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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 - 1941-7330
IS - 4
ER -