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...

Educators are seeking out mechanisms for reporting diagnostic information about the strengths and weaknesses of each student. Cognitive diagnostic assessment (CDA) is a form of assessment that could facilitate the educators in discovering their students' strengths and weaknesses. In CDA, the...

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,...

Modeling the processes underlying social network and attribute change allows researchers to better identify and understand dependencies present amongactors — people, places, or things. The connections that exist among these actors change over time, depend on the presence or absence of other...

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 approach described in this talk starts with Bock's (1972) nominal response model (NRM). The NRM is a multinomial logistic regression model for responses to items where the ordering of response options is not known a priori and the predictor or explanatory variable is unobserved (i.e., the...

The Rasch family of models considered in this paper includes models for polytomous items and multiple correlated latent traits, as well as for dichotomous items and a single latent variable. An R package is described that computes estimates of parameters and robust standard errors of a class of...

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...