Background: Standard methods for analysing data from large-scale assessments (LSA) cannot merely be adopted if hierarchical (or multilevel) regression modelling should be applied. Currently various approaches exist; they all follow generally a design-based model of estimation using the pseudo maximum likelihood method and adjusted weights for the…

We consider the problem of off-policy policy selection in reinforcement learning: using historical data generated from running one policy to compare two or more policies. We show that approaches based on importance sampling can be "unfair"--they can select the worse of two policies more often than not. We give two examples where the…

The omega (?) statistic is reputed to be one of the best indices for detecting answer copying on multiple choice tests, but its performance relies on the accurate estimation of copier ability, which is challenging because responses from the copiers may have been contaminated. We propose an algorithm that aims to identify and delete the suspected…

The main purpose of this study is to improve estimation efficiency in obtaining maximum marginal likelihood estimates of contextual effects in the framework of nonlinear multilevel latent variable model by adopting the Metropolis-Hastings Robbins-Monro algorithm (MH-RM). Results indicate that the MH-RM algorithm can produce estimates and standard…

The main purpose of this study is to improve estimation efficiency in obtaining maximum marginal likelihood estimates of contextual effects in the framework of nonlinear multilevel latent variable model by adopting the Metropolis-Hastings Robbins-Monro algorithm (MH-RM; Cai, 2008, 2010a, 2010b). Results indicate that the MH-RM algorithm can…

A Bayesian model formulation of the deterministic inputs, noisy "and" gate (DINA) model is presented. Gibbs sampling is employed to simulate from the joint posterior distribution of item guessing and slipping parameters, subject attribute parameters, and latent class probabilities. The procedure extends concepts in Béguin and Glas,…

Compressed sensing (CS) is an emerging signal acquisition framework that goes against the traditional Nyquist sampling paradigm. CS demonstrates that a sparse, or compressible, signal can be acquired using a low rate acquisition process. Since noise is always present in practical data acquisition systems, sensing and reconstruction methods are…

Survey sampling is fundamentally an applied field. The goal in this book is to put an array of tools at the fingertips of practitioners by explaining approaches long used by survey statisticians, illustrating how existing software can be used to solve survey problems, and developing some specialized software where needed. This book serves at least…

"Growth mixture models" (GMMs) with nonignorable missing data have drawn increasing attention in research communities but have not been fully studied. The goal of this article is to propose and to evaluate a Bayesian method to estimate the GMMs with latent class dependent missing data. An extended GMM is first presented in which class…

Rational models of cognition typically consider the abstract computational problems posed by the environment, assuming that people are capable of optimally solving those problems. This differs from more traditional formal models of cognition, which focus on the psychological processes responsible for behavior. A basic challenge for rational models…

The Teacher Education and Development Study in Mathematics (TEDS-M), conducted under the aegis of the International Association for the Evaluation of Educational Achievement (IEA), was designed to inform policy and practice in mathematics teacher education. For educational policymakers, TEDS-M contributes data on institutional arrangements that…

Formulas to determine the necessary sample sizes for parametric tests of group comparisons are available from several sources and appropriate when population distributions are normal. However, in the context of nonnormal population distributions, researchers recommend Yuen's trimmed mean test, but formulas to determine sample sizes have not been…

The purpose of this ITEMS module is to provide an introduction to Markov chain Monte Carlo (MCMC) estimation for item response models. A brief description of Bayesian inference is followed by an overview of the various facets of MCMC algorithms, including discussion of prior specification, sampling procedures, and methods for evaluating chain…

Describes the algorithm used to select a simple random sample of certain size without having to list all possible samples and a justification based on Pascal's triangle. Provides testing results by various computers. (YP)

The usual formula for variance depending on rounding off the sample mean lacks precision, especially when computer programs are used for the calculation. The well-known simplification of the total sums of squares does not always give benefit. Since the variance of two observations is easily calculated without the use of a sample mean, and the…