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,...

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...

The first part of this thesis, Chapter 2 through Chapter 4, explores procedures for assessing latent test dimensionality. In Chapter 2, the structure and theoretical properties of conditional item pair covariances given a latent composite are thoroughly investigated. Such information is useful...