The Equivalence of the Test Response Function to the Maximum Likelihood Ability Estimate for the Dichotomous Rasch Model: A Proof

Ben Babcock

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The Equivalence of the Test Response Function to the Maximum Likelihood Ability Estimate for the Dichotomous Rasch Model: A Proof

机译：测试响应函数对二分法Rasch模型的最大似然能力估计的等价性：证明

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While several proofs exist that the number keyed (or number correct) score is a sufficient statistic to estimate person measure (or ability, β) in the dichotomous Rasch model, there are few proofs about the direct mathematical link from β to the number correct score. This manuscript proves that the estimation link going from score to β is the test response function, which is the sum of the probabilities correct for all items given the difficulty (δ) values and β.

机译：虽然存在几个键控（或数字正确）分数的数量是一个足够的统计学来估计二分的Rasch模型中的人测量（或能力，β），但是关于从β的直接数学链接到数字正确得分的证据很少。该稿件证明，从得分到β的估计链路是测试响应函数，这是给予难度（Δ）值和β的所有项目的概率的总和。

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《Journal of applied measurement》 |2020年第3期|256-259|共4页
作者
Ben Babcock;
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The American Registry of Radiologic Technologists;

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1. Estimating the standard error of the maximum likelihood ability estimator in adaptive testing using the posterior-weighted test information function [J] . Penfield RD Educational and Psychological Measurement . 2007,第6期

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2. Formulating the Rasch differential item functioning model under the marginal maximum likelihood estimation context and its comparison with Mantel-Haenszel procedure in short test and small sample conditions [J] . Paek I., Wilson M. Educational and Psychological Measurement . 2011,第6期

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3. Spurious Latent Class Problem in the Mixed Rasch Model: A Comparison of Three Maximum Likelihood Estimation Methods under Different Ability Distributions [J] . Sedat Sen International Journal of Testing: Official Journal of the International Test Commission . 2018,第1期

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4. Reconstruction of Continuous Image Using Maximum Likelihood Estimates from Grouped Data for Measuring Light Intensity and Interpolation by Atomic Functions According to Aperture of Photosensitive Element of Sensor [C] . Vladislav Efremov, Irina Efremova, Alexander Malyshev International Russian Automation Conference . 2019

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5. Comparison of ability estimates using unidimensional and multidimensional scoring models for dichotomously scored items. [D] . Radwan, Nizam. 2005

机译：使用一维和多维计分模型对二分计分的项目进行能力估计的比较。
6. An average information restricted maximum likelihood algorithm for estimating reduced rank genetic covariance matrices or covariance functions for animal models with equal design matrices [O] . K Meyer 1997

机译：一种平均信息受限最大似然算法用于估计具有相同设计矩阵的动物模型的降级遗传协方差矩阵或协方差函数
7. Analysis of influence of the item total scores on the levels of ability of respondents in the dichotomous Rasch model based on the weighted maximum likelihood method [O] . E. B. Belov, M. V. Alekseev, N. P. Kitaev, 2019

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8. Bias Function of the Maximum Likelihood Estimate of Ability for Discrete Item Responses [R] . Samejima, F. 1987

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The Equivalence of the Test Response Function to the Maximum Likelihood Ability Estimate for the Dichotomous Rasch Model: A Proof

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