For analyzing item response data, item response theory (IRT) models treat the discrete responses to the items as driven by underlying continuous latent traits, and consider the form of conditional probability of the response to each item given the latent traits. In a similar fashion, log-linear...

Chapter 1 is concerned with confidence interval construction for the mean of a long-range dependent time series. It is well known that the moving block bootstrap method produces an inconsistent estimator of thedistribution of the normalized sample mean when its limiting distribution is not...

Given the rapid advancement of computer technology, the importance of administeringadaptive tests with polytomous items is in great need. With regard to the applicability ofadaptive testing using polytomous IRT models, adaptive testing can use polytomous items of either rating scales, or in some...

According to the weak local independence approachto defining dimensionality, the fundamental quantitiesfor determining a test’s dimensional structure are the covariancesof item-pair responses conditioned on examineetrait level. This paper describes threedimensionality...

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...