Some new connections for nonparametric item response modeling
Presidential address by Brian Junker, Department of Statistics, Carnegie Mellon University, Pittsburgh, USA
Chair: Paul de Boeck, Thursday 23rd July, 17.30 - 18.30, Palmeston Lecture Theatre, Fisher Building.
Statistical modeling of assessment (psychological testing) data has been going on since the beginning of the 20th century - almost as long as statistics as a formal discipline has existed. The most successful approach has been through item response theory (IRT) and its variations on parametric mixed effects logit and probit models, in which the random effect represents a generic measure of students' "proficiency'' (essentially, a finer-grained version of number-right scores). In parallel, several "nonparametric'' approaches focused on a general class of mixture-of-product-Bernoulli (and related) models, of which the parametric IRT models were the best known subclass. The primary goals of nonparametric IRT were to determine if desirable "measurement'' features held, and if so, to develop model-free or model-light methods of inference about students (hopefully at some computational savings). Current challenges in assessment modeling revolve around replacing the continuous ``proficiency'' random effect with a vector of discrete ``skill indicators'', converting the IRT model into a restricted latent class model. A nonparamteric approach to these so-called cognitive diagnosis models (CDM's) is also developing, with many of the same goals as nonparameteric IRT. In this talk I will highlight some of the history of nonparametric IRT and preview some new approaches in non-parametric and model-light CDM methods.