Synthesizing the Ability in Multidimensional Item Response Theory Models

• ÁLVARO MAURICIO MONTENEGRO DÍAZ ^[1] ; EDILBERTO CEPEDA ^[1]
  1. [1] Universidad Nacional de Colombia

     Universidad Nacional de Colombia

     Colombia

     
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 33, Nº. 1, 2010, págs. 127-147
• Idioma: inglés
• Títulos paralelos:
  • Habilidad sintética en modelos multidimensionales de teoría de respuesta al ítem
• Enlaces
  • Texto completo
• Resumen
  • español

    Un problema central asociado con los Modelos Multidimensionales de Teoría de Respuesta al Item (TRIM) es la imposibilidad de ordenar a los examinados. En este artículo, se obtienen dos índices sintéticos unidimensionales que son combinaciones lineales óptimas del vector de habilidades. Estos índices sintéticos son semejantes a la composición de referencia comúnmente usada en los modelos TRIM, pero son más fáciles de calcular. Los índices sintéticos se comparan con el parámetro de habilidad obtenido cuando un conjunto de datos multidimensionales es ajustado con un modelo TRI unidimensional.

  • English

    A central problem associated with Multidimensional Item Response Theory (MIRT) Models is the impossibility of ordering the examinees. In this paper, we obtain two unidimensional synthetic indices that are optimal linear combinations of the ability vector. These synthetic indices are similar to the reference composite commonly used in MIRT models, but they are easier to calculate and interpret. The synthetic indices are compared with the unidimensional ability obtained when a multidimensional data is fitted with an unidimensional IRT (UIRT) model.

