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ability value 9k algorithm for computing algorithm for finite Bock and Aitken category response functions computed at iteration Computing Item Parameter conditional expectation conditional probability continuous latent variable denoted derivative of Equation dichotomous item response discrete latent ability discrete latent variable discrete random variable equal to zero Equation 15 Equation 39 Equation 42 estimates of nk Estimation for Item fc=l i=l i=l fc=l item category response item response functions item response models iteration s consists ith randomly sampled latent ability variable latent class models latent random variable latent variable distribution likelihood for examinee Makov marginal likelihood marginal maximum likelihood maximum likelihood estimates models for dichotomous number of examinees number of items numerical quadrature observed item responses parameters for item partial derivatives population of examinees probability distribution provisional estimate randomly sampled examinee Rasch model side of Equation specified starting values step at iteration substituted into Equation value 8k variable for examinee