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Francis, Brian; Dittrich, Regina; Hatzinger, Reinhold

Modeling heterogeneity in ranked responses by nonparametric maximum likelihood: How do Europeans get their scientific knowledge? (English) Zbl 1220.62158

Ann. Appl. Stat. 4, No. 4, 2181-2202 (2010).
Summary: 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.

Cited in 8 Documents

MSC:

62P25 Applications of statistics to social sciences
62J15 Paired and multiple comparisons; multiple testing
62G05 Nonparametric estimation
65C60 Computational problems in statistics (MSC2010)
62F07 Statistical ranking and selection procedures

Keywords:

ranked data; random effects; NPML; paired comparisons; Bradley-Terry model; latent class analysis; mixture of experts; Eurobarometer

Software:

npmlreg; EMMIX; prefmod; R
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References:

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