Jorge González Burgos | Pontificia Universidad Catolica de Chile (original) (raw)

Papers by Jorge González Burgos

The Poisson's binomial (PB) is the probability distribution of the number of successes in indepen... more The Poisson's binomial (PB) is the probability distribution of the number of successes in independent but not necessarily identically distributed binary trials. The independent non-identically distributed case emerges naturally in the field of item response theory, where answers to a set of binary items are conditionally independent given the level of ability, but with different probabilities of success. In many applications, the number of successes represents the score obtained by individuals and the compound binomial (CB) distribution has been used to obtain score probabilities. It is shown here that the PB and the CB distributions lead to equivalent probabilities. Further that one of the proposed algorithms to calculate the PB probabilities coincides exactly with the well-known Lord and Wingersky (LW, 1984) algorithm for CBs. Surprisingly, we could not find any reference in the psychometric literature pointing to this equivalence. In a simulation study, different methods to calculate the PB distribution are compared with the LW algorithm. Providing an exact alternative to the traditional LW approximation for obtaining score distributions is a contribution to the field.

Wiberg, M., & González, J. (2016). Statistical assessment of estimated transformations in observed-score equating. Journal of Educational Measurement, 53(1), 106-125

Equating methods make use of an appropriate transformation function to map the scores of one test... more Equating methods make use of an appropriate transformation function to map the scores of one test form into the scale of another so that scores are comparable and can be used interchangeably. The equating literature shows that the ways of judging the success of an equating (i.e., the score transformation) might differ depending on the adopted framework. Rather than targeting different parts of the equating process and aiming to evaluate the process from different aspects, this paper views the equating transformation as a standard statistical estimator and discusses how this estimator should be assessed in an equating framework. For the kernel equating framework, a numerical illustration shows the potentials of viewing the equating transformation as a statistical estimator as opposed to assessing it using equating-specific criteria. A discussion on how this approach can be used to compare other equating estimators from different frameworks is also included.

In education studies value-added is by and large defined in terms of a test-score distribution me... more In education studies value-added is by and large defined in terms of a test-score distribution mean.
Therefore, all but a particular summary of the test score distribution is ignored. Developing a valueadded
definition that incorporates the entire conditional distribution of student’s scores given school
effects and control variables would produce a more complete picture of a school’s effectiveness and
as a result provide more accurate information that could better guide policy decisions. Motivated in
part by the current debate surrounding the recent proposal of eliminating co-pay institutions as part
of Chile’s education reform, we provide a new definition of value-added that is based on the quantiles
of the conditional test score distribution. Further, we show that the quantile based value-added can
be estimated within a quantile mixed model regression framework. We apply the methodology to
Chilean standardized test data and explore how information garnered facilitates school effectiveness
comparisons between public schools and those that are subsidized with and without co-pay.

The paper offers a general review of the basic concepts of both statistical model and parameter i... more The paper offers a general review of the basic concepts of both statistical model and parameter identification, and revisits the conceptual relationships between parameter identification and both parameter interpretability and properties of parameter estimates. All these issues are then exemplified for the 1PL, 2PL, and 1PL-G fixed-effects models. For the 3PL model, however, we provide a theorem proving that the item parameters are not identified, do not have an empirical interpretation and that it is not possible to obtain consistent and unbiased estimates of them.

González, J., Barrientos, A., & Quintana, F. (2015). Bayesian Nonparametric Estimation of Test Equating Functions with Covariates. Computational Statistics and Data Analysis, 89, 222-244.

Equating is an important step in the process of collecting, analyzing, and reporting test scores ... more Equating is an important step in the process of collecting, analyzing, and reporting test scores in any program of assessment. Methods of equating utilize functions to transform scores on two or more versions of a test, so that they can be compared and used interchangeably. In common practice, traditional methods of equating use either parametric or semi-parametric models where, apart from the test scores themselves, no additional information is used to estimate the equating transformation function. A flexible 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 proposed. A major feature of this approach is that the complete shape of the scores distribution may change as a function of the covariates. As a consequence, the form of the equating transformation can change according to covariate values. Applications of the proposed model to real and simulated data are discussed and compared to other current methods of equating

Santelices, M. V., Galleguillos, P., González, J., & Taut, S. (2015). Un Estudio Sobre la Calidad Docente en Chile: El Rol del Contexto en Donde Enseña el Profesor y Medidas de Valor Agregado. Psyhke, 24(1), 1-14

