Asignación de puntajes en exámenes estandarizados mediante el uso de redes neuronales y técnicas de equiparación psicométricas compatibles: Caso examen Saber 11 en Colombia

ilustraciones, diagramas

Autores:: Duplat Durán, Ricardo René

Tipo de recurso:

Fecha de publicación:: 2024

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: spa

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dc.title.spa.fl_str_mv	Asignación de puntajes en exámenes estandarizados mediante el uso de redes neuronales y técnicas de equiparación psicométricas compatibles: Caso examen Saber 11 en Colombia
dc.title.translated.eng.fl_str_mv	Assignment of standardized test scores using neural networks and compatible psychometric equating techniques: The case of the Saber 11 exam in Colombia.
title	Asignación de puntajes en exámenes estandarizados mediante el uso de redes neuronales y técnicas de equiparación psicométricas compatibles: Caso examen Saber 11 en Colombia
spellingShingle	Asignación de puntajes en exámenes estandarizados mediante el uso de redes neuronales y técnicas de equiparación psicométricas compatibles: Caso examen Saber 11 en Colombia 000 - Ciencias de la computación, información y obras generales::005 - Programación, programas, datos de computación 370 - Educación::373 - Educación secundaria Calificación de exámenes estandarizados Teoría de Respuesta al Ítem Redes Neuronales Artificiales Psicometría Equiparación de puntajes Modelo logístico de 2 parámetros AutoEncoders Standardized exam scoring Item Response Theory Artificial Neural Networks Psychometrics 2-parameter logistic model Score equating Evaluación del estudiante Psicometría Informática educativa Student evaluation Psychometrics Computer uses in education
title_short	Asignación de puntajes en exámenes estandarizados mediante el uso de redes neuronales y técnicas de equiparación psicométricas compatibles: Caso examen Saber 11 en Colombia
title_full	Asignación de puntajes en exámenes estandarizados mediante el uso de redes neuronales y técnicas de equiparación psicométricas compatibles: Caso examen Saber 11 en Colombia
title_fullStr	Asignación de puntajes en exámenes estandarizados mediante el uso de redes neuronales y técnicas de equiparación psicométricas compatibles: Caso examen Saber 11 en Colombia
title_full_unstemmed	Asignación de puntajes en exámenes estandarizados mediante el uso de redes neuronales y técnicas de equiparación psicométricas compatibles: Caso examen Saber 11 en Colombia
title_sort	Asignación de puntajes en exámenes estandarizados mediante el uso de redes neuronales y técnicas de equiparación psicométricas compatibles: Caso examen Saber 11 en Colombia
dc.creator.fl_str_mv	Duplat Durán, Ricardo René
dc.contributor.advisor.spa.fl_str_mv	Niño Vásquez, Luis Fernando
dc.contributor.author.spa.fl_str_mv	Duplat Durán, Ricardo René
dc.contributor.researchgroup.spa.fl_str_mv	laboratorio de Investigación en Sistemas Inteligentes Lisi
dc.subject.ddc.spa.fl_str_mv	000 - Ciencias de la computación, información y obras generales::005 - Programación, programas, datos de computación 370 - Educación::373 - Educación secundaria
topic	000 - Ciencias de la computación, información y obras generales::005 - Programación, programas, datos de computación 370 - Educación::373 - Educación secundaria Calificación de exámenes estandarizados Teoría de Respuesta al Ítem Redes Neuronales Artificiales Psicometría Equiparación de puntajes Modelo logístico de 2 parámetros AutoEncoders Standardized exam scoring Item Response Theory Artificial Neural Networks Psychometrics 2-parameter logistic model Score equating Evaluación del estudiante Psicometría Informática educativa Student evaluation Psychometrics Computer uses in education
dc.subject.proposal.spa.fl_str_mv	Calificación de exámenes estandarizados Teoría de Respuesta al Ítem Redes Neuronales Artificiales Psicometría Equiparación de puntajes Modelo logístico de 2 parámetros
