Bayesian nonparametric estimation of test equating functions with covariates

González, Jorge; Barrientos, Andrés F.; Quintana, Fernando A.

doi:10.1016/j.csda.2015.03.012

Cited by 12 publications

(24 citation statements)

References 42 publications

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“…Although other approaches based on a BNP models have been proposed (González et al, 2015b; Karabatsos & Walker, 2009a), we take advantage of the ideas in Kottas et al (2005) to obtain equated scores that are defined in the original scale of the tests: The LE method equates scores defined on a discrete scale into scores defined in a discrete scale. This idea, to the best of our knowledge, has not been developed before in the field of equating methods.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…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. Despite the fact that these proposals use more flexible models for the score distributions functions, none of these two approaches produce equated scores that are properly defined on the original discrete scale score.…”

Section: Latent Modeling Approachmentioning

confidence: 99%

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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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Section: Conclusion and Discussionmentioning

confidence: 99%

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

Self Cite

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“…In line with this conclusion, using both covariates and anchor items resulted in the smallest standard error of equating over a large range of test scores. The research conducted by Gonzalez et al (2015) revealed that the Bayesian non-parametric model for equating makes many assumptions that used to be vital for test equating unnecessary, demonstrating that even when there is no covariant, equating is possible. Wiberg and von Davier (2017) also stated the effect of covariates in various administrations would aid in the process of ensuring equal testing for test-takers.…”

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confidence: 99%

“…In other words, the relationship between the test and gender is insignificant for the two booklets, but the other relationships are significant. Although the relationship between the test and gender is not significant, it was used in other studies (Branberg & Wiberg, 2011;Gonzalez et al, 2015;Liou et al, 2001, andYurtçu, 2018). It was also taken as a covariate in this study.…”

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confidence: 99%

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The Impact of Covariate Variables on Kernel Equating under the Non-equivalent Groups

Arıkan

2020

Eğitimde Ve Psikolojide Ölçme Ve Değerlendirme Dergisi

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Latent variable models for harmonization of test scores: A case study on memory

et al. 2019

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Combining data from different studies has a long tradition within the scientific community. It requires that the same information is collected from each study to be able to pool individual data. When studies have implemented different methods or used different instruments (e.g., questionnaires) for measuring the same characteristics or constructs, the observed variables need to be harmonized in some way to obtain equivalent content information across studies. This paper formulates the main concepts for harmonizing test scores from different observational studies in terms of latent variable models. The concepts are formulated in terms of calibration, invariance, and exchangeability. Although similar ideas are present in measurement reliability and test equating, harmonization is different from measurement invariance and generalizes test equating. In addition, if a test score needs to be transformed to another test score, harmonization of variables is only possible under specific conditions. Observed test scores that connect all of the different studies, are necessary to be able to test the underlying assumptions of harmonization. The concepts of harmonization are illustrated on multiple memory test scores from three different Canadian studies.

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Bayesian nonparametric estimation of test equating functions with covariates

Cited by 12 publications

References 42 publications

A Bayesian Nonparametric Latent Approach for Score Distributions in Test Equating

A Bayesian Nonparametric Latent Approach for Score Distributions in Test Equating

The Impact of Covariate Variables on Kernel Equating under the Non-equivalent Groups

Latent variable models for harmonization of test scores: A case study on memory

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