Statistical Analysis of Questionnaires: A Unified Approach Based on R and Stata, 1st Edition (Hardback) book cover

Statistical Analysis of Questionnaires

A Unified Approach Based on R and Stata, 1st Edition

By Francesco Bartolucci, Silvia Bacci, Michela Gnaldi

Chapman and Hall/CRC

328 pages | 42 B/W Illus.

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Statistical Analysis of Questionnaires: A Unified Approach Based on R and Stata presents special statistical methods for analyzing data collected by questionnaires. The book takes an applied approach to testing and measurement tasks, mirroring the growing use of statistical methods and software in education, psychology, sociology, and other fields. It is suitable for graduate students in applied statistics and psychometrics and practitioners in education, health, and marketing.

The book covers the foundations of classical test theory (CTT), test reliability, validity, and scaling as well as item response theory (IRT) fundamentals and IRT for dichotomous and polytomous items. The authors explore the latest IRT extensions, such as IRT models with covariates, multidimensional IRT models, IRT models for hierarchical and longitudinal data, and latent class IRT models. They also describe estimation methods and diagnostics, including graphical diagnostic tools, parametric and nonparametric tests, and differential item functioning.

Stata and R software codes are included for each method. To enhance comprehension, the book employs real datasets in the examples and illustrates the software outputs in detail. The datasets are available on the authors’ web page.


"This book follows a well established approach to the psychometric analysis of questionnaire data as found in educational, survey and medical research. The authors provide an in-depth discussion of the analysis of score reliability and item properties grounded in classical test theory (CTT), and of the probabilistic modeling of individual responses based on latent variable models. … Chapter 5 is a bit different and focus on the estimation of item and person parameters and the diagnostic of IRT models. The first part is rather technical but it does a good job at describing Statistical Analysis of Questionnaires the pros and cons of each technique–joint, conditional and marginal maximum likelihood–and how they could be implemented using custom software. … The authors conclude (…) by highlighting multidimensional IRT models which allow to relax the strong hypothesis of unidimensionality that is attached to all previous models, as well as the main strengths of structural equation models which can be viewed as providing the glue between factor analytic methods and IRT.

Overall, the authors succeed at presenting a solid and reliable framework for psychometric analysis of questionnaire data."

— Christophe Lalanne, Paris-Diderot University, in the Journal of Statistical Software, November 2017

Table of Contents



Psychological Attributes as Latent Variables

Challenges in the Measurement of Latent Constructs

What Is a Questionnaire?

Main Steps in Questionnaire Construction

What Is Psychometric Theory?


Datasets Used for Examples

Classical Test Theory




Conceptual Approaches of Reliability

Reliability of Parallel and Nonparallel Tests

Procedures for Estimating Reliability

True Score Estimation

Item Analysis


Test Bias

Generalizability Theory


Item Response Theory Models for Dichotomous Items


Model Assumptions

Rasch Model

2PL Model

3PL Model

Random-Effects Approach

Summary about Model Estimation


Item Response Theory Models for Polytomous Items


Model Assumptions

Taxonomy of Models for Polytomous Responses

Models for Ordinal Responses

Models for Nominal Responses


Estimation Methods and Diagnostics


Joint Maximum Likelihood Method

Conditional Maximum Likelihood Method

Marginal Maximum Likelihood Method

Estimation of Models for Polytomous Items

Graphical Diagnostic Tools


Infit and Outfit Statistics

Differential Item Functioning



Some Extensions of Traditional Item Response Theory Models


Models with Covariates

Models for Clustered and Longitudinal Data

Multidimensional Models

Structural Equation Modeling Setting


Exercises appear at the end of each chapter.

About the Authors

Francesco Bartolucci is a professor of statistics in the Department of Economics at the University of Perugia. Dr. Bartolucci is an associate editor of Metron and Statistical Modelling: An International Journal. His research interests include latent variable models, marginal models for categorical data, and longitudinal categorical data. He has collaborated with many researchers and published articles on these topics in top statistical journals.

Silvia Bacci is an assistant professor of statistics in the Department of Economics at the University of Perugia. Her research interests include multidimensional and latent class item response theory models and extensions, estimation of item response theory models with R, latent Markov models for multivariate longitudinal data, and the application of these methods and models in educational and quality-of-life settings. She has published articles on these topics in international journals and participated in several research projects.

Michela Gnaldi is an assistant professor of applied statistics in the Department of Political Sciences at the University of Perugia. She is editorial manager of the Italian Journal of Applied Statistics. Her main research interest concerns measurement in education, with particular regard to multidimensional, multilevel, and latent class item response theory models. She has published articles on these topics in international journals and participated in several projects in Italy and the United Kingdom. She actively collaborates with the "Istituto Nazionale di Valutazione del Sistema dell’Istruzione" (INVALSI).

About the Series

Chapman & Hall/CRC Interdisciplinary Statistics

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Subject Categories

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