dc.subject.proposal.eng.fl_str_mv	AutoEncoders Standardized exam scoring Item Response Theory Artificial Neural Networks Psychometrics 2-parameter logistic model Score equating
dc.subject.unesco.spa.fl_str_mv	Evaluación del estudiante Psicometría Informática educativa
dc.subject.unesco.eng.fl_str_mv	Student evaluation Psychometrics Computer uses in education
description	ilustraciones, diagramas
publishDate	2024
dc.date.accessioned.none.fl_str_mv	2024-04-02T00:15:56Z
dc.date.available.none.fl_str_mv	2024-04-02T00:15:56Z
dc.date.issued.none.fl_str_mv	2024-01-28
dc.type.spa.fl_str_mv	Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv	info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv	info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv	Text
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dc.identifier.uri.none.fl_str_mv	https://repositorio.unal.edu.co/handle/unal/85835
dc.identifier.instname.spa.fl_str_mv	Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv	Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv	https://repositorio.unal.edu.co/
url	https://repositorio.unal.edu.co/handle/unal/85835 https://repositorio.unal.edu.co/
identifier_str_mv	Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia
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language	spa
dc.relation.references.spa.fl_str_mv	American Educational Research Association -AERA, American Psychological Association - APA, & National Council on Measurement in Education –NCME (2018). Estándares para pruebas educativas y psicológicas. American Educational Research Association. Amin, A. (2020), ``A Face Recognition System Based on Deep Learning (FRDLS) to Support the Entry and Supervision Procedures on Electronic Exams``. International Journal of Intelligent Computing and Information Sciences, 20(1). https://doi.org/10.21608/ijicis.2020.23149.1015 Basheer, Imad & Hajmeer, M.N.. (2001). Artificial Neural Networks: Fundamentals, Computing, Design, and Application. Journal of microbiological methods. 43. 3-31. Bock, R. D., & Zimowski, M. F. (1997). Multiple group IRT. In Handbook of modern item response theory (pp. 433-448). New York, NY: Springer New York. Bolt, D. M., Hare, R. D., Vitale, J. E., & Newman, J. P. (2004). A Multigroup Item Response Theory Analysis of the Psychopathy Checklist-Revised. Psychological assessment, 16(2), 155. Bozak, A., & Aybek, E. C. (2020). Comparison of Artificial Neural Networks and Logistic Regression Analysis in PISA Science Literacy Success Prediction. International Journal of Contemporary Educational Research. https://doi.org/10.33200/ijcer.693081 Bro, R., & Smilde, A. K. (2014). Principal component analysis. Analytical methods, 6(9), 2812-2831. Converse, G., Curi, M., & Oliveira, S. (2019). Autoencoders for educational assessment. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 11626 LNAI. https://doi.org/10.1007/978-3-030-23207-8\_8 Converse, G., Curi, M., Oliveira, S., & Templin, J. (2021). Estimation of multidimensional item response theory models with correlated latent variables using variational autoencoders. Machine Learning, 110(6). https://doi.org/10.1007/s10994-021-06005-7 Cortada de Kohan, N. (2005). Posibilidad de integración de las teorías cognitivas y la psicometría moderna. Interdisciplinaria, 22(1), 29-58. Curi, M., Converse, G. A., Hajewski, J., & Oliveira, S. (2019). Interpretable Variational Autoencoders for Cognitive Models. Proceedings of the International Joint Conference on Neural Networks, 2019-July. https://doi.org/10.1109/IJCNN.2019.8852333 Developers, T. (2022). TensorFlow. Zenodo. Dorans, N. J., & Kingston, N. M. (1985). The effects of violations of unidimensionality on the estimation of item and ability parameters and on item response theory equating of the GRE verbal scale. Journal of Educational Measurement, 22(4), 249-262. Dunn, T., Howlett, S. E., Stanojevic, S., Shehzad, A., Stanley, J., & Rockwood, K. (2022). Patterns