Maximum-Likelihood Estimation

Abstract

A naive approach to maximum-likelihood estimation would be to maximize the likelihood function jointly with respect to θ and β, using a standard technique such as a Newton–Raphson algorithm. To obtain consistent item parameter estimates, the person parameters must, in some sense, be removed from the model. One way of accomplishing this is to introduce the assumption of common distributions of the person parameter. Once the item parameters and, when applicable, the population distribution parameters are estimated, the person parameters can be estimated by treating all other parameters as known constants. The conditional maximum likelihood estimation equations for the partial credit model are relatively straightforward generalizations of the equations for the Rasch model.

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