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Browsing by Author "Harwell, Michael R."

Now showing 1 - 3 of 3
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    Computing elementary symmetric functions and their derivatives: A didactic
    (1996) Baker, Frank B.; Harwell, Michael R.
    The computation of elementary symmetric functions and their derivatives is an integral part of conditional maximum likelihood estimation of item parameters under the Rasch model. The conditional approach has the advantages of parameter estimates that are consistent (assuming the model is correct) and statistically rigorous goodness-of-fit tests. Despite these characteristics, the conditional approach has been limited by problems in computing the elementary symmetric functions. The introduction of recursive formulas for computing these functions and the availability of modem computers has largely mediated these problems; however, detailed documentation of how these formulas work is lacking. This paper describes how various recursion formulas work and how they are used to compute elementary symmetric functions and their derivatives. The availability of this information should promote a more thorough understanding of item parameter estimation in the Rasch model among both measurement specialists and practitioners. Index terms: algorithms, computational techniques, conditional maximum likelihood, elementary symmetric functions, Rasch model.
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    An empirical study of the effects of small datasets and varying prior variances on item parameter estimation in BILOG
    (1991) Harwell, Michael R.; Janosky, Janine E.
    Long-standing difficulties in estimating item parameters in item response theory (IRT) have been addressed recently with the application of Bayesian estimation models. The potential of these methods is enhanced by their availability in the BILOG computer program. This study investigated the ability of BILOG to recover known item parameters under varying conditions. Data were simulated for a two-parameter logistic IRT model under conditions of small numbers of examinees and items, and different variances for the prior distributions of discrimination parameters. The results suggest that for samples of at least 250 examinees and 15 items, BILOG accurately recovers known parameters using the default variance. The quality of the estimation suffers for smaller numbers of examinees under the default variance, and for larger prior variances in general. This raises questions about how practitioners select a prior variance for small numbers of examinees and items. Index terms: BILOG, item parameter estimation, item response theory, parameter recovery, prior distributions, simulation.
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    The use of prior distributions in marginalized Bayesian item parameter estimation: A didactic
    (1991) Harwell, Michael R.; Baker, Frank B.
    The marginal maximum likelihood estimation (MMLE) procedure (Bock & Lieberman, 1970; Bock & Aitkin, 1981) has led to advances in the estimation of item parameters in item response theory. Mislevy (1986) extended this approach by employing the hierarchical Bayesian estimation model of Lindley and Smith (1972). Mislevy’s procedure posits prior probability distributions for both ability and item parameters, and is implemented in the PC-BILOG computer program. This paper extends the work of Harwell, Baker, and Zwarts (1988), who provided the mathematical and implementation details of MMLE in an earlier didactic paper, by encompassing Mislevy’s marginalized Bayesian estimation of item parameters. The purpose was to communicate the essential conceptual and mathematical details of Mislevy’s procedure to practitioners and to users of PC-BILOG, thus making it more accessible. Index terms: Bayesian estimation, BILOG, item parameter estimation, item response theory.