of Symptom Tracking by Caregivers and Patients with Dementia and Mild Cognitive Impairment: Cross-sectional Study. Journal of Medical Internet Research, 24(1). https://doi.org/10.2196/29219 Eignor, D. R. (2006). Test Equating, Scaling, and Linking Methods and Practices. El-Alfy, E. S. M., & Abdel-Aal, R. E. (2008). Construction and analysis of educational tests using abductive machine learning. Computers and Education, 51(1). https://doi.org/10.1016/j.compedu.2007.03.003 García-González, J. R., Sánchez-Sánchez, P. A., Orozco, M., & Obredor, S. (2019). Extracción de Conocimiento para la Predicción y Análisis de los Resultados de la Prueba de Calidad de la Educación Superior en Colombia. Formación Universitaria, 12(4). https://doi.org/10.4067/s0718-50062019000400055 Goodfellow, Ian; Bengio, Yoshua; Courville, Aaron (2016). Deep Learning. MIT Press. ISBN 978-0262035613 Hambleton, R. K., & Jones, R. W. (1993). Comparison of classical test theory and item response theory and their applications to test development. Educational measurement: issues and practice, 12(3), 38-47. Hambleton, R. K., Swaminathan, H., & Rogers, H. J. (1991). Fundamentals of item response theory (Vol. 2). Sage. Hartig, J., & Höhler, J. (2009). Multidimensional IRT models for the assessment of competencies. Studies in Educational Evaluation, 35(2-3), 57-63. Hochreiter, S., & Schmidhuber, J. (1997). Long short-term memory. Neural computation, 9(8), 1735-1780. Holland, P. W., & Thayer, D. T. (1988). Differential item performance and the Mantel-Haenszel procedure. In H. Wainer & H. I. Braun (Eds.), Test validity (pp. 129–145). Hillsdale, NJ: Erlbaum. Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In Advances in Neural Information Processing Systems, pages 2672–2680, 2014. ICFES (2020). Resolución 268 De 2020. https://normograma.icfes.gov.co/docs/resolucion\_icfes\_0268\_2020.htm Icfes. (2021, Abril). Saber al detalle N 08. Retrieved from Icfes: https://www2.icfes.gov.co/documents/39286/2231027/Edicion+8+-+boletin+saber+al+detalle.pdf/0dbb437b-fded-f05d-5d2e-4426e1663e59?version=1.0&t=1647958807836#. Jara Pinzón, D., Riascos Villegas, Á. J., & Romero, M. (2010). Detección de copia en pruebas del Estado. Jung, J. Y., Tyack, L., & von Davier, M. (2022). Automated Scoring of Constructed-Response Items Using Artificial Neural Networks in International Large-scale Assessment. Psychological Test and Assessment Modeling, 64(4), 471-494. Khobahi, S.; Soltanalian, M. (2019). "Model-Aware Deep Architectures for One-Bit Compressive Variational Autoencoding" Kim, S. (2006), A Comparative Study of IRT Fixed Parameter Calibration Methods. Journal of Educational Measurement, 43: 355-381. https://doi.org/10.1111/j.1745-3984.2006.00021.x Kim, S. (2006), A Comparative Study of IRT Fixed Parameter Calibration Methods. Journal of Educational Measurement, 43: 355-381. https://doi.org/10.1111/j.1745-3984.2006.00021.x Kim, S. H., Cohen, A. S., & Kim, H. O. (1994). An investigation of Lord's procedure for the detection of differential item functioning. Applied Psychological Measurement, 18(3), 217-228. Kim, S. H., Cohen, A. S., & Kim, H. O. (1994). An investigation of Lord's procedure for the detection of differential item functioning. Applied Psychological Measurement, 18(3), 217-228. Kingma, D. P., & Welling, M. (2019). An introduction to variational autoencoders. In Foundations and Trends in Machine Learning (Vol. 12, Issue 4). https://doi.org/10.1561/2200000056 Kingma, Diederik P.; Welling, Max (2014-05-01). "Auto-Encoding Variational Bayes". arXiv:1312.6114 Kramer, Mark A. (1991). "Nonlinear principal component analysis using autoassociative neural networks" (PDF). AIChE Journal. 