Identifying Qualitative Between-Subject and Within-Subject Variability: A Method for Clustering Regime-Switching Dynamics.

Technological advancement provides an unprecedented amount of high-frequency data of human dynamic processes. In this paper, we introduce an approach for characterizing qualitative between and within-subject variability from quantitative changes in the multi-subject time-series data. We present the statistical model and examine the strengths and limitations of the approach in potential applications using Monte Carlo simulations. We illustrate its usage in characterizing clusters of dynamics with phase transitions with real-time hand movement data collected on an embodied learning platform designed to foster mathematical learning.

A Rasch Model and Rating System for Continuous Responses Collected in Large-Scale Learning Systems.

An extension to a rating system for tracking the evolution of parameters over time using continuous variables is introduced. The proposed rating system assumes a distribution for the continuous responses, which is agnostic to the origin of the continuous scores and thus can be used for applications as varied as continuous scores obtained from language testing to scores derived from accuracy and response time from elementary arithmetic learning systems. Large-scale, high-stakes, online, anywhere anytime learning and testing inherently comes with a number of unique problems that require new psychometric solutions. These include (1) the cold start problem, (2) problem of change, and (3) the problem of personalization and adaptation. We outline how our proposed method addresses each of these problems. Three simulations are carried out to demonstrate the utility of the proposed rating system.

Turning Simulation into Estimation: Generalized Exchange Algorithms for Exponential Family Models.

The Single Variable Exchange algorithm is based on a simple idea; any model that can be simulated can be estimated by producing draws from the posterior distribution. We build on this simple idea by framing the Exchange algorithm as a mixture of Metropolis transition kernels and propose strategies that automatically select the more efficient transition kernels. In this manner we achieve significant improvements in convergence rate and autocorrelation of the Markov chain without relying on more than being able to simulate from the model. Our focus will be on statistical models in the Exponential Family and use two simple models from educational measurement to illustrate the contribution.

What can we learn from Plausible Values?

In this paper, we show that the marginal distribution of plausible values is a consistent estimator of the true latent variable distribution, and, furthermore, that convergence is monotone in an embedding in which the number of items tends to infinity. We use this result to clarify some of the misconceptions that exist about plausible values, and also show how they can be used in the analyses of educational surveys.

A Gibbs Sampler for the (Extended) Marginal Rasch Model.

In their seminal work on characterizing the manifest probabilities of latent trait models, Cressie and Holland give a theoretically important characterization of the marginal Rasch model. Because their representation of the marginal Rasch model does not involve any latent trait, nor any specific distribution of a latent trait, it opens up the possibility for constructing a Markov chain - Monte Carlo method for Bayesian inference for the marginal Rasch model that does not rely on data augmentation. Such an approach would be highly efficient as its computational cost does not depend on the number of respondents, which makes it suitable for large-scale educational measurement. In this paper, such an approach will be developed and its operating characteristics illustrated with simulated data.

Bayesian inference for low-rank Ising networks.

Estimating the structure of Ising networks is a notoriously difficult problem. We demonstrate that using a latent variable representation of the Ising network, we can employ a full-data-information approach to uncover the network structure. Thereby, only ignoring information encoded in the prior distribution (of the latent variables). The full-data-information approach avoids having to compute the partition function and is thus computationally feasible, even for networks with many nodes. We illustrate the full-data-information approach with the estimation of dense networks.

A Statistical Test for Differential Item Pair Functioning.

This paper presents an IRT-based statistical test for differential item functioning (DIF). The test is developed for items conforming to the Rasch (Probabilistic models for some intelligence and attainment tests, The Danish Institute of Educational Research, Copenhagen, 1960) model but we will outline its extension to more complex IRT models. Its difference from the existing procedures is that DIF is defined in terms of the relative difficulties of pairs of items and not in terms of the difficulties of individual items. The argument is that the difficulty of an item is not identified from the observations, whereas the relative difficulties are. This leads to a test that is closely related to Lord's (Applications of item response theory to practical testing problems, Erlbaum, Hillsdale, 1980) test for item DIF albeit with a different and more correct interpretation. Illustrations with real and simulated data are provided.

An Introduction to the DA-T Gibbs Sampler for the Two-Parameter Logistic (2PL) Model and Beyond

The DA-T Gibbs sampler is proposed by Maris and Maris (2002) as aBayesian estimation method for a wide variety of Item Response Theory(IRT) models. The present paper provides an expository account of the DATGibbs sampler for the 2PL model. However, the scope is not limited tothe 2PL model. It is demonstrated how the DA-T Gibbs sampler for the 2PLmay be used to build, quite easily, Gibbs samplers for other IRT models.Furthermore, the paper contains a novel, intuitive derivation of the Gibbssampler and could be read for a graduate course on sampling

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Structural equation modelling of multiple facet data: extending models for multitrait-multimethod data

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A limited dependent variable model for heritability estimation with non-random ascertained samples.

In a questionnaire study, a random sample of Dutch families was asked whether they suffered from asthma and related symptoms. From these families, a selected sample was invited to come to the hospital for further phenotyping. Families were selected if at least one family member reported a history of asthma and the twins were 18 years of age or older. Not all families that were thus selected volunteered, leaving us with a fraction of the original sample. The aim of this paper is to describe a limited dependent variable model that can be used in such situations in order to obtain estimates that are representative of the population from which the sample was originally drawn. The model is a linear (DeFries-Fulker) regression model corrected for sample selection. This correction is possible when (some of) the characteristics that determine whether subjects volunteer (or not) are known for all subjects, including those that did not volunteer. The questionnaire study is of interest by itself but serves mainly to provide a concrete illustration of our method. The present model is used to analyze the data and the results are compared to those obtained with other methods: raw (or direct) likelihood estimation, multiple imputation, and sample weighting. Throughout, Rubin's general theory of inference with missing data serves as an integrating framework.