Browsing by Author "González Burgos, Jorge Andrés"

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    A bayesian nonparametric latent approach for score distributions in test equating
    (2020) Varas Cáceres, Inés María; González Burgos, Jorge Andrés; Quintana Quintana, Fernando
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    A Family of Discrete Kernels for Presmoothing Test Score Distributions
    (Springer, 2024) González Burgos, Jorge Andrés; Wiberg Roll, Marie; CEDEUS (Chile)
    In the fields of educational measurement and testing, score distributions are often estimated by the sample relative frequency distribution. As many score distributions are discrete and may have irregularities, it has been common practice to use presmoothing techniques to correct for such irregularities of the score distributions. A common way to conduct presmoothing has been to use log-linear models. In this chapter, we introduce a novel class of discrete kernels that can effectively estimate the probability mass function of scores, providing a presmoothing solution. The chapter includes an empirical illustration demonstrating that the proposed discrete kernel estimates perform as well as or better than the existing methods like log-linear models in presmoothing score distributions. The practical implications of this finding are discussed, highlighting the potential benefits of using discrete kernels in educational measurement contexts. Additionally, the chapter identifies several areas for further research, indicating opportunities for advancing the field’s methodology and practices.
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    A Family of Discrete Kernels for Presmoothing Test Score Distributions
    (Springer, 2024) González Burgos, Jorge Andrés; Wiberg, Marie
    In the fields of educational measurement and testing, score distributions are often estimated by the sample relative frequency distribution. As many score distributions are discrete and may have irregularities, it has been common practice to use presmoothing techniques to correct for such irregularities of the score distributions. A common way to conduct presmoothing has been to use log-linear models. In this chapter, we introduce a novel class of discrete kernels that can effectively estimate the probability mass function of scores, providing a presmoothing solution. The chapter includes an empirical illustration demonstrating that the proposed discrete kernel estimates perform as well as or better than the existing methods like log-linear models in presmoothing score distributions. The practical implications of this finding are discussed, highlighting the potential benefits of using discrete kernels in educational measurement contexts. Additionally, the chapter identifies several areas for further research, indicating opportunities for advancing the field’s methodology and practices.
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    A Note on the Poisson's Binomial Distribution in Item Response Theory
    (2016) González Burgos, Jorge Andrés; Wiberg, Marie; von Davier, Alina A.
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    A power comparison of various tests of univariate normality on Ex-Gaussian distributions
    (2013) Marmolejo Ramos, F.; González Burgos, Jorge Andrés
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    An Illustration on the Quantile-Based Calculation of the Standard Error of Equating in Kernel Equating
    (Springer Cham, 2021) González Burgos, Jorge Andrés; Wallin, Gabriel
    Liou and Cheng (J Educ Behav Stat 20(3):259–286, 1995) discussed large-sample approximations for the standard error of equating (SEE) using the results of Bahadur (Ann Math Stat 37(3):577–580, 1966) and Ghosh (Ann Math Stat 42(6):1957–1961, 1971) on the asymptotic representation of sample quantiles. In this paper we revisit the Bahadur representation of sample quantiles, describe its use for the calculation of the SEE of Kernel equating, and present a comparison with the more traditionally used Delta method.
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    Applying test equating methods, using R
    (2017) González Burgos, Jorge Andrés; Wiberg, Marie
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    Continuation Ratio Model for Polytomous Items Under Complex Sampling Design
    (Springer Cham, 2022) Carrasco Ogaz, Diego; Torres Irribarra, David; González Burgos, Jorge Andrés
    The use of polytomous items as part of background or context questionnaires and complex sampling designs are two features common in international large-scale assessments (ILSA). Popular choices to model polytomous items within ILSA include the partial credit model, the graded response model, and confirmatory factor analysis. However, an absent model in ILSA studies is the continuation ratio model. The continuation ratio model is a flexible alternative and a very extendable response model applicable in different situations. Although existing software can fit this model, not all these tools can incorporate complex sampling design features present in ILSA studies. This study aims to illustrate a method to fit a continuation ratio model including complex sampling design information, thus expanding the modelling tools available for secondary users of large-scale assessment studies.
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    Continuation ratio model for polytomous responses with censored like latent classes
    (Springer, 2023) Carrasco Ogaz, Diego; Torres Irribarra, David; González Burgos, Jorge Andrés
    Polytomous item responses are prevalent in background or context questionnaires of International large-scale assessments (ILSA). Responses to these types of instruments can vary in their symmetry or skewness. Zero inflation of responses can lead to biased estimates of item parameters in the response model and also to a downward bias in the conditional model when the zero inflated component is not accounted for in the model. In this paper, we propose to use a mixture continuation ratio response model to approximate the non-normality of the latent variable distribution. We use responses to bullying items from an ILSA study, which typically present positive asymmetry. The present model allows us to distinguish bullying victimization risk profiles among students, retrieve bullying victimization risk scores, and determine the population prevalence of the bullying events. This study also aims to illustrate how to fit a mixture continuation ratio model, including complex sampling design, thus expanding the modeling tools available for secondary users of large-scale assessment studies.
