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.
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 Response Theory Models for Dichotomous Items
Summary about Model Estimation
Item Response Theory Models for Polytomous Items
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
Structural Equation Modeling Setting
Exercises appear at the end of each chapter.
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).
"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