Este estudio espera contribuir a la discusión sobre calidad docente en Chile a través de dos enfo... more Este estudio espera contribuir a la discusión sobre calidad docente en Chile a través de dos enfoques: el primero se basa en estimaciones de valor agregado del profesor o "efecto Profesor" en el aprendizaje. En él se explora el rol de las características del profesor y del contexto en que éste trabaja (escuela y municipio) en la estimación del efecto Profesor. El segundo enfoque intenta predecir el desempeño de los alumnos utilizando las variables de contexto y características del profesor. Con respecto al primer enfoque, los resultados muestran inestabilidad en las estimaciones de valor agregado, ante el ajuste de distintos modelos que incorporan covariables progresivamente. Por otra parte, el análisis de desempeño de los alumnos arroja como resultado que, de las variables de contexto, la escuela es más importante que el municipio para la predicción. A nivel del profesor, sólo resulta estadísticamente significativa la participación en perfeccionamientos profesionales, desestimándose el valor de la experiencia y de la formación inicial.

González, J., Barrientos, A. F., & Quintana, F. A. (2015). A Dependent Bayesian Nonparametric Model for Test Equating. In Millsap, R.E., Bolt, D.M., van der Ark, L.A., Wang, W.-C. (Eds.) Quantitative Psychology Research. Springer Proceedings in Mathematics & Statistics, Vol. 89., pp 213-226

Equating methods utilize functions to transform scores on two or more versions of a test, so tha... more Equating methods utilize functions to transform scores on two or more
versions of a test, so that they can be compared and used interchangeably. In common
practice, traditional methods of equating use parametric models where, apart
from the test scores themselves, no additional information is used for the estimation
of the equating transformation. We propose a flexible 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. A major feature
of this approach is that the complete shape of the score distribution may change
as a function of the covariates. As a consequence, the form of the equating transformation
can change according to covariate values. We discuss applications of the
proposed model to real and simulated data. We conclude that our method has good
performance compared to alternative approaches

González, J. (2014). SNSequate: Standard and Nonstandard Statistical Models and Methods for Test Equating. Journal of Statistical Software, 59(7), 1-30

Equating is a family of statistical models and methods that are used to adjust scores on two or m... more 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 di erent 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 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 IRT linking methods. It also supports newest methods such as local equating, kernel equating, and IRT 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 di erences between them. Future directions for the package are also discussed.

San Martín, E., González, J., & Tuerlinckx, F. (2015). On the unidentifiability of the fixed-effects 3PL model. Psychometrika, 80(2), 450-467.

The paper offers a general review of the basic concepts of both statistical model and parameter i... more The paper offers a general review of the basic concepts of both statistical model and parameter identification, and revisit the conceptual relationships between parameter identification and both parameter interpretability and properties of parameter estimates. All these issues are then exemplified for the 1PL, 2PL and 1PL-G fixed-effects models. For the 3PL model, however, we provide a theorem proving that the item parameters are not identified, do not have an empirical interpretation and that it is not possible to obtain consistent and unbiased estimates of them

González, J., De Boeck, P., and Tuerlinckx, F. (2014).Linear mixed modeling for data from a doublemixed factorial design with covariates. A case study on semantic categorization response times. Journal ofthe Royal Statistical Society: Series C (Applied Statistics), 63(2), 289-302. , Feb 26, 2014

Linear mixed modeling is a useful approach for double mixed factorial designs with covariates. It... more Linear mixed modeling is a useful approach for double mixed factorial designs with covariates. It is explained how these designs are appropriate for the study of human behavior as a function of characteristics of persons and situations and stimuli in the situations. The behavior of subjects nested in types of persons responding to stimuli nested in types of stimuli defines a mixed factorial design. The inclusion of additional covariates of the observational units can help to further explain the behavior under study. A linear mixed modeling approach for such designs allows a combined focus on fixed effects (general effects) and individual and stimulus differences in these effects. This combination has the potential to advance the integration of two different sub-disciplines of psychology: general psychology and differential psychology, so that they can borrow strength from each other. An application is presented with semantic categorization response time data from a factorial design with age groups by word types and with age of acquisition as an additional covariate of the words. The results throw light on the processes underlying the effect of age of acquisition and on individual differences and word differences.

González, J., and von Davier, M. (2013). Statistical Models and Inference for the True Equating Transformationin the Context of Local Equating. Journal of Educational Measurement, 50(3), 315-320

criterion of equity of equating, van der Linden (this issue) revisits the so-called local equatin... more criterion of equity of equating, van der Linden (this issue) revisits the so-called local equating method and offers alternative as well as new thoughts on several topics appearing in the field such as the types of transformations, symmetry, reliability, population invariance, used in equating. A remarkable aspect is to define equating as a standard statistical inference problem in which the true equating transformation is the parameter of interest which has to be estimated and assessed as any standard evaluation of an estimator of an unknown parameter in statistics. We believe that putting equating methods in a general statistical model framework would be an interesting an useful next step in the area. Van der Linden (this issue) conceptual paper on equating is certainly an important contribution to this task.

