Abstract
Ordinal outcomes are common in the social, behavioral, and health sciences, but there is no commonly accepted approach to analyzing them. Researchers make a number of different seemingly arbitrary recoding decisions implying different levels of measurement and theoretical assumptions. As a result, a wide array of models are used to analyze ordinal outcomes, including the linear regression model, binary response model, ordered models, and count models. In this tutorial, we present a diverse set of ordered models (most of which are under-utilized in applied research) and argue that researchers should approach the analysis of ordinal outcomes in a more systematic fashion by taking into consideration both theoretical and empirical concerns, and prioritizing ordered models given the flexibility they provide. Additionally, we consider the challenges that ordinal independent variables pose for analysts that often go unnoticed in the literature and offer simple ways to decide how to include ordinal independent variables in ordered regression models in ways that are easier to justify on conceptual and empirical grounds. We illustrate several ordered regression models with an empirical example, general self-rated health, and conclude with recommendations for building a sounder approach to ordinal data analysis.
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Notes
There are constrained and unconstrained partial models, which yields four versions of each approach.
For a discussion of the constrained partial model, see Fullerton and Xu (2016, p.65).
Espinosa and Hennig (2019) developed an ordinal model that allows one to impose a monotonicity constraint on ordinal independent variables via constrained MLE (p.872). The models we present in this study do not impose this inequality constraint. Ordinal patterns may emerge for groups of binary independent variables, but they are not imposed in the models.
The “poor” category only had 1.53% of the overall sample. The LR test for combining the “fair” and “poor” categories was not significant (Χ2 = 9.798, p = 0.367), providing an empirical justification for this approach.
The “fairly likely” category only had 4.36% of the sample, and the “very likely” category only had 2.59% of the sample. The LR tests for combining these categories was not significant (Χ2 = 6.688, p = 0.571).
We used the gologit2 (Williams 2006) command in Stata to estimate the cumulative models. Although the focus in this example is on cumulative models, we also estimated stage and adjacent models for comparison purposes. The results are substantively similar to the cumulative results. We used the gencrm command (Bauldry et al., 2018) and the regular mlogit command in Stata to estimate the stage and adjacent models, respectively. See the online appendix for the results and details regarding estimation using Stata.
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Fullerton, A.S., Anderson, K.F. Ordered Regression Models: a Tutorial. Prev Sci 24, 431–443 (2023). https://doi.org/10.1007/s11121-021-01302-y
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DOI: https://doi.org/10.1007/s11121-021-01302-y