The issues studied in this thesis are: the assumption of local independence (LI) in item response theory (IRT) models in the first three chapters, and differential item functioning (DIF) in IRT in the last chapter. A new term "conditional trivariance" for three items is defined, which is a...

The simultaneous and nonparametric estimation of latent abilities and item characteristic curves is considered. In particular, the joint asymptotic properties of ordinal ability estimation and kernel smoothed nonparametric item characteristic curve estimation is investigated under relatively...

It has long been part of the Item Response Theory (IRT) folklore that under the usual empirical Bayes unidimensional IRT modeling approach, the posterior distribution of examinee ability given test response is approximately normal for a long test. Under very general non-parametric assumptions,...