REGRESIÓN LATENTE EN MODELOS DE RESPUESTA AL ÍTEM LOGÍSTICOS DE TRES PARÁMETROS
Resumen
Se presenta la estimación máximo-verosímil para un modelo de regresión del atributo latente de los modelos de respuesta al ítem logísticos de tres parámetros empleando conjuntamente el modelo de medida IRT. Mediante simulaciones se comparan las estimaciones de los parámetros de regresión y de varianza residual obtenidos mediante el procedimiento propuesto con los que se obtendrían bajo la regresión de las estimaciones usuales del atributo como variable de respuesta. Se encontró que el modelo propuesto proporciona mejores estimaciones puntuales de los parámetros de regresión que las obtenidas mediante la regresión usual por OLS con habilidades estimadas como variable de respuesta. Sin embargo, los errores estándar asintóticos, así como la estimación de la varianza residual, resultan muy pequeños.
Citas
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[13]. FOX, J-P. (2004) Applications of multilevel IRT modeling. School Effectiveness and School Improvement, 15:261-280.
[14]. WILSON, M. & DE BOECK, P. (2004) Descriptive and explanatory item response models. In Paul de Boeck and Mark Wilson, editors, Explanatory Item Response Models: A Generalized Linear and Nonlinear Approach, pages 43-74. Springer-Verlag, New York
[15]. FOX, J.-P (2005). Multilevel IRT using dichotomous and polytomous response data. British Journal of Mathematical and Statistical Psychology, 58:145-172.
[16]. THOMAS, D. R. & LU, I. R. R. Two-step regression with latent variables, revisited. Proceedings of Statistics Canada Symposium 2005 - Methodological Challenges for Future Information Needs.
[17]. PINTO HEYDLER, M. Teoría de respuesta al ítem: Estimación y modelación. 2006
[18]. ANTAL, T. On the latent regression model of Item Response Theory. Technical Report RR-07-12, Educational Testing Service, USA.
[19]. BACCI, S. (2007) Analysis of longitudinal HrQoL using latent regression in the context of Rasch modelling. In Catherine Huber, Nikolaos Limnios, Mounir Mesbah, and Mikhail Nikulin, editors, Mathematical Methods in Survival Analysis, Reliability and Quality of Life. Wiley-ISTE, Inglaterra.
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[22]. TOOMET, O. & HENNINGSEN, A. (2008). maxLik: Maximum Likelihood Estimation.
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[2]. MISLEVY, R. J. ET AL. (1992) Estimating population characteristics from sparse matrix samples of item responses. Journal of Educational Measurement, 29(2):133-161.
[3]. ADAMS, R. J., WILSON, M., & WU, M. (1997). Multilevel item response models: An approach to errors in variables regression. Journal of Educational and Behavioral Statistics, 22:47-76.
[4]. MISLEVY, R. J. & BOCK, R. D. BILOG 3 for Windows.
[5]. FOX, J.-P. & GLAS, C. A.W. (2001) Bayesian estimation of a multilevel IRT model using Gibbs sampling. Psychometrika, 66(2):271-288
[6]. KAMATA, A. (2001) Item analysis by the hierarchical generalized linear model. Journal of Educational Measurement 38(1):79-93.
[7]. WANG, C., DOUGLAS, J., & ANDERSON, S. (2002). Item response models for Joint analysis of quality of life and survival. Statistics in Medicine, 21:129-142.
[8]. FOX, J.-P. & GLAS, C. A.W. (2003) Bayesian modeling of measurement error in predictor variables using item response theory. Psychometrika, 68:169-191.
[9]. RAUDENBUSH, S. W, JOHNSON, C., & SAMPSON, R. J. (2003). A multivariate, multilevel Rasch model with application to self-reported criminal behavior. Sociological Methodology, 33:169-211.
[10]. CEPEDA C., E. & PELA' EZ A., J. M. (2004) Modeling abilities in 3-IRT models. Revista Colombiana de Estadística, 27(1):27-41.
[11]. CHRISTENSEN, K. B. ET AL. (2004) Latent regression in log-linear Rasch models. Communications in statistics: Theory and Methods, 33(6):1295-1313
[12]. PAUL DE BOECK & MARK WILSON, (ED.) (2004) Explanatory Item Response Models: A Generalized Linear and Nonlinear Approach. Springer-Verlag, New York.
[13]. FOX, J-P. (2004) Applications of multilevel IRT modeling. School Effectiveness and School Improvement, 15:261-280.
[14]. WILSON, M. & DE BOECK, P. (2004) Descriptive and explanatory item response models. In Paul de Boeck and Mark Wilson, editors, Explanatory Item Response Models: A Generalized Linear and Nonlinear Approach, pages 43-74. Springer-Verlag, New York
[15]. FOX, J.-P (2005). Multilevel IRT using dichotomous and polytomous response data. British Journal of Mathematical and Statistical Psychology, 58:145-172.
[16]. THOMAS, D. R. & LU, I. R. R. Two-step regression with latent variables, revisited. Proceedings of Statistics Canada Symposium 2005 - Methodological Challenges for Future Information Needs.
[17]. PINTO HEYDLER, M. Teoría de respuesta al ítem: Estimación y modelación. 2006
[18]. ANTAL, T. On the latent regression model of Item Response Theory. Technical Report RR-07-12, Educational Testing Service, USA.
[19]. BACCI, S. (2007) Analysis of longitudinal HrQoL using latent regression in the context of Rasch modelling. In Catherine Huber, Nikolaos Limnios, Mounir Mesbah, and Mikhail Nikulin, editors, Mathematical Methods in Survival Analysis, Reliability and Quality of Life. Wiley-ISTE, Inglaterra.
[20]. BROSTRÖM, G. glmmML: Generalized linear models with clustering. R package version 0.72-0.
[21]. DEVELOPMENT CORE TEAM (2008): A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria URL http://www.R-project.org
[22]. TOOMET, O. & HENNINGSEN, A. (2008). maxLik: Maximum Likelihood Estimation.
[23]. URL http://CRAN.Rproject.org, http://www.maxLik.org. R package version 0.5-2.