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    Erratum to : on the unidentifiability of the fixed-effects 3PL model
    (2015) San Martín, Ernesto; González Burgos, Jorge Andrés; Tuerlinckx, Francis
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    Un Estudio Sobre la Calidad Docente en Chile : El Rol del Contexto en Donde Enseña el Profesor y Medidas de Valor Agregado
    (2015) Santelices Etchegaray, María Verónica; Galleguillos, Pilar; González Burgos, Jorge Andrés; Taut, Sandy
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    Exploring complete school effectiveness via quantile value added
    (2017) Page, Garritt L.; San Martín, Ernesto; Orellana, Javiera; González Burgos, Jorge Andrés
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    Flexible bayesian inference for families of random densities.
    (2020) Galasso Díaz, Bastián; González Burgos, Jorge Andrés; Pontificia Universidad Católica de Chile. Facultad de Matemáticas
    A main goal of this thesis is to propose and study novel flexible Bayesian models for setups that entail families of random densities. Two specific contexts will be examined: one involves phase-varying point processes, whereas the other involves functional principal component analysis. The common denominator underlying these contexts is the need to model families of random measures to each of which corresponds a different data generating process. On both contexts, prior processes will be used so to devise priors on the target objects of interest. In more detail, one context entails separating amplitude variation from phase variation in a multiple point process setting. In this framework, I pioneer the development of priors on spaces of warping maps by proposing a novel Bayesian semiparametric approach for modeling registration of multiple point processes. Specifically, I develop induced priors for warp maps via a Bernstein polynomial prior so to learn about the structural measure of the point process and about the phase variation in the process. Theoretical properties of the induced prior, including support and posterior consistency, are established under a fairly mild proviso. Also, numerical experiments are conducted to assess the performance of this new approach; finally, a real data application in climatology illustrates the proposed methodology. The other context that will be considered in this thesis involves modeling families of random densities using functional principal component analysis through the so-called Karhunen–Loève decomposition. For this, I develop a data-driven prior based on the Karhunen–Loève decomposition which can be used to borrowing strength across samples. The proposed approach defines a prior on the space of families of densities. Theoretical properties are developed to ensure that the trajectories from an infinite mixture belong to L 2 which is a necessary condition for the Karhunen–Loève decomposition to hold. Numerical experiments are conducted to assess the performance of the proposed approach against competing methods, and we offer an illustration by revisiting Galton’s height parents dataset.
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    From missing data to informative GPA predictions: Navigating selection process beliefs with the partial identifiability approach
    (John Wiley and Sons Ltd, 2024) Alarcón Bustamante, Eduardo Sebastián; González Burgos, Jorge Andrés; Torres Irribarra, David Esteban; San Martin Gutiérrez, Ernesto Javier
    The extent to which college admissions test scores can forecast college grade point average (GPA) is often evaluated in predictive validity studies using regression analyses. A problem in college admissions processes is that we observe test scores for all the applicants; however, we cannot observe the GPA of applicants who were not selected. The standard solution to tackle this problem has relied upon strong assumptions to identify the exact value of the regression function in the presence of missing data. In this paper, we present an alternative approach based on the theory of partial identifiability that considers a variety of milder assumptions to learn about the regression function. Using a university admissions dataset we illustrate how results can vary as a function of the assumptions that one is willing to make about the selection process.
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    Generalized Kernel Equating with Applications in R
    (Taylor & Francis, 2024) Wiberg, Marie; González Burgos, Jorge Andrés; von Davier, Alina A.
    Generalized Kernel Equating is a comprehensive guide for statisticians, psychometricians, and educational researchers aiming to master test score equating. This book introduces the Generalized Kernel Equating (GKE) framework, providing the necessary tools and methodologies for accurate and fair score comparisons.The book presents test score equating as a statistical problem and covers all commonly used data collection designs. It details the five steps of the GKE framework: presmoothing, estimating score probabilities, continuization, equating transformation, and evaluating the equating transformation. Various presmoothing strategies are explored, including log-linear models, item response theory models, beta4 models, and discrete kernel estimators. The estimation of score probabilities when using IRT models is described and Gaussian kernel continuization is extended to other kernels such as uniform, logistic, epanechnikov and adaptive kernels. Several bandwidth selection methods are described. The kernel equating transformation and variants of it are defined, and both equating-specific and statistical measures for evaluating equating transformations are included. Real data examples, guiding readers through the GKE steps with detailed R code and explanations are provided. Readers are equipped with an advanced knowledge and practical skills for implementing test score equating methods.
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    Linking measurements : a bayesian nonparametric approach.
    (2019) Varas Cáceres, Inés María; González Burgos, Jorge Andrés; Pontificia Universidad Católica de Chile. Facultad de Matemáticas
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    On the unidentifiability of the fixed-effects 3PL model
    (2015) San Martín, Ernesto; González Burgos, Jorge Andrés; Tuerlinckx, Francis
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    Possible Factors Which May Impact Kernel Equating of Mixed-Format Tests
    (Springer Cham, 2021) Wiberg, Marie; González Burgos, Jorge Andrés
    Mixed-format tests contain items with different formats such as dichotomously scored and polytomously scored items. The aim of this study was to examine the impact of item discrimination, sample size, and proportion of polytomously scored items on item response theory (IRT) kernel equating of mixed-format tests under the equivalent groups design. A simulation study was performed to examine the aim. The results from the simulation study showed that the percent relative errors were low and stable for all conditions, whereas differences in standard errors and equated values where found for the conditions with different sample sizes and item discriminations. Also, the standard errors were higher when the proportion of polytomously scored items in the test where higher.