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Modelling atypical students response patterns using multidimensional parametric models

Modelling atypical students response patterns using multidimensional parametric models. Gilles Raîche, UQAM Sébastien Béland, UQAM David Magis, Université de Liège Jean-Guy Blais, Université de Montréal Pierre Brochu, CMEC Large-Scale Assessments: Policy, Research and Practice CSSE / CERA

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Modelling atypical students response patterns using multidimensional parametric models

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  1. Modelling atypical students response patterns using multidimensional parametric models Gilles Raîche, UQAM Sébastien Béland, UQAM David Magis, Université de Liège Jean-Guy Blais, Université de Montréal Pierre Brochu, CMEC Large-Scale Assessments: Policy, Research and Practice CSSE / CERA Montréal, 2010

  2. SUMMARY • Introduction and Objectives • Unidimensional IRT Models • IRT Person Parameters Models • Person response Curve • Multidimensional Item Response Models • Estimation • An R Package: irtProb • Examples • Other Considerations • References and contacts

  3. INTRODUCTION • Presentation • IRT Models of Interest • Unidimensional latent proficiency • Dichotomous response • Monotonic • Logistic Probability Distribution

  4. OBJECTIVES • Simulation of Inappropriate Response Patterns • Person Misfit Detection Indices • Distributional Properties of Person Misfit Indices • Adjusted Proficiency Level Estimation in Presence of Person Misfit

  5. UNIDIMENSIONAL IRT MODELS 3 Parameter Logistic (3PL) (Birnbaum, 1968) 4 Parameters Logistic (4PL) (McDonald, 1967) where if ai is considered as a standard deviation

  6. PERSON RESPONSE CURVE (Trabin and Weiss, 1983)

  7. MULTIDIMENSIONAL ITEM RESPONSE MODELS • Personal Variance (σ2) (Ferrando, 2004; Thurstone, 1927) • Personal Inattention (δ) • Personal Pseudo-Guessing (χ) (Strandmark and Linn, 1987)

  8. MULTIDIMENSIONAL ITEM RESPONSE MODELS • Higher Order Models

  9. ESTIMATION OF SUBJECT PARAMETERS • Package: irtProb • MAP Estimators • A Priori Probability Distribution • σ : U(0,4) • θ: U(-4,4) • X: U(0,1) • δ : U(0,1)

  10. A R PACKAGE: irtProb • Available on R Cran Site • Functionnalities • Estimation of Person Parameters (MAP) • Likelihood Curves • Person Characteristic Curves • Probability, Density and Random Functions • Simulation of Response Patterns • Classical <-> IRT Item Parameters • Model Selection

  11. EXAMPLES – 01 (X) 1 σ = 0, δ = 0, b = -5 to 5, c = 0, d = 0, 40 items, 100 simulated sujects Model 1: θ only Model 2: θ and Pseudo-Guessing Model 3 σ, θ, Pseudo-Guessing and δ

  12. EXAMPLES – 01 (X)

  13. EXAMPLES – 02 (X) 1 σ = 0, δ = 0, b = -5 to 5, c = 0, d = 0, 40 items, 100 simulated subjects Model 1: θ only Model 2: θ and Pseudo-Guessing Model 3 σ, θ, Pseudo-Guessing and δ

  14. EXAMPLES – 02 (X)

  15. EXAMPLES – 03 (σ) 1 X = 0, δ = 0, b = -5 to 5, c = 0, d = 0, 40 items, 100 simulated subjects Model 1: θ only Model 2: θ and σ Model 3 σ, θ, Pseudo-Guessing and δ

  16. EXAMPLES – 03 (σ)

  17. OTHER CONSIDERATIONS • Multidimensional EAP Estimation Very Computer Intensive • Warm Weighted Likelihood Estimator • Item Parameters Estimation • Confidence Interval For The Additionnal Person Parameters • Other Person Fit Indices: Pseudo-Guessing and Inattention

  18. REFERENCES / 1 Barton, M. A. and Lord, F. M. (1981). An upper asymptote for the three-parameter logistic item-response model. Research bullelin 81-20. Princeton, NJ: Educational Testing Service. Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee’s ability. In F. M. Lord and M. Novick (Eds): Statistical theories of mental test scores. New York, NJ: Addison-Wesley. Ferrando, P. J. (2004). Person reliability in personality measurement: an item response theory analysis. Applied Psychological Measurement, 28(2), 126-140. Hulin, C. L., Drasgow, F., and Parsons, C. K. (1983). Item response theory. Homewood, IL: Irwin. Levine, M. V., and Drasgow, F. (1983). Appropriateness measurement: validating studies and variable ability models. In D. J. Weiss (Ed.): New horizons in testing. New York, NJ: Academic Press. Magis, D. (2007). Enhanced estimation methods in IRT. In D. Magis (Ed.): Influence, information and item response theory in discrete data analysis. Doctoral dissertation, Liège, Belgium: University de Liège.

  19. REFERENCES / 2 McDonald, R. P. (1967). Nonlinear factor analysis. Psyhometric Monographs, 15. Raîche, G., and Blais, J.-G. (2003). Efficacité du dépistage des étudiants et des étudiants qui cherchent à obtenir un résultat faible au test de classement en anglais, langue seconde, au collégial. In J.-G. Blais, and G. Raîche (Ed.): Regards sur la modélisation de la mesure enen éducation et en sciences sociales. Ste-Foy, QC: Presses de l’Université Laval. Strandmark, N. L. and Linn, R. L. (1987). A generalized logistic item response model parameterizing test score inappropriateness. Applied Psychological Measurement, 11(4), 355-370. Thurstone, L. L. (1927). A law of comparative judgment. Psychological Review, 34, 273-286. Trabin, T. E., and Weiss, D. J. (1983). The person response curve : fit of individuals to item response theory models. In D. J. Weiss (Ed.): New horizons in testing. New York, NJ: Academic Press.

  20. CONTACTS • Gilles Raîche • http://camri.uqam.ca • Sébastien Béland • sebastien.beland.1@hotmail.com • David Magis • david.magis@psy.kuleuven.be • Jean-Guy Blais • http://www.griemetic.ca • Pierre Brochu • p.broche@cmec.ca

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