• Referencias bibliográficas
  • Ackerman, T.. (1989). 'Unidimensional IRT Calibration of Compensatory and Noncompensatory Multidimensional Items'. Applied Psychological...
  • Aguilera, A.,Pérez-Aguila, R.. (2004). 'WSCG SHORT Communications papers proceedings'. Union Agency - Science Press, Czech Republic....
  • Ansley, T.,Forsyth, R.. (1985). 'An Examination of the Charateristics of Unidimensional IRT Parameter Estimates Derived from Two Dimensional...
  • Antal, T.. (2007). 'On multidimensional item response theory: a coordinate free approach'. Electronic Journal of Statistics. 1. 290-306
  • Baker, F. B.,Seok-Ho, K.. (2004). Item Response Theory. 2. Marcel Decker Inc..
  • Bock, R. D.. (1972). 'Estimating Item Parameters and Latent Ability when Responses are Scored in Two or more Nominal Categories'....
  • Bock, R. D.,Aitkin, M.. (1981). 'Marginal Maximum Likelihood Estimation of Item Parameters: Application of an EM Algorithm'. Psychometrika....
  • Bock, R. D.,Jones, L. V.. (1968). The Measurement and Prediction of the Judge and Choice. San Francisco: Holden-Day.
  • Bégin, A.,Glass, C. A.. (2001). 'MCMC estimation and some Model-Fit Analysis of Multidimensional IRT Models'. Psychometrika. 66. 541-562
  • Carroll, J. W. B.,Levine, M.. (2007). 'Multidimensional Modeling with Unidimensional Approximations'. Journal of Mathematical Psychology....
  • De la Torre, J.,Patz, R.. (2005). 'Making the Most of what we have: A Practical Application of Multidimensional Item Response Theory in...
  • Doody, E.. (1985). Examining the Effects of Multidimensional Data on Ability and Item Parameter Estimation using the Three-Parameter Logistic...
  • Folk, V.,Green, V.. (1989). 'Adaptive Estimation when the Unidimensionality Assumption of IRT is Violated'. Applied Psychological...
  • Fraser, C.. (1988). 'NOHARM II: A Fortran Program for Fitting Unidimensional and Multidimensional Normal Ogive Models of Latent Trait...
  • Hambleton, R. K.,Swaminathan, H.,Rogers, H. J.. (1991). Fundamentals of Item Response Theory. Sage Publications. Newbury Park.
  • Kendall, M.. (1961). A Course in the Geometry of n Dimensions. Charles Griffin and Company Limited.
  • Kromrey, D.,Parshall, C.,Chason, W.. (1999). 'SUGI 24'. SAS.
  • Levine, M.. (2003). 'Dimension in Latent Variable Models'. Journal of Mathematical Psychology. 47. 450-466
  • Levine, M.. (2003). 'Dimension in Latent Variable Models'. Journal of Mathematical Psychology. 47. 450-466
  • Mathai, M.. (1999). 'Random p-Content of a p-Parallelotope in Euclideann-Space'. Advances in Applied Probability. 31. 343-354
  • Mortari, D.. (2001). 'On the Rigid Rotation Concept in n-Dimensional Spaces'. Journal of the Astronautical Sciences. 49. 401-420
  • Peña, D.. (2002). Análisis de Datos Multivariantes. McGraw Hill.
  • Peña, D.,Rodríguez, J.. (2003). 'Descriptive Measures of Multivariate Scatter and Linear Dependence'. Journal of Multivariate Analysis....
  • Reckase, M.. (1985). 'The Difficulty of Test Items that Measure more than one Ability'. Applied Psycological Measurement. 9. 401-412
  • Reckase, M.. (1990). Unidimensional Data from Multidimensional Data from Unidimensional Tests. 'Paper presented at the annual meeting...
  • Reckase, M.. (1997). 'The Past and the Future of Multidimensional Item Response Theory'. Applied Psychological Measurement. 21. 25-36
  • Reckase, M.. (2007). 'Multidimensional Item Response Theory'. Handbook of Statistics. 26. 607-642
  • Reckase, M.. (2009). Multidimensional Item Response Theory. Springer.
  • Reckase, M.,Ackerman, T.. (1988). 'Building a Unidimensional Test Using Multidimensional Items'. Journal of Educational Measurement....
  • Reckase, M.,Carlson, J.,Ackerman, T.. (1986). The Interpretation of the Unidimensional IRT Parameters when Estimate from Multidimensional...
  • Reckase, M.,Stout, W.. (1995). Conditions under which Items that Assess Multiple Ablilities will be fit by Unidimensional IRT Models. 'The...
  • Rizopoulos, D.. (2006). 'Ltm: An R Package for Latent Variable Modeling and Item Response Theory Models'. Journal of Statistical Software....
  • Sheng, Y.. (2007). 'Comparing Multiunidimensional and Unidimensional Item Response Theory Models'. Educational and Psychological Measurement....
  • Sheng, Y.. (2008). 'Bayesian Multidimensional IRT Models with a Hierarchical Structure'. Educational and Psychological Measurement....
  • Stout, W.. (1990). 'A new Item Response Theory Modeling Approach with Applications to Unidimensionality Assessment and Ability Estimation'....
  • Stout, W.,Douglas, B.,Junker, B.,Roussos, L.. (1999). DIMTEST. The William Stout Institute for Measurement, Champaing, IL.
  • Sympson, J.. (1978). 'Proceedings of the 1977 Computarized Adaptive Testing Conference'. Minneapolis: University of Minnesota, Department...
  • (2008). Team, R. D. C. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna.
  • Walker, C.,Beretvas, S.. (2003). 'Comparing Multidimensional and Unidimensional Proficiency Calssifications: Multidimensional IRT as Diagnostic...
  • Wang, M.. (1985). Fitting a Unidimensional Model to Multidimensional Item Response Data: The effect of latent space misspecification on the...
  • Wang, M.. (1986). ''. The Office of Naval Research Contractors Meeting.
  • Way, W.,Ansley, T.,Forsyth, R.. (1988). 'The Comparative Effects of Compensatory and Noncompensatory Two-dimensional Data Items on Unidimensional...
  • Wilson, D.,Wood, R.,Gibbons, R.. (1987). 'Scientific Software'. Mooresville IN.
  • Yen, W.. (1985). 'Increasing Item Complexity: A Possible Cause of Scale Shrinkage for Unidimensional Item Response Theory'. Psychometrika....
  • Zhang, J.,Stout, W.. (1999). 'Conditional Covariance Structure of Generalized Compensatory Multidimensional Items'. Psychometrika....
  • Zhao, J.,McMorris, R.,Pruzek, R.. (2002). The Robusnetss of the Unidimensional 3PL IRT when Applied to Two-Dimensional Data in Computarized...