Flexible uncertainty in mixture models for ordinal responses

ABSTRACT

In classical mixture models for ordinal data with an uncertainty component, the Uniform distribution is used to model indecision. In the approach proposed here, the discrete Uniform distribution is replaced by a more flexible distribution, which is centered in the middle of the response categories. The resulting model allows to distinguish between a tendency to middle categories and a tendency to extreme categories. By linking these preferences to explanatory variables, one can investigate which persons show a tendency to these response styles. It is demonstrated that severe bias might occur if inadvertently the Uniform distribution is used to model uncertainty. An application to attitudes on the performance of health services illustrates the advantages of the more flexible model.

KEYWORDS:

• Ordinal responses
• response styles
• rating scales
• mixture models
• CUP model
• CUB model

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 62H86

Disclosure statement

No potential conflict of interest was reported by the authors.