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.
Zwinderman, Aeilko H & Van den Wollenberg, Arnold L. (1990). Robustness of marginal maximum likelihood estimation in the Rasch model. Applied Psychological Measurement, 14, 73-81. doi:10.1177/014662169001400107
Zwinderman, Aeilko H.; Van den Wollenberg, Arnold L..
Robustness of marginal maximum likelihood estimation in the Rasch model.
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