Incomplete Categorical Data Design

Non-Randomized Response Techniques for Sensitive Questions in Surveys

By Guo-Liang Tian, Man-Lai Tang

© 2013 – Chapman and Hall/CRC

319 pages | 37 B/W Illus.

Purchasing Options:
Hardback: 9781439855331
pub: 2013-08-16
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About the Book

Respondents to survey questions involving sensitive information, such as sexual behavior, illegal drug usage, tax evasion, and income, may refuse to answer the questions or provide untruthful answers to protect their privacy. This creates a challenge in drawing valid inferences from potentially inaccurate data. Addressing this difficulty, non-randomized response approaches enable sample survey practitioners and applied statisticians to protect the privacy of respondents and properly analyze the gathered data.

Incomplete Categorical Data Design: Non-Randomized Response Techniques for Sensitive Questions in Surveys is the first book on non-randomized response designs and statistical analysis methods. The techniques covered integrate the strengths of existing approaches, including randomized response models, incomplete categorical data design, the EM algorithm, the bootstrap method, and the data augmentation algorithm.

A self-contained, systematic introduction, the book shows you how to draw valid statistical inferences from survey data with sensitive characteristics. It guides you in applying the non-randomized response approach in surveys and new non-randomized response designs. All R codes for the examples are available at


"The strong points of this text are the timing (it is the first book on its topic) and the fact that it uses both Bayesian and frequentist procedures for solving these interesting problems. The level of mathematical detail appears appropriate for Ph.D. students in statistics or related disciplines. I believe the text will be useful for self-study by scientists and statisticians, and potentially useful in some applied courses or as a supplement to a more theoretical course …"

Journal of the American Statistical Association, March 2015

"For all these models and generalizations thereof, a detailed discourse of hypothesis testing, estimation, large sample inference, and findings from finite sample simulation is presented. Examples accompany the discussion models and methodologies, making the book quite self-contained. The book contains, nonetheless, a comprehensive list of references in the area. … The book provides an in-depth description of all aspects surrounding inferences and analyses of the different methods to deal with sensitive survey questions. When this is added to the knowledge of conducting interviews with specific subject subgroups, one is well equipped to conduct a survey with the least possible bias."

International Statistical Review, 82, 2014

Table of Contents


Randomized Response Models

Item Count Techniques

Non-Randomized Response Models

Scope of the Rest of the Book

The Crosswise Model

The Warner Model

A Non-Randomized Warner Model: The Crosswise Model

Bayesian Methods for the Crosswise Model

Analyzing the Induced Abortion Data

An Experimental Survey Measuring Plagiarism

The Triangular Model

The Triangular Design

Comparison with the Warner Model

Asymptotic Properties of the MLE

Bayesian Methods for the Triangular Model

Analyzing the Sexual Behavior Data

Case Studies on Premarital Sexual Behavior

Sample Sizes for the Crosswise and Triangular Models

Precision and Power Analysis Methods

The Triangular Model for One-Sample Problem

The Crosswise Model for One-Sample Problem

Comparison for the Crosswise and Triangular Models

The Triangular Model for Two-Sample Problem

An Example

The Multi-Category Triangular Model

A Brief Literature Review

The Survey Design

Likelihood-Based Inferences

Bayesian Inferences

Questionnaire on Sexual Activities in Korean Adolescents

The Hidden Sensitivity Model


The Survey Design

Likelihood-Based Inferences

Information Loss and Design Consideration

Simulation Studies

Bayesian Inferences under Dirichlet Prior

Bayesian Inferences under Other Priors

Analyzing HIV Data in an AIDS Study

The Parallel Model

The Unrelated Question Model

A Non-Randomized Unrelated Question Model: The Parallel Model

Comparison with the Crosswise Model

Comparison with the Triangular Model

Bayesian Inferences

An Example: Induced Abortion in Mexico

A Case Study on College Students’ Premarital Sexual Behavior at Wuhan

A Case Study on Plagiarism at The University of Hong Kong


Sample Size Calculation for the Parallel Model

Sample Sizes for One-Sample Problem

Comparison with the Crosswise Model

Comparison with the Triangular Model

Sample Size for Two-Sample Problem

An Example

The Multi-Category Parallel Model

The Survey Design

Likelihood-Based Inferences

Bayesian Inferences

A Special Case of the Multi-Category Parallel Model

Comparison with the Multi-Category Triangular Model

An Example


A Variant of the Parallel Model

The Survey Design and Basic Properties

Statistical Inferences on π

Statistical Inferences on θ

Bootstrap Confidence Intervals

Bayesian Inferences

Comparison with the Crosswise Model

Comparison with the Triangular Model

The Noncompliance Behavior

An Illustrative Example of Sexual Practices

Case Studies on Cheating Behavior in Examinations


The Combination Questionnaire Model

The Survey Design

Likelihood-Based Inferences

Bayesian Inferences

Analyzing Cervical Cancer Data in Atlanta

Group Dirichlet Distribution

Appendix A The EM and DA Algorithms

Appendix B The Exact IBF Sampling

Appendix C Some Statistical Distributions


Author Index

Subject Index

About the Authors

Guo-Liang Tian is an associate professor of statistics in the Department of Statistics and Actuarial Science at the University of Hong Kong. Dr. Tian has published more than 60 (bio)statistical and medical papers in international peer-reviewed journals on missing data analysis, constrained parameter models and variable selection, sample surveys with sensitive questions, and cancer clinical trial and design. He is also the co-author of two books. He received a PhD in statistics from the Institute of Applied Mathematics, Chinese Academy of Science.

Man-Lai Tang is an associate professor in the Department of Mathematics at Hong Kong Baptist University. Dr. Tang is an editorial board member of Advances and Applications in Statistical Sciences and the Journal of Probability and Statistics; associate editor of Communications in Statistics-Theory and Methods and Communications in Statistics-Simulation and Computation; and editorial advisory board member of the Open Medical Informatics Journal. His research interests include exact methods for discrete data, equivalence/non-inferiority trials, and biostatistics. He received a PhD in biostatistics from UCLA.

About the Series

Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General