Author: Atalanta GhoshPublisher:
ISBN:
Category :
Languages : en
Pages : 216
Book Description
Bayesian Analysis of Item Response Models for Binary Data
Author: Atalanta GhoshBayesian Item Response Modeling
Author: Jean-Paul FoxPublisher: Springer Science & Business Media
ISBN: 1441907424
Category : Social Science
Languages : en
Pages : 323
Book Description
The modeling of item response data is governed by item response theory, also referred to as modern test theory. The eld of inquiry of item response theory has become very large and shows the enormous progress that has been made. The mainstream literature is focused on frequentist statistical methods for - timating model parameters and evaluating model t. However, the Bayesian methodology has shown great potential, particularly for making further - provements in the statistical modeling process. The Bayesian approach has two important features that make it attractive for modeling item response data. First, it enables the possibility of incorpor- ing nondata information beyond the observed responses into the analysis. The Bayesian methodology is also very clear about how additional information can be used. Second, the Bayesian approach comes with powerful simulation-based estimation methods. These methods make it possible to handle all kinds of priors and data-generating models. One of my motives for writing this book is to give an introduction to the Bayesian methodology for modeling and analyzing item response data. A Bayesian counterpart is presented to the many popular item response theory books (e.g., Baker and Kim 2004; De Boeck and Wilson, 2004; Hambleton and Swaminathan, 1985; van der Linden and Hambleton, 1997) that are mainly or completely focused on frequentist methods. The usefulness of the Bayesian methodology is illustrated by discussing and applying a range of Bayesian item response models.
Bayesian Analysis of Item Response Theory Models Using SAS
Author: Clement A. StonePublisher:
ISBN: 9781642953022
Category : Computers
Languages : en
Pages : 280
Book Description
Written especially for psychometricians, scale developers, and practitioners interested in applications of Bayesian estimation and model checking of item response theory (IRT) models, this book teaches you how to accomplish all of this with the SAS MCMC Procedure. Because of its tutorial structure, Bayesian Analysis of Item Response Theory Models Using SAS will be of immediate practical use to SAS users with some introductory background in IRT models and the Bayesian paradigm. Working through this book's examples, you will learn how to write the PROC MCMC programming code to estimate various simple and more complex IRT models, including the choice and specification of prior distributions, specification of the likelihood model, and interpretation of results. Specifically, you will learn PROC MCMC programming code for estimating particular models and ways to interpret results that illustrate convergence diagnostics and inferences for parameters, as well as results that can be used by scale developers-for example, the plotting of item response functions. In addition, you will learn how to compare competing IRT models for an application, as well as evaluate the fit of models with the use of posterior predictive model checking methods. Numerous programs for conducting these analyses are provided and annotated so that you can easily modify them for your applications.
Bayesian Analysis of Item Response Curves
Author: Robert K. TsutakawaPublisher:
ISBN:
Category : Bayesian statistical hypothesis testing
Languages : en
Pages : 60
Book Description
Item response curves for a set of binary responses are studied from a bayesian viewpoint of estimating the item parameters. For the two-parameter logistic model with normally distributed ability, restricted bivariate beta priors are used to illustrate the computation of the posterior mode via the EM algorithm. The procedure is illustrated by data from a mathematics test. (Author).
Explanatory Item Response Models
Author: Paul de BoeckPublisher: Springer Science & Business Media
ISBN: 1475739907
Category : Social Science
Languages : en
Pages : 394
Book Description
This edited volume gives a new and integrated introduction to item response models (predominantly used in measurement applications in psychology, education, and other social science areas) from the viewpoint of the statistical theory of generalized linear and nonlinear mixed models. It also includes a chapter on the statistical background and one on useful software.
Ordinal Data Modeling
Author: Valen E. JohnsonPublisher: Springer Science & Business Media
ISBN: 0387227024
Category : Social Science
Languages : en
Pages : 258
Book Description
Ordinal Data Modeling is a comprehensive treatment of ordinal data models from both likelihood and Bayesian perspectives. A unique feature of this text is its emphasis on applications. All models developed in the book are motivated by real datasets, and considerable attention is devoted to the description of diagnostic plots and residual analyses. Software and datasets used for all analyses described in the text are available on websites listed in the preface.
