Analysis of multinomial models under inequality constraints: Applications to measurement theory

2009 ◽  
Vol 53 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Clintin P. Davis-Stober
Keyword(s):  
Measurement Theory ◽  
Inequality Constraints ◽  
Multinomial Models

scholarly journals multibridge: An R Package To Evaluate Informed Hypotheses in Binomial and Multinomial Models

2021 ◽  
Author(s):  
Alexandra Sarafoglou ◽  
Frederik Aust ◽  
Maarten Marsman ◽  
Eric-Jan Wagenmakers ◽  
Julia M. Haaf
Keyword(s):  
Null Hypothesis ◽  
Multinomial Distribution ◽  
Inequality Constraints ◽  
R Package ◽  
Equality Constraints ◽  
Frequency Data ◽  
Multinomial Models ◽  
Bridge Sampling ◽  
Restricted Parameter Space ◽  
Accurate Comparison

The multibridge R package allows a Bayesian evaluation of informed hypotheses H_r applied to frequency data from an independent binomial or multinomial distribution. multibridge uses bridge sampling to efficiently compute Bayes factors for the following hypotheses concerning the latent category proportions theta: (a) hypotheses that postulate equality constraints (e.g., theta_1 = theta_2 = theta_3); (b) hypotheses that postulate inequality constraints (e.g., theta_1 < theta_2 < theta_3) or (theta_1 > theta_2 > theta_3); (c) hypotheses that postulate mixtures of inequality constraints and equality constraints (e.g., theta_1 < theta_2 = theta_3); and (d) hypotheses that postulate mixtures of (a)--(c) (e.g., theta_1 < theta_2 = theta_3, theta_4). Any informed hypothesis H_r may be compared against the encompassing hypothesis H_e that all category proportions vary freely, or against the null hypothesis H_0 that all category proportions are equal. multibridge facilitates the fast and accurate comparison of large models with many constraints and models for which relatively little posterior mass falls in the restricted parameter space. This paper describes the underlying methodology and illustrates the use of multibridge through fully reproducible examples.

A Hierarchy of Multinomial Models for Multidimensional Source Monitoring

Methodology ◽  
2005 ◽  
Vol 1 (1) ◽  
pp. 2-17 ◽  
Author(s):  
Thorsten Meiser
Keyword(s):  
Cognitive Processes ◽  
Source Monitoring ◽  
Source Information ◽  
Model Comparisons ◽  
Storage And Retrieval ◽  
Multinomial Processing Tree ◽  
Multinomial Models ◽  
Hierarchical Relationship ◽  
Statistical Framework ◽  
Tree Models

Abstract. Several models have been proposed for the measurement of cognitive processes in source monitoring. They are specified within the statistical framework of multinomial processing tree models and differ in their assumptions on the storage and retrieval of multidimensional source information. In the present article, a hierarchical relationship is demonstrated between multinomial models for crossed source information ( Meiser & Bröder, 2002 ), for partial source memory ( Dodson, Holland, & Shimamura, 1998 ) and for several sources ( Batchelder, Hu, & Riefer, 1994 ). The hierarchical relationship allows model comparisons and facilitates the specification of identifiability conditions. Conditions for global identifiability are discussed, and model comparisons are illustrated by reanalyses and by a new experiment on the storage and retrieval of multidimensional source information.

Tracking and Targeting: Investigating Item Performance on the English Section of a University Entrance Examination over a 4-Year Period

2008 ◽  
Vol 30 (1) ◽  
pp. 105
Author(s):  
Christopher Weaver ◽  
Yoko Sato
Keyword(s):  
Test Performance ◽  
Systematic Approach ◽  
Rating Scales ◽  
Item Difficulty ◽  
Language Skills ◽  
Measurement Theory ◽  
Entrance Examination ◽  
University Admissions ◽  
Entrance Examinations ◽  
National University

This empirical study introduces population targeting and cut-off point targeting as a systematic approach to evaluating the performance of items in the English section of university entrance examinations. Using Rasch measurement theory, we found that the item difficulty and the types of items in a series of national university entrance examinations varied considerably over a 4-year period. However, there was progress towards improved test performance in terms of an increased number of items assessing different language skills and content areas as well as an increased number targeting test takers’ knowledge of English. This study also found that productive items rather than receptive items better targeted test takers’ overall knowledge of English. Moreover, productive items were more consistently located around the probable cut point for university admissions. The paper concludes with a detailed account of a number of probable factors that could influence item performance, such as the use of rating scales. 本論文では、ある国立大学における大学入試の英語の問題の変化を実証的に検証したものである。テスト項目の結果を検証するための体系的なアプローチとして、「母集団を対象としたアプローチ」および「足きり点を対象としたアプローチ」という方法を導入した。ラッシュ・モデリングを用いて分析した結果、過去４年間の間に、項目の困難度および項目の型について、様々な技能を測定していること、内容も多様であること、英語の知識を検証している項目が増えたこと、などの点で大きく変化していることがわかった。さらに、産出能力の方が受容能力を測定する項目よりも入学者決定の際の足きり点の周辺に収束する傾向が見られた。項目ごとの成績に影響を及ぼす可能性のある多様な要因について詳細な検討を行った。

Distributed proximal-gradient method for convex optimization with inequality constraints

2015 ◽  
Vol 56 ◽  
pp. 160 ◽  
Author(s):  
Jueyou Li ◽  
Changzhi Wu ◽  
Zhiyou Wu ◽  
Qiang Long ◽  
Xiangyu Wang
Keyword(s):  
Convex Optimization ◽  
Gradient Method ◽  
Inequality Constraints ◽  
Proximal Gradient Method
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