## Estimation of latent ability using a response pattern of graded scores |

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### Contents

Definition of Response Pattern and Operating Characteristic | 3 |

Maximum Likelihood Estimator and Bayes Modal Estimator based on the Response Pattern | 5 |

Sufficient Conditions for the Existence of the Unique Maximum Likelihood Estimator and the Unique Bayes Modal Estimator When the Entire Resp... | 9 |

Copyright | |

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### Common terms and phrases

amount of information asymptotes Bayes estimator Bayes modal estimator characteristic of graded characteristic of item curve defined denote dichotomous items discriminating powers dotted line entire response pattern error of measurement estimates assigned example expectation Factor Analysis figure of Figure fixed value formula given response pattern graded item responses graded response hypothetical test individual item responses information function information given instance item characteristic function item g item parameters items are scored items C2 latent ability latent density function latent variable LIS-U logistic model maximum likelihood estimator mean-square error model for dichotomous monotonically decreasing normal ogive model operating characteristic patterns h philosophy of scoring positive and negative possible response pattern previous chapter range response category response patterns contained response to item Samejima satisfies condition satisfy the requirements scored dichotomously simple test score solid line solve standard error sufficient statistic symmetric test score category transformed unique maximum likelihood value of estimate variance