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

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Modeling heterogeneity in ranked responses by nonparametric maximum likelihood : How do Europeans get their scientific knowledge? / Francis, Brian; Dittrich, Regina; Hatzinger, Reinhold.

In: Annals of Applied Statistics, Vol. 4, No. 4, 2010, p. 2181-2202.

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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?. In: Annals of Applied Statistics. 2010 ; Vol. 4, No. 4. pp. 2181-2202.

Bibtex

@article{0832496851ae40728e38584fb64eaa09,
title = "Modeling heterogeneity in ranked responses by nonparametric maximum likelihood: How do Europeans get their scientific knowledge?",
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.",
keywords = "Ranked data, random effects, NPML , paired comparisons , Bradley–Terry model , latent class analysis , mixture of experts, Eurobarometer",
author = "Brian Francis and Regina Dittrich and Reinhold Hatzinger",
note = "Published in at http://dx.doi.org/10.1214/10-AOAS366 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
year = "2010",
doi = "10.1214/10-AOAS366",
language = "English",
volume = "4",
pages = "2181--2202",
journal = "Annals of Applied Statistics",
issn = "1932-6157",
publisher = "Institute of Mathematical Statistics",
number = "4",

}

RIS

TY - JOUR

T1 - Modeling heterogeneity in ranked responses by nonparametric maximum likelihood

T2 - How do Europeans get their scientific knowledge?

AU - Francis, Brian

AU - Dittrich, Regina

AU - Hatzinger, Reinhold

N1 - Published in at http://dx.doi.org/10.1214/10-AOAS366 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Ranked data

KW - random effects

KW - NPML

KW - paired comparisons

KW - Bradley–Terry model

KW - latent class analysis

KW - mixture of experts

KW - Eurobarometer

U2 - 10.1214/10-AOAS366

DO - 10.1214/10-AOAS366

M3 - Journal article

VL - 4

SP - 2181

EP - 2202

JO - Annals of Applied Statistics

JF - Annals of Applied Statistics

SN - 1932-6157

IS - 4

ER -