CML based estimation of extended Rasch models with the eRm package in R

Patrick Mair · Reinhold Hatzinger

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

Abstract

This paper presents an open source tool for computing extended Rasch models. It is realized in R (R Development Core Team, 2006) and available as package eRm. In addition to ordinary Rasch models extended models such as linear logistic test models, (linear) rating scale models and (linear) partial credit models can be estimated. A striking feature of this package is the implementation of conditional maximum likelihood estimation techniques which relate directly to Rasch's original concept of specific objectivity. The mathematical and epistemological benefits of this estimation method are discussed. Moreover, the capabilities of the eRm routine with respect to structural item response designs are demonstrated.

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References

1969Statistical Theories of Mental Test Scores 1961Probabilistic Models for Some Intelligence and Attainment Tests 2000Item response theory for psychologists 1982A Rasch Model for Partial Credit Scoring 1978A Rating Formulation for Ordered Response Categories 1981Marginal Maximum Likelihood Estimation of Item Parameters: Application of an EM Algorithm 1987Latent Class Analysis 1968Some latent trait models and their use in inferring an examinee's ability

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