von Davier, M., González, J., and von Davier, A. (2013).Local Equating using the Rasch Model, the OPLM,and the 2PL IRT Model – or – What is it anyway if the model captures everything there is to know about thetest takers? Journal of Educational Measurement, 50(3), 295-303

Local equating is based on Lord's (1980) criterion of equity. It defines a family of true transfo... more Local equating is based on Lord's (1980) criterion of equity. It defines a family of true transformations that aiming at the ideal of equitable equating. van der Linden (this issue) offers a detailed discussion of common issues in observed score equating relative to this local approach. By assuming an underlying IRT model, one of the main features of local equating is that it adjusts the equated raw scores using conditional distributions of raw scores given an estimate of the ability of interest. In this paper we argue that when using a Rasch model for the estimation of the true transformation, this feature disappears, while the One Parameter Logistic Model (OPLM) and the 2PL do provide a local adjustment of the equated score.

González, J. (2013). Book Review: Statistical Models for Test Equating, Scaling, and Linking. Applied Psychological Methods, 37(4), 336-339

Marmolejo-Ramos, F., González, J. (2013). A power comparison of various normality tests of univariate normality on Ex-Gaussian distributions. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 9(4), 137-149

A power analysis of seven normality tests against the Ex-Gaussian distribution (EGd) is presented... more A power analysis of seven normality tests against the Ex-Gaussian distribution (EGd) is presented. The EGd is selected on the basis that it is a particularly well-suited distribution to accommodate positively skewed distributions such as those observed in reaction times data. A pre-assessment of the power of the selected tests across various types of distributions was done via a meta-analysis and a comparison with other power analyses reported in the literature was also performed. General recommendations are given as to which tests should be used to test normality in data suspected to resemble an EG distribution. Additionally, some topics for future research regarding the use of confidence intervals and the computation of accurate critical values are outlined.

San Martin, E., & González, J. (2010). Bayesian Identifiability: Contributions to an Inconclusive Debate. Chilean Journal of Statistics, 1(2), 69-91

Using the concept of reduction by sufficiency of a Bayesian model, the issue of Bayesian identifi... more Using the concept of reduction by sufficiency of a Bayesian model, the issue of Bayesian identifiability is discussed. Various statements given in the literature on Bayesian identifiability are revised. Particular attention is put on the possibility of updating unidentified parameters. This issue is discussed under a general framework and also carefully illustrated in a fully discrete Bayesian model.

González, J. (2010). Bayesian methods in psychological research. The case of IRT. International Journal of Psychological Research, 3(1), 164-176

Bayesian methods have become increasingly popular in social sciences due to its flexibility in ac... more Bayesian methods have become increasingly popular in social sciences due to its flexibility in accommodating numerous models from different fields. The domain of item response theory is a good example of fruitful research, incorporating in the lasts years new developments and models, which are being estimated using the Bayesian approach. This is partly because of the availability of free software such as WinBUGS and R, which has permitted researchers to explore new possibilities.

San Martín, E.,González, J., & Tuerlinckx, F. (2009). Identified parameters, parameter of interest and their relationship. Measurement: Interdisciplinary Research and Perspective, 7, 97-105

González, J., Tuerlinckx, F., & De Boeck, P. (2009). Analyzing structural relations in multivariate dyadic binary data. Applied Multivariate Research, 13, 77-92.

In social network studies, most often only a single relation (or link) between the actors is inve... more In social network studies, most often only a single relation (or link) between the actors is investigated. When more than one link has been recorded, the twoway sociomatrix becomes a three-way array with the set of links being the third way. In this paper, we present a model which simultaneously accounts for the three ways in the data. Random effects are used to model the between-actor variability, both on senders and receivers side. In addition, structural relations between the linking variables are investigated. The model is applied to a study of popularity and strength in a class of students. It is shown that popularity can be seen as a linear function of strength on the receivers' side, but not on the senders' side.

González, J., De Boeck, P., & Tuerlinckx, F. (2008). A double-structure structural equation model for three-mode data. Psychological Methods, 13, 337-353

This article has been published. The reference is: González, J., De Boeck, P., and Tuerlinckx, F.... more This article has been published. The reference is: González, J., De Boeck, P., and Tuerlinckx, F. (2008). A Double-Structure Structural Equation Model for Three-Mode Data. Psychological Methods, 13, 337-353.

del Pino, G., San Martín, E., González, J., & De Boeck, P. (2008). On the relationships between sum score based estimation and joint maximum likelihood estimation. Psychometrika, 73, 145-151

in press). On the relationships between sum score based estimation and joint maximum likelihood e... more in press). On the relationships between sum score based estimation and joint maximum likelihood estimation. Psychometrika.