Open AccessUnidimensional Vertical Scaling in Multidimensional Space
Author(s) -
Carlson James E.
Publication year - 2017
Publication title -
ets research report series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.235
H-Index - 5
ISSN - 2330-8516
DOI - 10.1002/ets2.12157
Subject(s) - space (punctuation) , multidimensional scaling , limiting , scaling , set (abstract data type) , representation (politics) , limit (mathematics) , test (biology) , mathematics , scale (ratio) , type (biology) , statistics , computer science , mathematical analysis , geometry , physics , mechanical engineering , paleontology , quantum mechanics , politics , law , political science , engineering , biology , programming language , operating system , ecology
In this paper, I consider a set of test items that are located in a multidimensional space, S M , but are located along a curved line in S M and can be scaled unidimensionally. Furthermore, I am demonstrating a case in which the test items are administered across 6 levels, such as occurs in K–12 assessment across 6 grade levels, and for which a unidimensional vertical scale can be developed. I am limiting my coverage to dichotomously scored items because the models are much simpler than those for polytomously scored items. However, the concepts discussed can be extended to the latter type of item. I also limit my demonstrations to a 2‐dimensional space, S 2 , so I can geometrically represent my points in a 2‐dimensional representation in this article. These concepts can also be extended to a higher‐dimensional case.