37 (2): 233–243. doi:10.1002/aic.690370209. Lalor, J. P., Wu, H., & Yu, H. (2017). CIFT: Crowd-Informed Fine-Tuning to Improve Machine Learning Ability. ArXiv: Computation and Language, 6(February). Lin, T., Wang, Y., Liu, X., & Qiu, X. (2022). A survey of transformers. AI Open. Linacre, J. M. (1994). Constructing measurement with a Many-Facet Rasch model. In Objective measurement: Theory into practice: Volume 2. Londregan, J. (2021). Handbook of Item Response Theory, Volume 1. Measurement: Interdisciplinary Research and Perspectives, 19(1). https://doi.org/10.1080/15366367.2020.1771960 Lord, F. M. (1983). Unbiased estimators of ability parameters, of their variance, and of their parallel-forms reliability. Psychometrika, 48(2), 233-245. Mann, B., Ryder, N., Subbiah, M., Kaplan, J., Dhariwal, P., Neelakantan, A., ... & Amodei, D. (2020). Language models are few-shot learners. arXiv preprint arXiv:2005.14165. Martínez, R., Hernández, M., & Hernández, M. (2014). Psicometría. Alianza Editorial. MinEducacion (2022) Regresan las Pruebas Saber 3°, 5°, 7° y 9°. https://www.mineducacion.gov.co/portal/salaprensa/Noticias/410085:Regresan-las-Pruebas-Saber-3-5-7-y-9-para-cerca-de-200-mil-estudiantes-de-1-300-sedes-educativas-de-todo-el-pais Mitchell, Tom (1997). Machine Learning. New York: McGraw Hill. ISBN 0-07-042807-7. OCLC 36417892 Muñiz, J. (2018) Introducción a la Psicometría. Teoría Clásica y TRI. Muñiz, José. (2010). Las Teorías de los Tests: Teoría Clásica y Teoría de Respuesta a los Ítems. Papeles del psicólogo: revista del Colegio Oficial de Psicólogos, ISSN 0214-7823, Vol. 31, Nº. 1, 2010 (Ejemplar dedicado a: Metodología al servicio del psicólogo), pags. 57-66. 31. Mutch, C., & Tisak, J. (2005). Measurement error and the correlation between positive and negative affect: Spearman (1904, 1907) revisited. Psychological reports, 96(1), 43-46. Novick, M. R. (1966). The axioms and principal results of classical test theory. Journal of Mathematical Psychology, 3(1). https://doi.org/10.1016/0022-2496(66)90002-2 OpenAI (2023). GPT-4 Technical Report. arXiv:2303.08774. https://doi.org/10.48550/arXiv.2303.08774 Ostini, Remo; Nering, Michael L. (2005). Polytomous Item Response Theory Models. Quantitative Applications in the Social Sciences. Vol. 144. SAGE. ISBN 978-0-7619-3068-6. Phelps, R. P. (2011). Standards for educational & psychological testing. New Orleans, LA: American Psychological Association. PISA 2019, Released Field Trial and Main Survey New Reading Items. https://www.oecd.org/pisa/test/PISA2018_Released_REA_Items_12112019.pdf Radford, A., Narasimhan, K., Salimans, T., & Sutskever, I. (2018). Improving language understanding by generative pre-training Radford, A., Wu, J., Child, R., Luan, D., Amodei, D., & Sutskever, I. (2019). Language models are unsupervised multitask learners. OpenAI blog, 1(8), 9. Radford, A., Wu, J., Child, R., Luan, D., Amodei, D., & Sutskever, I. (2019). 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In Games and Simulations in Online Learning: Research and Development Frameworks. https://doi.org/10.4018/978-1-59904-304-3.ch017 Stone, JV (2013), "Bayes' Rule: A Tutorial Introduction to Bayesian Analysis" Sun, F., Liu, J., Wu, J., Pei, C., Lin, X., Ou, W., & Jiang, P. (2019, November). BERT4Rec: Sequential recommendation with bidirectional encoder representations from transformer. In Proceedings of the 28th ACM international conference on information and knowledge management (pp. 1441-1450). Thissen, D. & Orlando, M. (2001). Item response theory for items scored in two categories. In D. Thissen & Wainer, H. (Eds.), Test Scoring (pp. 73-140). Mahwah, NJ: Lawrence Erlbaum Associates, Inc. Thurstone, L. L., & Chave, E. (1929). J. The measurement of attitudes. Chicago, III.: University of Chicago Press. Tran, Viet Hung (2018). "Copula Variational Bayes inference via information geometry". arXiv:1803.10998 Vakadkar, K., Purkayastha, D., & Krishnan, D. (2021). Detection of Autism Spectrum Disorder in Children Using Machine Learning Techniques. SN Computer Science, 2(5), 1-9. Van Rossum, G., & Drake, F. L. (2009). Python 3 Reference Manual. Scotts Valley, CA: CreateSpace. Virla, M. Q. (2010). Confiabilidad y coeficiente Alpha de Cronbach. Telos, 12(2), 248-252. Warm, T. A. (1989). Weighted likelihood estimation of ability in item response theory. Psychometrika, 54(3), 427-450. Wolins, L., Wright, B. D., & Rasch, G. (1982). Probabilistic Models for some Intelligence and Attainment Tests. Journal of the American Statistical Association, 77(377). https://doi.org/10.2307/2287805
