A Bayesian Nonparametric Approach to Test Equating

Karabatsos, George; Walker, Stephen G.

doi:10.1007/s11336-008-9096-6

Cited by 14 publications

(19 citation statements)

References 21 publications

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“…Computer programming skills allow students and researchers to develop new methods and to invent new solutions not yet fully supported by commercial or open-source software programs (e.g., Neelon, O’Malley, and Normand (2011), Neelon, Zhu, and Neelon (2015), Neelon, Swamy, Burgette, and Miranda (2011), and Elliott, Gallo, Ten Have, Bogner, and Katz (2005)). The ability to code one’s own Bayesian computation promises other new possibilities, such as Bayesian nonparametric methods (e.g., Gershman and Blei (2012), Karabatsos and Walker (2009b), Karabatsos, Talbott, and Walker (2015), Karabatsos and Walker (2009a), Karabatsos (2006), Jara, Hanson, Quintana, Müller, and Rosner (2011)).…”

Section: Overviewmentioning

confidence: 99%

Bayesian Latent Class Analysis Tutorial

Lord-Bessen

Shiyko

et al. 2018

Multivariate Behavioral Research

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This article is a how-to guide on Bayesian computation using Gibbs sampling, demonstrated in the context of Latent Class Analysis (LCA). It is written for students in quantitative psychology or related fields who have a working knowledge of Bayes Theorem and conditional probability and have experience in writing computer programs in the statistical language R . The overall goals are to provide an accessible and self-contained tutorial, along with a practical computation tool. We begin with how Bayesian computation is typically described in academic articles. Technical difficulties are addressed by a hypothetical, worked-out example. We show how Bayesian computation can be broken down into a series of simpler calculations, which can then be assembled together to complete a computationally more complex model. The details are described much more explicitly than what is typically available in elementary introductions to Bayesian modeling so that readers are not overwhelmed by the mathematics. Moreover, the provided computer program shows how Bayesian LCA can be implemented with relative ease. The computer program is then applied in a large, real-world data set and explained line-by-line. We outline the general steps in how to extend these considerations to other methodological applications. We conclude with suggestions for further readings.

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Section: Overviewmentioning

confidence: 99%

Bayesian Latent Class Analysis Tutorial

Lord-Bessen

Shiyko

et al. 2018

Multivariate Behavioral Research

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“…These methods have shown good performance compared to alternative approaches (e.g., Karabatsos and Walker 2009). A Bayesian nonparametric model for test equating which allows the use of covariates in the estimation of the score distribution functions that lead to the equating transformation is described in González, Barrientos, and Quintana (2013).…”

Section: Discussionmentioning

confidence: 99%

SNSequate: Standard and Nonstandard Statistical Models and Methods for Test Equating

González¹

2014

J. Stat. Soft.

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Equating is a family of statistical models and methods that are used to adjust scores on two or more versions of a test, so that the scores from different tests may be used interchangeably. In this paper we present the R package SNSequate which implements both standard and nonstandard statistical models and methods for test equating. The package construction was motivated by the need of having a modular, simple, yet comprehensive, and general software that carries out traditional and new equating methods. SNSequate currently implements the traditional mean, linear and equipercentile equating methods, as well as the mean-mean, mean-sigma, Haebara and Stocking-Lord item response theory linking methods. It also supports the newest methods such as local equating, kernel equating, and item response theory parameter linking methods based on asymmetric item characteristic functions. Practical examples are given to illustrate the capabilities of the software. A list of other programs for equating is presented, highlighting the main differences between them. Future directions for the package are also discussed.

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“…As was pointed out by Karabatsos and Walker (2011), traditional equating methods are all based on parametric assumptions to build a continuous version of the cdfs of X and Y . Instead, Karabatsos and Walker (2009a) proposed a BNP model using Bernstein polynomials process priors for ( F X , F Y ) that account for dependence between the score distributions. As an extension, González et al (2015a, 2015b) developed a BNP model for test equating which allows the use of covariates based on Bernstein polynomials models.…”

Section: Latent Modeling Approachmentioning

confidence: 99%

A Bayesian Nonparametric Latent Approach for Score Distributions in Test Equating

Varas¹,

González

Quintana

2020

Journal of Educational and Behavioral Statistics

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Equating is a family of statistical models and methods used to adjust scores on different test forms so that they can be comparable and used interchangeably. Equated scores are obtained estimating the equating transformation function, which maps the scores on the scale of one test form into their equivalents on the scale of other one. All the statistical models that have been proposed for estimating this function are based on continuous approximations of the score distributions, leading to equated scores lying on a continuous scale even though score scales are usually subsets of the integer numbers (e.g., the total number of correct answers). In this article, we develop a new equating method from which equated scores defined on the original discrete scale are obtained. Considering scores as ordinal random variables, we propose a continuous latent variable formulation to perform an equipercentile-like equating based on a Bayesian nonparametric model for score distributions. The proposed model is applied to simulated and real data collected under an equivalent group design. Some methods to assess the performance of our model are also discussed. Compared with discrete versions of equated scored obtained from traditional equating methods, the results show that the proposed method has better performance.

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A Bayesian Nonparametric Approach to Test Equating

Abstract: Bayesian nonparametrics, bivariate Bernstein polynomial prior, Dirichlet process prior, test equating, equipercentile equating, linear equating,

Cited by 14 publications

References 21 publications

Bayesian Latent Class Analysis Tutorial

Bayesian Latent Class Analysis Tutorial

SNSequate: Standard and Nonstandard Statistical Models and Methods for Test Equating

A Bayesian Nonparametric Latent Approach for Score Distributions in Test Equating

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