33 research outputs found
Bayesian inference for multistage and other incomplete designs
No full textFollowing Maris, Bechger and San-Martin (2015), we develop a Markov chain - Monte Carlo method for Bayesian inference tailored to handle data collected in multistage and other incomplete designs. We illustrate its operating characteristics with simulated data, and provide a real application. To appear as: Koops, J. and Bechger, T. and Maris, G. (2021); Bayesian inference for multistage and other incomplete designs. In Research for Practical Issues and Solutions in Computerized Multistage Testing. Routledge, London
Boltzmann Machines as Multidimensional Item Response Theory Models
No full textWe show that Boltzmann machines can formally be represented as multidimensional item response theory models. This relationship inspired a new learning principle and new ways to regularize Boltzmann machines to make them more interpretable. The core results carry over to a broader class of models including Gaussian-Bernoulli restricted Boltzmann machines
A limited dependent variable model for heritability estimation with non-random ascertained samples
Get PDFIn 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
An Introduction to the DA-T Gibbs Sampler for the Two-Parameter Logistic (2PL) Model and Beyond
No full textThe DA-T Gibbs sampler is proposed by Maris and Maris (2002) as a
 Bayesian estimation method for a wide variety of Item Response Theory
 (IRT) models. The present paper provides an expository account of the DAT
 Gibbs sampler for the 2PL model. However, the scope is not limited to
 the 2PL model. It is demonstrated how the DA-T Gibbs sampler for the 2PL
 may be used to build, quite easily, Gibbs samplers for other IRT models.
 Furthermore, the paper contains a novel, intuitive derivation of the Gibbs
 sampler and could be read for a graduate course on sampling
A note on the equivalence of the graded response model and the sequential model
No full textitem response theory, sequential scoring, sequential model, graded response model,
The Ising on the Tree: The Master Model for Learning, Assessment, and Navigation
No full textLearning and assessment are intrinsically linked. However, the research, tools, and statistical models used within the two fields differ greatly. This has created a disconnect: The goals and missions of educational institutions are codified in the language and ideas of learning, but evaluated, monitored, and administered with the tools of assessment. We propose a novel statistical model, the Master model, capable of being the engine behind a modern learning and assessment system. The Master model combines three key concepts from the assessment and learning literature from the past century: A learning model should be multidimensional and hierarchical and should incorporate learning progressions. The Master model is a multidimensional latent variable model, more specifically a latent class model, that not only ranks learners from best to worst but also provides detailed diagnostic feedback to tell learners what they know, and more importantly, what they don't know. By incorporating a hierarchical structure of the latent variables, the Master model reproduces the positive manifold, a phenomenon that continues to be replicated in assessment data where scores between cognitive tests correlate positively. Finally, expert and data-driven annotation can incorporate learning progressions directly into the latent variables. With these three key concepts, the Master model can track the estimate of a learner’s latent skills, track the efficacy of various educational resources such as videos, and recommend which resources the learner should next focus on in order to maximize their learning
Identifiability of nonlinear logistic test models
No full textlinear logistic test model, identifiability, item response theory, componential item response theory, nonlinear logistic test models,