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dc.format.extent.spa.fl_str_mv	x, 81 páginas
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dc.coverage.country.spa.fl_str_mv	Colombia
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dc.publisher.spa.fl_str_mv	Universidad Nacional de Colombia
dc.publisher.program.spa.fl_str_mv	Bogotá - Ingeniería - Maestría en Ingeniería - Ingeniería de Sistemas y Computación
dc.publisher.faculty.spa.fl_str_mv	Facultad de Ingeniería
dc.publisher.place.spa.fl_str_mv	Bogotá, Colombia
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institution	Universidad Nacional de Colombia
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spelling	Atribución-NoComercial 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Niño Vásquez, Luis Fernandobc784b82735e16fe53653c3f5c8f3bbeDuplat Durán, Ricardo Renéd6edc3d91fb55aaf254a538bafd6c27blaboratorio de Investigación en Sistemas Inteligentes Lisi2024-04-02T00:15:56Z2024-04-02T00:15:56Z2024-01-28https://repositorio.unal.edu.co/handle/unal/85835Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, diagramasLos exámenes estandarizados son valiosas herramientas para evaluar de manera objetiva tanto las características cognitivas como no cognitivas de una población específica. Para construir escalas de medición que reflejen con precisión los constructos que estos exámenes buscan evaluar, se recurre comúnmente a la Teoría de Respuesta al Ítem (TRI), una técnica estadística. Sin embargo, la TRI presenta limitaciones cuando sus supuestos no se cumplen, comprometiendo la comparabilidad a lo largo del tiempo y entre subpoblaciones. Este trabajo de grado se propone desarrollar una metodología innovadora que utiliza Redes Neuronales Artificiales (RNA), específicamente a través de AutoEncoders (AE), para preservar las ventajas de la TRI y aplicarla incluso cuando sus supuestos no se cumplen, buscando incluso mejorar la calidad de ajuste y pronóstico. La investigación se basa en el análisis del examen Saber 11 aplicado en los años 2018 y 2019, durante los calendarios A y B en el país. Se obtuvieron resultados que en algunos casos superan el rendimiento de un modelo clásico de la TRI, como el modelo logístico de 2 parámetros (2PL). Esta metodología propuesta no solo busca subsanar las limitaciones de la TRI en ciertos contextos, sino que también busca optimizar la precisión en la asignación de puntajes en exámenes estandarizados mediante técnicas de equiparación compatibles con la psicometría. La aplicación de RNA, en particular a través de AE, emerge como una prometedora alternativa que contribuye al avance de la evaluación estandarizada, ofreciendo mayor flexibilidad y robustez en la medición de constructos educativos. (Texto tomado de la fuente).Standardized exams are valuable tools for objectively assessing both cognitive and non-cognitive characteristics of a specific population. To construct measurement scales that accurately reflect the constructs these exams aim to evaluate, the Item Response Theory (IRT), a statistical technique, is commonly employed. However, IRT has limitations when its assumptions are not met, compromising comparability over time and among subpopulations. This thesis aims to develop an innovative methodology using Artificial Neural Networks (ANNs), specifically through AutoEncoders (AE), to preserve the advantages of IRT and apply it even when its assumptions are not met, seeking to enhance the quality of fit and forecasting. The research is based on the analysis of the Saber 11 exam