Although immediacy is one of the necessary criteria to show strong evidence of a causal relation in SCDs, no inferential statistical tool is currently used to demonstrate it. We propose a Bayesian unknown change-point model to investigate and quantify immediacy in SCD analysis. Unlike visual analysis that considers only 3-5 observations in…

Student misconceptions have been studied for decades from a curricular/instructional perspective and from the assessment/test level perspective. Numerous misconception assessment tools have been developed in order to measure students' misconceptions relative to the correct content. Often, these tools are used to make a variety of educational…

Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is…

In this article, we have suggested a new modified mixed randomized response (RR) model and studied its properties. It is shown that the proposed mixed RR model is always more efficient than the Kim and Warde's mixed RR model. The proposed mixed RR model has also been extended to stratified sampling. Numerical illustrations and graphical…

In "Progress in International Reading Literacy Study" (PIRLS) educational inequalities are measured, amongst others, through the relationship between students' reading achievements and the home resource for learning (HRL) scale. By applying the partial credit model and using the WLE estimates for the person parameters it is accepted that…

Describing the variation in test scores between and within school districts is critical for: (1) for policy-related and descriptive work that investigates the sorting of students among districts and the differential effectiveness of those districts; and (2) for methodological work planning future experiments or interventions. Intraclass…

As a global measure of precision, item response theory (IRT) estimated reliability is derived for four coefficients (Cronbach's a, Feldt-Raju, stratified a, and marginal reliability). Models with different underlying assumptions concerning test-part similarity are discussed. A detailed computational example is presented for the targeted…

Modeling the distribution of site level effects is an important problem, but it is also an incredibly difficult one. Current methods rely on distributional assumptions in multilevel models for estimation. There it is hoped that the partial pooling of site level estimates with overall estimates, designed to take into account individual variation as…

A latent multivariate regression model is developed that employs a generalized asymmetric Laplace (GAL) prior distribution for regression coefficients. The model is designed for high-dimensional applications where an approximate sparsity condition is satisfied, such that many regression coefficients are near zero after accounting for all the model…

This study analysed polytomous items' psychometric properties according to nonparametric item response theory (NIRT) models. Thus, simulated datasets--three different test lengths (10, 20 and 30 items), three sample distributions (normal, right and left skewed) and three samples sizes (100, 250 and 500)--were generated by conducting 20…

This paper introduces the generalized beta (GB) model as a new modeling tool in the educational assessment area and evaluation analysis, specifically. Unlike normal model, GB model allows us to capture some real characteristics of data and it is an important tool for understanding the phenomenon of learning. This paper develops a contrast with the…

Two methods are currently in use at Educational Testing Service (ETS) for equating observed item difficulty statistics. The first method involves the linear equating of item statistics in an observed sample to reference statistics on the same items. The second method, or the item response curve (IRC) method, involves the summation of conditional…

The nominal response model (NRM), a much understudied polytomous item response theory (IRT) model, provides researchers the unique opportunity to evaluate within-item category distinctions. Polytomous IRT models, such as the NRM, are frequently applied to psychological assessments representing constructs that are unlikely to be normally…

The quantal hypothesis is central to the modern understanding of how a neurotransmitter is released from synapses. This hypothesis expresses that a neurotransmitter is packaged together in quanta that are released probabilistically. The experiments that led to the quantal hypothesis are often related in introductory neuroscience textbooks, but…

Word frequencies in natural language follow a highly skewed Zipfian distribution, but the consequences of this distribution for language acquisition are only beginning to be understood. Typically, learning experiments that are meant to simulate language acquisition use uniform word frequency distributions. We examine the effects of Zipfian…