Robustness of Marginal Maximum Likelihoo Estimation in the Rasch odel

Abstract

Simulation studies examined the effect of misspeci fication of the latent ability (θ) distribution on the ac curacy and efficiency of marginal maximum likelihood (MML) item parameter estimates and on MML statistics to test sufficiency and conditional independence. Re sults were compared to the conditional maximum like lihood (CML) approach. Results showed that if θ is as sumed to be normally distributed when its distribution is actually skewed, MML estimators lose accuracy and efficiency when compared to CML estimators. The ef fects are not large, though they increase as the skew- ness of the number-correct score distribution increases. However, statistics to test the sufficiency and condi tional independence assumptions of the Rasch model in the MML approach are very sensitive to misspecifi cation of the θ distribution. Index terms: ability dis tribution, conditional likelihood, efficiency, goodness of fit, marginal likelihood, Rasch model, robustness.

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