Open AccessMixture models for rating data: the method of moments via Groebner bases
Author(s) -
Maria Iannario,
Rosaria Simone
Publication year - 2017
Publication title -
journal of algebraic statistics
Language(s) - English
Resource type - Journals
ISSN - 1309-3452
DOI - 10.18409/jas.v8i2.60
Subject(s) - estimator , overdispersion , computer science , moment (physics) , mathematical optimization , context (archaeology) , maximization , set (abstract data type) , mathematics , algorithm , statistics , poisson distribution , count data , paleontology , physics , classical mechanics , biology , programming language
A recent thread of research in ordinal data analysis involves a class of mixture models that designs the responses as the combination of the two main aspects driving the decision pro- cess: a feeling and an uncertainty components. This novel paradigm has been proven flexible to account also for overdispersion. In this context, Groebner bases are exploited to estimate model parameters by implementing the method of moments. In order to strengthen the validity of the moment procedure so derived, alternatives parameter estimates are tested by means of a simulation experiment. Results show that the moment estimators are satisfactory per se, and that they significantly reduce the bias and perform more efficiently than others when they are set as starting values for the Expectation-Maximization algorithm.