Assigning scores for ordered categorical responses

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.

KEYWORDS:

• Global odds ratio
• linear-by-linear association model
• median measure
• ordered stereotype model
• uneven spacing

Acknowledgments

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.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Daniel Fernández http://orcid.org/0000-0003-0012-2094

Additional information

Funding

This work was supported by the the Marsden [grant number E2987-3648] from the Royal Society of New Zealand.