How to Interpret the Effect of Covariates on the Extreme Categories in Ordinal Data Models

Abstract

This contribution deals with effect measures for covariates in ordinal data models to address the interpretation of the results on the extreme categories of the scales, evaluate possible response styles, and motivate collapsing of extreme categories. It provides a simpler interpretation of the influence of the covariates on the probability of the response categories both in standard cumulative link models under the proportional odds assumption and in the recent extension of the Combination of Uncertainty and Preference of the respondents models, the mixture models introduced to account for uncertainty in rating systems. The article shows by means of marginal effect measures that the effects of the covariates are underestimated when the uncertainty component is neglected. Visualization tools for the effect of covariates are proposed, and measures of relative size and partial effect based on rates of change are evaluated by the use of real data sets.

A mixture distribution for modelling bivariate ordinal data

“…Since responses from surveys involve psychological behaviours of the respondents, it is important to take into account the potential biases that may have been introduced. Apart from indecision or uncertainty, the uncertainty component of the CUB model can also be used to account for other elements such as difficulty in expressing an actual feeling, limited knowledge, fatigue or willingness to satisfy the interviewer (Iannario and Piccolo 2016;Iannario and Tarantola 2023). As shown by Colombi et al (2019), the ignorance of the uncertainty component during the modelling stage would lead to substantial biases in the estimation results.…”

A Novel Indicator to Correct for Individual Reported Heterogeneity. An Application to Self-Evaluation of Later-Life Depression

“…Tutz and Schneider (2019) highlight that the CUP model presents better fit and performance in terms of AIC, BIC and prognostic measures than standard ordinal models. More specifically, when the uncertainty component is not considered, the effect of the explanatory variables tends to be underestimated (Iannario and Tarantola, 2023). In extreme cases, neglecting the uncertainty component produces misspecification of the model.…”

“…All of them are encompassed in the GEM (Generalized mixture model with uncertainty) framework (Iannario and Piccolo, 2016). Here, we consider the special case of CUP models introduced in Tutz et al (2017) and applied in several contexts (see, among others, Iannario and Tarantola, 2021; 2023); CUP models are made up of the Proportional Odds Models for the preference part. In this framework, the uncertainty component represents aspects such as motivation, concentration, fatigue, boredom, amnesia, carelessness in marking answers and luck in guessing; it is also related to ambiguous or tricky items, poor directions, survey submission, length of the questionnaire and so on.…”