Robustness of marginal maximum likelihood estimation in the Rasch model

Simulation studies examined the effect of misspecification of the latent ability (θ) distribution on the accuracy and efficiency of marginal maximum likelihood (MML) item parameter estimates and on MML statistics to test sufficiency and conditional independence. Results were compared to the conditional maximum likelihood (CML) approach. Results showed that if θ is assumed to be normally distributed when its distribution is actually skewed, MML estimators lose accuracy and efficiency when compared to CML estimators. The effects are not large, though they increase as the skewness of the number-correct score distribution increases. However, statistics to test the sufficiency and conditional independence assumptions of the Rasch model in the MML approach are very sensitive to misspecification of the θ distribution. Index terms: ability distribution, conditional likelihood, efficiency, goodness of fit, marginal likelihood, Rasch model, robustness