A Rasch Hierarchical Measurement Model

Kimberly S. Maier

70 citations0/0 files storedJournal of Educational and Behavioral Statistics

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Psychometric Methodologies and Testing Educational Assessment and Pedagogy Statistical Methods and Bayesian Inference

Abstract

In this article, a hierarchical measurement model is developed that enables researchers to measure a latent trait variable and model the error variance corresponding to multiple levels. The Rasch hierarchical measurement model (HMM) results when a Rasch IRT model and a one-way ANOVA with random effects are combined ( Bryk & Raudenbush, 1992 ; Goldstein, 1987 ; Rasch, 1960 ). This model is appropriate for modeling dichotomous response strings nested within a contextual level. Examples of this type of structure include responses from students nested within schools and multiple response strings nested within people. Model parameter estimates of the Rasch HMM were obtained using the Bayesian data analysis methods of Gibbs sampling and the Metropolis-Hastings algorithm ( Gelfand, Hills, Racine-Poon, & Smith, 1990 ; Hastings, 1970 ; Metropolis, Rosenbluth, Rosenbluth, Teller, & Teller, 1953 ). The model is illustrated with two simulated data sets and data from the Sloan Study of Youth and Social Development. The results are discussed and parameter estimates for the simulated data sets are compared to parameter estimates obtained using a two-step estimation approach.

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References

1969Statistical Theories of Mental Test Scores 1961Probabilistic Models for Some Intelligence and Attainment Tests 1997Handbook of Modern Item Response Theory 1984Item Response Theory: Principles and Applications 1985Item Response Theory 1993Item Response Theory: Parameter Estimation Techniques.1999A Straightforward Approach to Markov Chain Monte Carlo Methods for Item Response Models 1994Item Response Theory: Parameter Estimation Techniques.

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2012Bayesian tests of measurement invariance 2007Multilevel IRT Modeling in Practice with the Packagemlirt 2006DIF Identification Using HGLM for Polytomous Items 2003The Use of Multilevel Item Response Theory Modeling in Applied Research: An Illustration

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