The class of cub models: statistical foundations, inferential issues and empirical evidence

Journal of Educational and Behavioral Statistics

2021

A mixture of logit models is proposed that discriminates between responses to rating questions that are affected by a tendency to prefer middle or extremes of the scale regardless of the content of the item (response styles) and purely content-driven preferences. Explanatory variables are used to characterize the content-driven way of answering as well as the tendency to middle or extreme categories. The proposed model is extended to account for the presence of response styles in the case of several items, and the association among responses is described, both when they are content driven or dictated by response styles. In addition, stochastic orderings, related to the tendency to select middle or extreme categories, are introduced and investigated. A simulation study describes the effectiveness of the proposed model, and an application to a questionnaire on attitudes toward ethnic minorities illustrates the applicability of the modeling approach.

Section: Some Alternative Approachesmentioning

confidence: 99%

A Rating Scale Mixture Model to Account for the Tendency to Middle and Extreme Categories

Colombi

Giordano

Journal of Educational and Behavioral Statistics

2021

“…Explanatory variables can determine the probabilities of the mixture. D’Elia and Piccolo (2005), Iannario and Piccolo (2010), Iannario (2012), Tutz et al (2017), and Iannario et al (2020) all considered models of this type, and Piccolo and Simone (2019) provided an extensive overview.…”

Section: Introductionmentioning

confidence: 99%

Uncertain Choices: The Heterogeneous Multinomial Logit Model

Sociological Methodology

2021

In this article, a modeling strategy is proposed that accounts for heterogeneity in nominal responses that is typically ignored when using common multinomial logit models. Heterogeneity can arise from unobserved variance heterogeneity, but it may also represent uncertainty in choosing from alternatives or, more generally, result from varying coefficients determined by effect modifiers. It is demonstrated that the bias in parameter estimation in multinomial logit models can be substantial if heterogeneity is present but ignored. The modeling strategy avoids biased estimates and allows researchers to investigate which variables determine uncertainty in choice behavior. Several applications demonstrate the usefulness of the model.

“…In recent years, the inclusion of uncertainty in ordinal regression has been investigated by Piccolo (2003), Iannario and Piccolo (2016), Gottard et al (2016), Tutz et al (2017), and Simone and Tutz (2018), a comprehensive overview has been given by Piccolo and Simone (2019). The basic assumption behind the so-called CUB models, which stands for Combination of a Uniform and a shifted Binomial distribution, is that the choice of a response category is determined by a mixture of a distinct preference and uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty in Latent Trait Models

Applied Psychological Measurement

Schauberger

2020

A model that extends the Rasch model and the Partial Credit Model to account for subject-specific uncertainty when responding to items is proposed. It is demonstrated that ignoring the subject-specific uncertainty may yield biased estimates of model parameters. In the extended version of the model, uncertainty and the underlying trait are linked to explanatory variables. The parameterization allows to identify subgroups that differ in uncertainty and the underlying trait. The modeling approach is illustrated using data on the confidence of citizens in public institutions.