Abstract
Objective: The collection and use of ordinal variables are common in many psychological and psychiatric studies. Although the models for continuous variables have similarities to those for ordinal variables, there are advantages when a model developed for modeling ordinal data is used such as avoiding “floor” and “ceiling” effects and avoiding to assign scores, as it happens in continuous models, which can produce results sensitive to the score assigned. This paper introduces and focuses on the application of the ordered stereotype model, which was developed for modeling ordinal outcomes and is not so popular as other models such as linear regression and proportional odds models. This paper aims to compare the performance of the ordered stereotype model with other more commonly used models among researchers and practitioners. Methods: This article compares the performance of the stereotype model against the proportional odd and linear regression models, with three, four, and five levels of ordinal categories and sample sizes 100, 500, and 1000. This paper also discusses the problem of treating ordinal responses as continuous using a simulation study. The trend odds model is also presented in the application. Results: Three types of models were fitted in one real‐life example, including ordered stereotype, proportional odds, and trend odds models. They reached similar conclusions in terms of the significance of covariates. The simulation study evaluated the performance of the ordered stereotype model under four cases. The performance varies depending on the scenarios. Conclusions: The method presented can be applied to several areas of psychiatry dealing with ordinal outcomes. One of the main advantages of this model is that it breaks with the assumption of levels of the ordinal response are equally spaced, which might be not true.
Highlights
1.1 BackgroundAn ordinal variable is one with a categorical data scale which describes order, and where the distinct levels of such a variable differ in degree of dissimilarity more than in quality (Agresti, 2010)
There are many existing methods developed for modeling ordinal data that respect the ordinal nature of the data and have advantages such as making as few assumptions as possible, having greater power for detecting relevant trends, and using measures that are similar to those used in ordinary regression for quantitative variables
Given that the proportional odds model is more parsimonious than the ordered stereotype model, we could check how much information has been missed by fitting a proportional odds model instead of an ordered stereotype model
Summary
An ordinal variable is one with a categorical data scale which describes order, and where the distinct levels of such a variable differ in degree of dissimilarity more than in quality (Agresti, 2010). It can predict values outside the range of possible ordinal outcomes Another disadvantage of applying ordinary regression to ordinal data is to produce misleading results due to ‘‘floor’’ and ‘‘ceiling’’ effects on the dependent variable (see Agresti, 2010, section 1.3.1 and comments regarding this issue in McKelvey & Zavoina, 1975; Winship & Mare, 1984; Bauer & Sterba, 2011; and Hedeker, 2015). Recent research develop new methods to allow the flexibility on the proportional odds structure for modeling ordinal data such as the trend odds model (Capuano & Dawson, 2013; Capuano et al, 2016, Capuano, Wilson, Schneider, Leurgans, & Bennett, 2018) and the unconstrained and constrained versions of the partial adjacent category logit model (Fullerton & Xu, 2018).
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