance matrix are calculated. We further consider the parameters’confidence intervals (CI) as well as their Bayesian inferences. In addition, a special case of the multi-category parallel model is given, and we develop some numerical results. Furthermore, we also derive the very conditions when the multi-category parallel model is more effi-cient than the multi-category triangular model. Finally, we employ an example of cervical cancer to illustrate our proposed method. This paper is made up of eight parts:In Chapter One, we introduce some background of sample survey with sensitive questions. Furthermore, we show the relevant research progress of the randomized response techniques and the non-randomized response approaches which were intro-duced in recent years;In Chapter Two, we give some basic concepts and the basic model about the multi-categories parallel model;In Chapter Three, we discuss the likelihood-based statistical inferences of the multi-category parallel model:In Chapter Four, we give the Bayes-based statistical inferences of the multi-category parallel model;In Chapter Five, we discuss the four-category parallel model, which is a special case of the multi-category parallel model;In Chapter Six, we compare the multi-category parallel model with the multi-category triangular model, and give the condition when the former model is more efficient than the later model;In Chapter Seven, we employ the example of cervical cancer to illustrate the multi-category parallel model;In Chapter Eight, we make a conclusion for the multi-category parallel model.