Statistical inference for rankings in the presence of panel segmentation


Show simple item record Xie, Lin 2011-12-12T16:11:54Z 2011-12-12T16:11:54Z 2011-12-12
dc.description.abstract Panels of judges are often used to estimate consumer preferences for m items such as food products. Judges can either evaluate each item on several ordinal scales and indirectly produce an overall ranking, or directly report a ranking of the items. A complete ranking orders all the items from best to worst. A partial ranking, as we use the term, only reports rankings of the best q out of m items. Direct ranking, the subject of this report, does not require the widespread but questionable practice of treating ordinal measurement as though they were on ratio or interval scales. Here, we develop and study segmentation models in which the panel may consist of relatively homogeneous subgroups, the segments. Judges within a subgroup will tend to agree among themselves and differ from judges in the other subgroups. We develop and study the statistical analysis of mixture models where it is not known to which segment a judge belongs or in some cases how many segments there are. Viewing segment membership indicator variables as latent data, an E-M algorithm was used to find the maximum likelihood estimators of the parameters specifying a mixture of Mallow’s (1957) distance models for complete and partial rankings. A simulation study was conducted to evaluate the behavior of the E-M algorithm in terms of such issues as the fraction of data sets for which the algorithm fails to converge and the sensitivity of initial values to the convergence rate and the performance of the maximum likelihood estimators in terms of bias and mean square error, where applicable. A Bayesian approach was developed and credible set estimators was constructed. Simulation was used to evaluate the performance of these credible sets as confidence sets. A method for predicting segment membership from covariates measured on a judge was derived using a logistic model applied to a mixture of Mallows probability distance models. The effects of covariates on segment membership were assessed. Likelihood sets for parameters specifying mixtures of Mallows distance models were constructed and explored. en_US
dc.language.iso en_US en_US
dc.publisher Kansas State University en
dc.subject Partial ranking en_US
dc.subject Segmentation en_US
dc.subject Mixture model en_US
dc.subject Mallows model en_US
dc.subject Profile likelihood estimation;Bayesian Analysis;Covariate Model; EM algorithm; en_US
dc.title Statistical inference for rankings in the presence of panel segmentation en_US
dc.type Dissertation en_US Doctor of Philosophy en_US
dc.description.level Doctoral en_US
dc.description.department Department of Statistics en_US
dc.description.advisor Paul Nelson en_US
dc.subject.umi Statistics (0463) en_US 2012 en_US December en_US

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