Mixture models for rating data: the method of moments via Groebner bases

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.

Test Scaling and Value-Added Measurement

Conventional value-added assessment requires that achievement be reported on an interval scale. While many metrics do not have this property, application of item response theory (IRT) is said to produce interval scales. However, it is difficult to confirm that the requisite conditions are met. Even when they are, the properties of the data that make a test IRT scalable may not be the properties we seek to represent in an achievement scale, as shown by the lack of surface plausibility of many scales resulting from the application of IRT. An alternative, ordinal data analysis, is presented. It is shown that value-added estimates are sensitive to the choice of ordinal methods over conventional techniques. Value-added practitioners should ask themselves whether they are so confident of the metric properties of these scales that they are willing to attribute differences to the superiority of the latter.