administered in 2018 and 2019, during schedules A and B in the country. Results were obtained that, in some cases, outperform the performance of a classical IRT model, such as the 2-parameter logistic model (2PL). This proposed methodology not only aims to address the limitations of IRT in certain contexts but also seeks to optimize accuracy in score assignment in standardized exams through equating techniques compatible with psychometrics. The application of ANN, particularly through AE, emerges as a promising alternative contributing to the advancement of standardized assessment, offering greater flexibility and robustness in measuring educational constructs.MaestríaMagíster en Ingeniería - Ingeniería de Sistemas y ComputaciónSistemas inteligentesx, 81 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ingeniería - Maestría en Ingeniería - Ingeniería de Sistemas y ComputaciónFacultad de IngenieríaBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá000 - Ciencias de la computación, información y obras generales::005 - Programación, programas, datos de computación370 - Educación::373 - Educación secundariaCalificación de exámenes estandarizadosTeoría de Respuesta al ÍtemRedes Neuronales ArtificialesPsicometríaEquiparación de puntajesModelo logístico de 2 parámetrosAutoEncodersStandardized exam scoringItem Response TheoryArtificial Neural NetworksPsychometrics2-parameter logistic modelScore equatingEvaluación del estudiantePsicometríaInformática educativaStudent evaluationPsychometricsComputer uses in educationAsignación de puntajes en exámenes estandarizados mediante el uso de redes neuronales y técnicas de equiparación psicométricas compatibles: Caso examen Saber 11 en ColombiaAssignment of standardized test scores using neural networks and compatible psychometric equating techniques: The case of the Saber 11 exam in Colombia.Trabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMColombiahttp://vocab.getty.edu/page/tgn/1000050American Educational Research Association -AERA, American Psychological Association - APA, & National Council on Measurement in Education –NCME (2018). Estándares para pruebas educativas y psicológicas. American Educational Research Association.Amin, A. (2020), ``A Face Recognition System Based on Deep Learning (FRDLS) to Support the Entry and Supervision Procedures on Electronic Exams``. International Journal of Intelligent Computing and Information Sciences, 20(1). https://doi.org/10.21608/ijicis.2020.23149.1015Basheer, Imad & Hajmeer, M.N.. (2001). Artificial Neural Networks: Fundamentals, Computing, Design, and Application. Journal of microbiological methods. 43. 3-31.Bock, R. D., & Zimowski, M. F. (1997). Multiple group IRT. In Handbook of modern item response theory (pp. 433-448). New York, NY: Springer New York.Bolt, D. M., Hare, R. D., Vitale, J. E., & Newman, J. P. (2004). A Multigroup Item Response Theory Analysis of the Psychopathy Checklist-Revised. Psychological assessment, 16(2), 155.Bozak, A., & Aybek, E. C. (2020). 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Journal of the American Statistical Association, 77(377). https://doi.org/10.2307/2287805EstudiantesInvestigadoresMaestrosPúblico generalLICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/85835/1/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD51ORIGINAL1032412151.2024.pdf1032412151.2024.pdfTesis de Maestría en Ingeniería - Ingeniería de Sistemas y Computaciónapplication/pdf3705956https://repositorio.unal.edu.co/bitstream/unal/85835/2/1032412151.2024.pdf4af15c23a9984c3b4daa322a84e6fac5MD52THUMBNAIL1032412151.2024.pdf.jpg1032412151.2024.pdf.jpgGenerated Thumbnailimage/jpeg5712https://repositorio.unal.edu.co/bitstream/unal/85835/3/1032412151.2024.pdf.jpga8b7b2a0eef84a389dbaa7c2d637af2bMD53unal/85835oai:repositorio.unal.edu.co:unal/858352024-04-01 23:04:23.315Repositorio Institucional Universidad Nacional de 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