Modeling heterogeneity in ranked responses by nonparametric maximum likelihood: How do Europeans get their scientific knowledge?

TL;DR

This paper introduces a nonparametric maximum likelihood approach to model heterogeneity in ranked responses, specifically applied to survey data on sources of scientific knowledge among Europeans, incorporating respondent covariates and using an EM algorithm.

Contribution

It develops a novel nonparametric mixed model for ranked data that accounts for heterogeneity and covariates, extending the analysis of paired comparison data.

Findings

The model effectively captures heterogeneity in ranked responses.

It allows incorporation of respondent covariates into the analysis.

The approach is adaptable to paired comparison data.

Abstract

This paper is motivated by a Eurobarometer survey on science knowledge. As part of the survey, respondents were asked to rank sources of science information in order of importance. The official statistical analysis of these data however failed to use the complete ranking information. We instead propose a method which treats ranked data as a set of paired comparisons which places the problem in the standard framework of generalized linear models and also allows respondent covariates to be incorporated. An extension is proposed to allow for heterogeneity in the ranked responses. The resulting model uses a nonparametric formulation of the random effects structure, fitted using the EM algorithm. Each mass point is multivalued, with a parameter for each item. The resultant model is equivalent to a covariate latent class model, where the latent class profiles are provided by the mass point components and the covariates act on the class profiles. This provides an alternative interpretation of the fitted model. The approach is also suitable for paired comparison data.