Ability estimation for conventional tests

Kim, Jwa K.; Nicewander, W. Alan

doi:10.1007/bf02294829

Cited by 46 publications

(40 citation statements)

References 6 publications

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“…Therefore, to get a more quantitative evaluation of the statistical properties of the Bayesian item selection criteria relative to the maximuminformation criterion, a simulation study was run. The results for the item selection criteria in this paper complement earlier results reported for Bayesian and maximum-likelihood ability estimation for conventional linear tests (Kim & Nicewander, 1993;Warm, 1989) and adaptive tests (Warm, 1989).…”

Section: Large-sample Equivalencesupporting

confidence: 83%

Bayesian item selection criteria for adaptive testing

Linden

1998

Psychometrika

127

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R. J. Owen (1975) proposed an approximate empirical Bayes procedure for item selection in adaptive testing. The procedure replaces the true posterior by a normal approximation with closed-form expressions for its first two moments. This approximation was necessary to minimize the computational complexity,involved in a fully Bayesian approach, but is no longer necessary given the computational power currently available in adaptive testing. This paper suggests several item selection criteria for adaptive testing that are all based on the use of the true posterior. Some of the statistical properties of the ability estimator produced by these criteria are discussed and empirically characterized. An empirical study with 300 test items showed that the maximum predicted posterior expected information criterion had excellent mean-squared error for more extreme values of theta, and is the criterion elect for application in short adaptive tests. An appendix presents Owen's equations. (Contains 17 references.) (Author/SLD) ******************************************************************************** Reproductions supplied by EDRS are the best that can be made from the original document. ******************************************************************************** Owen (1975) proposed an approximate empirical Bayes procedure for item selection in adaptive testing. The procedure replaces the true posterior by a normal approximation with closed-form expressions for its first two moments. This approximation was necessary to minimize the computational complexity involved in a fully Bayesian approach but is no longer necessary given the computational power currently available in adaptive testing. This paper suggests several item selection criteria for adaptive testing which are all based on the use of the true posterior. Some of the statistical properties of the ability estimator produced by these criteria are discussed and empirically characterized.Bayesian Selection Criteria 4

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Section: Large-sample Equivalencesupporting

confidence: 83%

Bayesian item selection criteria for adaptive testing

Linden

1998

Psychometrika

127

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“…This inequality is due to the bias of IRT ability estimates and does not happen for the CTT test scores because they are, by definition, unbiased estimates of true scores (Lord & Novick, 1968). Previous research (Kim & Nicewander, 1993;Lord, 1983;Samejima, 1994;Warm, 1989) showed that this bias occurs for any of the ability estimators developed so far, including the ML, MAP, and EAP estimators. However, as discussed in detail later in this paper, most of the previous studies did not pay much attention to the possible inequality between the ρ 2 θθ and ρθθ , presenting formulas for the IRT coefficient by adopting only one of the two definitions of the reliability coefficient.…”

Section: Introductionmentioning

confidence: 94%

A Note on the Reliability Coefficients for Item Response Model-Based Ability Estimates

Kim

2011

Psychometrika

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“…• des tests comportant n = 11, 31 et 101 items, à réponses 0 ou 1 ; • le paramètre ai a été généré selon une distribution Gamma(10 ; 0,1), produisant des valeurs de caractéristiques µ = 1, σ 2 = 0,100, γ1 = 0,632 et γ2 = 0,600 (pour γ1 et γ2, voir (3)), soit des valeurs plausibles dans le domaine des applications TRI ; les valeurs ai présentées dans le petit exemple à 5 items ci-dessus sont représentatives ; • le paramètre bi a été étalé régulièrement de b1 = -3,5 à bn = +3,5 par intervalles égaux à 7 / (n-1) ; cette structure représente un test équilibré, de niveau de difficulté modéré selon Kim et Nicewander (1993) ; • le paramètre a été étalé régulièrement de = -3,5 à = 3,5 par intervalles de 0,1, plutôt que d'être généré par le biais d'une variable de loi normale (2). Les ingrédients du modèle TRI à deux paramètres étant ainsi définis, le programme informatique simulait alors des protocoles aléatoires répondant à ce contexte.…”

Section: Conditions Et Paramètres De L'étudeunclassified

“…Cette corrélation globale donne un léger avantage à l'estimateur BME, tandis le score brut X se tient tout près des autres, comme il a souvent été démontré (Kim et Nicewander, 1993;Galdin et Laurencelle, 2010). Nous avons donc établi les fonctions de régression linéaire « = b⋅ + a » pour les issus de chacun de nos Figure 3.…”

Section: Prédiction Linéaire à Partir Du Vraiunclassified