{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/87423"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/87423","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Contributions to Estimation in Item Response Theory","abstract":"In the logistic item response theory models, the number of parameters tends to infinity together with the sample size. Thus, there has been a longstanding question of whether the joint maximum likelihood estimates for these models are consistent. The main contribution of this paper is the study of the asymptotic properties and computation of the joint maximum likelihood estimates, as well as an alternative estimation procedure, one-step estimation. The one-step estimates are much easier to compute, yet are consistent and first-order equivalent to the joint maximum likelihood estimates under certain conditions on the sample sizes if the marginal distribution of the ability parameter is correctly specified. The one-step estimates are also highly robust against modest misspecifications of the ability distribution. We also study the accuracy of variance estimates for the one-step estimates. Finally, we study tests of the goodness of fit for the models. We show that Rao's score test is superior to the existing chi-square tests.","abstract_html":"In the logistic item response theory models, the number of parameters tends to infinity together with the sample size. Thus, there has been a longstanding question of whether the joint maximum likelihood estimates for these models are consistent. The main contribution of this paper is the study of the asymptotic properties and computation of the joint maximum likelihood estimates, as well as an alternative estimation procedure, one-step estimation. The one-step estimates are much easier to compute, yet are consistent and first-order equivalent to the joint maximum likelihood estimates under certain conditions on the sample sizes if the marginal distribution of the ability parameter is correctly specified. The one-step estimates are also highly robust against modest misspecifications of the ability distribution. We also study the accuracy of variance estimates for the one-step estimates. Finally, we study tests of the goodness of fit for the models. 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Thus, there has been a longstanding question of whether the joint maximum likelihood estimates for these models are consistent. The main contribution of this paper is the study of the asymptotic properties and computation of the joint maximum likelihood estimates, as well as an alternative estimation procedure, one-step estimation. The one-step estimates are much easier to compute, yet are consistent and first-order equivalent to the joint maximum likelihood estimates under certain conditions on the sample sizes if the marginal distribution of the ability parameter is correctly specified. The one-step estimates are also highly robust against modest misspecifications of the ability distribution. We also study the accuracy of variance estimates for the one-step estimates. Finally, we study tests of the goodness of fit for the models. We show that Rao's score test is superior to the existing chi-square tests.","Made available in DSpace on 2015-09-28T16:02:49Z (GMT). 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