Improved Item Relational Structure Theory Based on Liu’s Item Ordering Consistency Property

2016 ◽  
pp. 341-346
Author(s):  
Hsiang-Chuan Liu ◽  
Jing-Ming Ju
Keyword(s):  
Relational Structure ◽  
Structure Theory ◽  
Consistency Property ◽  
Relational Structure Theory

Item Relational Structure Theory Based on Liu’s Improved Nonparametric IRT Theory

2013 ◽  
Vol 479-480 ◽  
pp. 1193-1196
Author(s):  
Hsiang Chuan Liu ◽  
Yen Kuei Yu ◽  
Hsien Chang Tsai
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Joint Probability ◽  
Relational Structure ◽  
Structure Theory ◽  
Response Theory ◽  
Nonparametric Item Response Theory ◽  
Relational Structures ◽  
Relational Structure Theory ◽  
Nonparametric Item Response

In this paper, an extensional item relational structure theory based on the improved nonparametric item response theory is proposed. Item relational structure theory (Takeya, 1991) was developed to detect item relational structures of a group of subjects. The differences of these structures and experts knowledge structures can provide more information for planning remedial instruction, developing instruction materials, or educational researches. In this study, Lius improved nonparametric item response theory ( Liu, 2000, 2013) without the local independence assumption is used to estimate the joint probability of two items, and construct personal item relational structures. A Mathematics example is also provided in this paper to illustrate the advantages of the proposed method

Polytomous Item Relational Structure Theory Based on Empirical Distribution Critical Value

2012 ◽  
Vol 472-475 ◽  
pp. 1329-1332 ◽  
Author(s):  
Hsiang Chuan Liu ◽  
Wei Sung Chen ◽  
Hsien Chang Tsai
Keyword(s):  
Empirical Distribution ◽  
Critical Value ◽  
Threshold Limit Value ◽  
Relational Structure ◽  
Structure Theory ◽  
Polytomous Items ◽  
Polytomous Item ◽  
Limit Value ◽  
Threshold Limit ◽  
Relational Structure Theory

The threshold limit value of Takeya’s item relational structure theory is a fixed value, which is lacking of statistical meaning, in our previous paper, an improved threshold limit value by using the empirical distribution critical value was proposed, it was showed that the new theory is more sensitive and effective than the old one. However, for constructing the item relational structure, both of them can only be used for dichotomous items, not for polytomous items. In this paper, the empirical distribution critical value based polytomous item relational structure theory is proposed, it is a generalization of our previously improved theory. A calculus example was also provided in this paper to illustrate the advantages of the proposed method.

Liu’s Polytomous Item Relational Structure Theory Based on Q-Matrix Theory

2013 ◽  
Vol 311 ◽  
pp. 93-98
Author(s):  
Hsiang Chuan Liu ◽  
Bai Cheng Jeng ◽  
Hsien Chang Tsai ◽  
Yen Kuei Yu ◽  
Ching Yu Lu
Keyword(s):  
Matrix Theory ◽  
Relational Structure ◽  
Structure Theory ◽  
Validity Index ◽  
Polytomous Item ◽  
Structural Graph ◽  
Q Matrix ◽  
Fitting In ◽  
Relational Structure Theory ◽  
The Given

In this paper, an improved polytomous item relational structure theory based on Q-matrix theory is proposed, using Tatsuoka’s Q-matrix theory, we can construct the test with all efficient items which are fitting in with the given relational structure of cognitive attributes, and then, before the test, using Liu’s before-test item ordering theory, an ideal relational structural graph of itemscan be constructed, and the real efficient items can be obtained accordingly. After testing the students, an after-test structure of items can be estimated by using the Liu’s polytomous item relational structure theory. Furthermore, using Liu’s criterion related validity index, we can evaluate the estimated item relational structure of the test, and the results could be useful for cognitive diagnosis and remedial instruction.

Language Highlights Relational Structure

2006 ◽  
Author(s):  
Stella Christie ◽  
Dedre Gentner
Keyword(s):  
Relational Structure

Combining First-Principles and Data Modeling for the Accurate Prediction of the Refractive Index of Organic Polymers

2017 ◽  
Author(s):  
Mohammad Atif Faiz Afzal ◽  
Chong Cheng ◽  
Johannes Hachmann
Keyword(s):  
First Principles ◽  
Data Modeling ◽  
Accurate Prediction ◽  
Index Of Refraction ◽  
Structure Theory ◽  
Organic Polymers ◽  
Number Density ◽  
Lorenz Equation ◽  
In Silico Studies ◽  
Wide Range

Organic materials with a high index of refraction (RI) are attracting considerable interest due to their potential application in optic and optoelectronic devices. However, most of these applications require an RI value of 1.7 or larger, while typical carbon-based polymers only exhibit values in the range of 1.3–1.5. This paper introduces an efficient computational protocol for the accurate prediction of RI values in polymers to facilitate in silico studies that an guide the discovery and design of next-generation high-RI materials. Our protocol is based on the Lorentz-Lorenz equation and is parametrized by the polarizability and number density values of a given candidate compound. In the proposed scheme, we compute the former using first-principles electronic structure theory and the latter using an approximation based on van der Waals volumes. The critical parameter in the number density approximation is the packing fraction of the bulk polymer, for which we have devised a machine learning model. We demonstrate the performance of the proposed RI protocol by testing its predictions against the experimentally known RI values of 112 optical polymers. Our approach to combine first-principles and data modeling emerges as both a successful and highly economical path to determining the RI values for a wide range of organic polymers.

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