A novel generalized item relational structure theory based on Liu’s normalization and consistency criteria

Hsiang Chuan Liu, Ben Chang Shia, Jing Ming Ju, Tsuey Lan Wang, Chih Hsiung Su, Yi Tien Lin

Research output: Contribution to journalArticle

Abstract

In this study, based on weighted mean, we can extend any item ordering theory from dichotomous scoring to polytomous scoring. However, before this study, there is no validity criterion to detect any item ordering theory for polytomous scoring whether is valid or not; this paper defines finite correlation coefficient and item difficulty for polytomous scoring corresponding to dichotomous scoring; based on these new definitions, we propose the generalized criteria of completeness, normalization and consistency for polytomous scoring corresponding to the original ones for dichotomous scoring, respectively. Two well-known item ordering theories: Takeya’s IRS and Liu et al.‘s LIRS, can be extended from dichotomous scoring to polytomous scoring, denoted as GIRS and GLIRS. And then, several important properties of them and counter examples are provided. This paper points out that not only does IRS not satisfy the three above-mentioned original criteria, but also its generalization, GIRS, does not satisfy the generalized criteria of them, and only the new theory, GLIRS, can satisfy both of the generalized and the original criteria of completeness, normalization and strict consistency.

Original languageEnglish
Pages (from-to)2957-2962
Number of pages6
JournalICIC Express Letters
Volume10
Issue number12
Publication statusPublished - 2016

Keywords

  • Generalized liu’s item relational structure theory
  • Item relational structure theory
  • Liu’s item relational structure theory

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science(all)

Cite this

A novel generalized item relational structure theory based on Liu’s normalization and consistency criteria. / Liu, Hsiang Chuan; Shia, Ben Chang; Ju, Jing Ming; Wang, Tsuey Lan; Su, Chih Hsiung; Lin, Yi Tien.

In: ICIC Express Letters, Vol. 10, No. 12, 2016, p. 2957-2962.

Research output: Contribution to journalArticle

Liu, Hsiang Chuan ; Shia, Ben Chang ; Ju, Jing Ming ; Wang, Tsuey Lan ; Su, Chih Hsiung ; Lin, Yi Tien. / A novel generalized item relational structure theory based on Liu’s normalization and consistency criteria. In: ICIC Express Letters. 2016 ; Vol. 10, No. 12. pp. 2957-2962.
@article{b144f64ce9984fe18ad2a9d2ddfa439d,
title = "A novel generalized item relational structure theory based on Liu’s normalization and consistency criteria",
abstract = "In this study, based on weighted mean, we can extend any item ordering theory from dichotomous scoring to polytomous scoring. However, before this study, there is no validity criterion to detect any item ordering theory for polytomous scoring whether is valid or not; this paper defines finite correlation coefficient and item difficulty for polytomous scoring corresponding to dichotomous scoring; based on these new definitions, we propose the generalized criteria of completeness, normalization and consistency for polytomous scoring corresponding to the original ones for dichotomous scoring, respectively. Two well-known item ordering theories: Takeya’s IRS and Liu et al.‘s LIRS, can be extended from dichotomous scoring to polytomous scoring, denoted as GIRS and GLIRS. And then, several important properties of them and counter examples are provided. This paper points out that not only does IRS not satisfy the three above-mentioned original criteria, but also its generalization, GIRS, does not satisfy the generalized criteria of them, and only the new theory, GLIRS, can satisfy both of the generalized and the original criteria of completeness, normalization and strict consistency.",
keywords = "Generalized liu’s item relational structure theory, Item relational structure theory, Liu’s item relational structure theory",
author = "Liu, {Hsiang Chuan} and Shia, {Ben Chang} and Ju, {Jing Ming} and Wang, {Tsuey Lan} and Su, {Chih Hsiung} and Lin, {Yi Tien}",
year = "2016",
language = "English",
volume = "10",
pages = "2957--2962",
journal = "ICIC Express Letters",
issn = "1881-803X",
publisher = "ICIC Express Letters Office",
number = "12",

}

TY - JOUR

T1 - A novel generalized item relational structure theory based on Liu’s normalization and consistency criteria

AU - Liu, Hsiang Chuan

AU - Shia, Ben Chang

AU - Ju, Jing Ming

AU - Wang, Tsuey Lan

AU - Su, Chih Hsiung

AU - Lin, Yi Tien

PY - 2016

Y1 - 2016

N2 - In this study, based on weighted mean, we can extend any item ordering theory from dichotomous scoring to polytomous scoring. However, before this study, there is no validity criterion to detect any item ordering theory for polytomous scoring whether is valid or not; this paper defines finite correlation coefficient and item difficulty for polytomous scoring corresponding to dichotomous scoring; based on these new definitions, we propose the generalized criteria of completeness, normalization and consistency for polytomous scoring corresponding to the original ones for dichotomous scoring, respectively. Two well-known item ordering theories: Takeya’s IRS and Liu et al.‘s LIRS, can be extended from dichotomous scoring to polytomous scoring, denoted as GIRS and GLIRS. And then, several important properties of them and counter examples are provided. This paper points out that not only does IRS not satisfy the three above-mentioned original criteria, but also its generalization, GIRS, does not satisfy the generalized criteria of them, and only the new theory, GLIRS, can satisfy both of the generalized and the original criteria of completeness, normalization and strict consistency.

AB - In this study, based on weighted mean, we can extend any item ordering theory from dichotomous scoring to polytomous scoring. However, before this study, there is no validity criterion to detect any item ordering theory for polytomous scoring whether is valid or not; this paper defines finite correlation coefficient and item difficulty for polytomous scoring corresponding to dichotomous scoring; based on these new definitions, we propose the generalized criteria of completeness, normalization and consistency for polytomous scoring corresponding to the original ones for dichotomous scoring, respectively. Two well-known item ordering theories: Takeya’s IRS and Liu et al.‘s LIRS, can be extended from dichotomous scoring to polytomous scoring, denoted as GIRS and GLIRS. And then, several important properties of them and counter examples are provided. This paper points out that not only does IRS not satisfy the three above-mentioned original criteria, but also its generalization, GIRS, does not satisfy the generalized criteria of them, and only the new theory, GLIRS, can satisfy both of the generalized and the original criteria of completeness, normalization and strict consistency.

KW - Generalized liu’s item relational structure theory

KW - Item relational structure theory

KW - Liu’s item relational structure theory

UR - http://www.scopus.com/inward/record.url?scp=85006043618&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85006043618&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85006043618

VL - 10

SP - 2957

EP - 2962

JO - ICIC Express Letters

JF - ICIC Express Letters

SN - 1881-803X

IS - 12

ER -