Some topics in nonparametric and parametric IRT, with some thoughts about the future

1 Abstract Item response theory (IRT) has arguably been one of the most successful and widely used statistical modeling techniques in psychometrics, with applications in developmental, social, educational and cognitive psychology for example, as well as in medical research, demography and other social science settings. In this paper I will try to briefly summarize some of the important research in nonparametric and parametric IRT today. I will try to show that a broad understanding of IRT as an instance of mathematical statistics in the service of substantive psychology, together with an appreciation of some of the current measurement challenges in education and cognitive psychology, lead us to assessment models that do not look very much like today's IRT models, but for which the tools and conceptual framework of nonparametric and parametric IRT are still quite well suited.