Title
Assigning scores for ordered categorical responses
Date Issued
18 May 2020
Access level
open access
Resource Type
journal article
Author(s)
Fernández D.
Liu I.
Gu P.Y.
University of Queensland
Publisher(s)
Taylor and Francis Ltd.
Abstract
Deciding on the best statistical method to apply when the response variable is ordinal is essential because the way the categories are ordered in the data is relevant as it could change the results of the analysis. Although the models for continuous variables have similarities to those for ordinal variables, this paper presents the advantages of the use of the ordering information on the outcomes with methods developed for modeling ordinal data such as the ordered stereotype model. The novelty of this article lies in showing the dangers of assigning equally spaced scores to ordered response categories in statistical analysis, which are illustrated with a simulation study and a case study. We propose a new way to use the score parameters, which incorporates the fitted spacing dictated by the data. Additionally, this article uses score parameter estimates in the ordered stereotype model to propose a new measure to calculate continuous medians in the raw data: the adjusted c-median. It benefits the general audience who can easily understand the median as a summary statistic. Supplementary materials for this article are available online.
Start page
1261
End page
1281
Volume
47
Issue
7
Language
English
OCDE Knowledge area
Estadísticas, Probabilidad
Scopus EID
2-s2.0-85074026954
Source
Journal of Applied Statistics
ISSN of the container
02664763
Sponsor(s)
This work was supported by the the Marsden [grant number E2987-3648] from the Royal Society of New Zealand. The authors are sincerely grateful to Prof Alan Agresti for allowing us to use his example in floor and ceiling effects in supplementary materials. Some portions of Sections 1, 2.1, 2.2, 2.3, and 6, and Figure 2 are derived from the following PhD thesis ‘Daniel Fernandez Martinez. 2015. Mixture-based Clustering for the Ordered Stereotype Model. Victoria University of Wellington. Wellington, New Zealand’ whose authorship is the same first author of this article.
Sources of information: Directorio de Producción Científica Scopus