Bayesian Irt Models with General and Specific Traits
Author: Yanyan ShengPublisher: VDM Publishing
ISBN: 9783836464369
Category : Mathematics
Languages : en
Pages : 100
Book Description
Modeling the interaction between persons and items for binary response data, item response theory (IRT) has been found useful in a wide variety of applications. Over the past decades, studies have been conducted on the development and application of unidimensional as well as multidimensional IRT models. However, little literature exists on IRT-based models that incorporate one general trait and several specific trait dimensions. This book, therefore, proposes such models in the Bayesian hierarchical framework, assesses their performances in various testing situations and further compares them with the conventional IRT models using Bayesian model choice techniques. Results from the analysis suggest that the proposed models offer a better way to represent the test situations not realized in existing models. The methodology and analysis should shed some light on the development of complex IRT models and the statistical procedures for parameter estimation, and should be especially useful to professionals in educational and psychological measurement, or anyone who may be considering utilizing IRT models for assessing persons' continuous latent traits.
Handbook of Item Response Theory
Author: Wim J. van der LindenPublisher: CRC Press
ISBN: 1315362813
Category : Mathematics
Languages : en
Pages : 454
Book Description
Drawing on the work of internationally acclaimed experts in the field, Handbook of Item Response Theory, Volume Two: Statistical Tools presents classical and modern statistical tools used in item response theory (IRT). While IRT heavily depends on the use of statistical tools for handling its models and applications, systematic introductions and reviews that emphasize their relevance to IRT are hardly found in the statistical literature. This second volume in a three-volume set fills this void. Volume Two covers common probability distributions, the issue of models with both intentional and nuisance parameters, the use of information criteria, methods for dealing with missing data, and model identification issues. It also addresses recent developments in parameter estimation and model fit and comparison, such as Bayesian approaches, specifically Markov chain Monte Carlo (MCMC) methods.
Bayesian Analysis of Item Response Theory and Its Applications to Longitudinal Education Data
Author: Abhisek SahaPublisher:
ISBN:
Category : Electronic dissertations
Languages : en
Pages :
Book Description
Inferences on ability in item response theory (IRT) have been mainly based on item responses while response time is often ignored. This is a loss of information especially with the advent of computerized tests. Most of the IRT models may not apply to these modern computerized tests as they still suffer from at least one of the three problems, local independence, randomized item and individually varying test dates, due to the flexibility and complex designs of computerized (adaptive) tests. In Chapter 2, we propose a new class of state space models, namely dynamic item responses and response times models (DIR-RT models), which conjointly model response time with time series of dichotomous responses. It aims to improve the accuracy of ability estimation via auxilary information from response time. A simulation study is conducted to ensure correctness of proposed sampling schemes to estimate parameters, whereas an empirical study is conducted using MetaMetrics datasets to demonstrate its implications in practice. In Chapter 3, we have investigated the difficulty in implementing the standard model diagnostic methods while comparing two popular response time models (i.e., monotone and inverted U-shape). A new variant of conditional deviance information criterion (DIC) is proposed and some simulation studies are conducted to check its performance. The results of model comparison support the inverted U shaped model, as discussed in Chapter 1, which can better capture examinees' behaviors and psychology in exams. The estimates of ability via Dynamic Item Response models (DIR) or DIR-RT model often are non-monotonic and zig-zagged because of irregularly spaced time-points though the inherent mean ability growth process is monotonic and smooth. Also the parametric assumption of ability process may not be always exact. To have more flexible yet smooth and monotonic estimates of ability we propose a semi-parametric dynamic item response model and study the robustness of the proposed model. Finally, as every student’s growth is different from others, it may be of importance to identify groups of fast learners from slow learners. The growth curves are clustered into distinct groups based on learning rates. A spline derivative based clustering method is suggested in light of its efficacy on some simulated data in Chapter 5 as part of future works.
Bayesian Analysis for the Social Sciences
Author: Simon JackmanPublisher: John Wiley & Sons
ISBN: 9780470686638
Category : Mathematics
Languages : en
Pages : 598
Book Description
Bayesian methods are increasingly being used in the social sciences, as the problems encountered lend themselves so naturally to the subjective qualities of Bayesian methodology. This book provides an accessible introduction to Bayesian methods, tailored specifically for social science students. It contains lots of real examples from political science, psychology, sociology, and economics, exercises in all chapters, and detailed descriptions of all the key concepts, without assuming any background in statistics beyond a first course. It features examples of how to implement the methods using WinBUGS – the most-widely used Bayesian analysis software in the world – and R – an open-source statistical software. The book is supported by a Website featuring WinBUGS and R code, and data sets.