Brian W. Junker
Statistics Department
Carnegie Mellon University
The Role of Nonparametric Analysis in Assessment Modeling: Then and Now
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.
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