A Hyperbolic Cosine Unfolding Model for Evaluating Rater Accuracy in Writing Assessments

2016 ◽  
pp. 183-197 ◽  
Author(s):  
Jue Wang ◽  
George Engelhard
Keyword(s):  
Writing Assessments ◽  
Unfolding Model ◽  
Hyperbolic Cosine ◽  
Rater Accuracy

scholarly journals Evaluating Rater Accuracy in Rater-Mediated Assessments Using an Unfolding Model

2016 ◽  
Vol 76 (6) ◽  
pp. 1005-1025 ◽  
Author(s):  
Jue Wang ◽  
George Engelhard ◽  
Edward W. Wolfe
Keyword(s):  
Writing Assessment ◽  
Performance Assessments ◽  
Unfolding Model ◽  
New Methods ◽  
Hyperbolic Cosine ◽  
The World ◽  
Rater Accuracy ◽  
The Difference ◽  
Expert Ratings

The number of performance assessments continues to increase around the world, and it is important to explore new methods for evaluating the quality of ratings obtained from raters. This study describes an unfolding model for examining rater accuracy. Accuracy is defined as the difference between observed and expert ratings. Dichotomous accuracy ratings (0 = inaccurate, 1 = accurate) are unfolded into three latent categories: inaccurate below expert ratings, accurate ratings, and inaccurate above expert ratings. The hyperbolic cosine model (HCM) is used to examine dichotomous accuracy ratings from a statewide writing assessment. This study suggests that HCM is a promising approach for examining rater accuracy, and that the HCM can provide a useful interpretive framework for evaluating the quality of ratings obtained within the context of rater-mediated assessments.

Evaluating rater accuracy and perception for integrated writing assessments using a mixed-methods approach

2017 ◽  
Vol 33 ◽  
pp. 36-47 ◽  
Author(s):  
Jue Wang ◽  
George Engelhard ◽  
Kevin Raczynski ◽  
Tian Song ◽  
Edward W. Wolfe
Keyword(s):  
Mixed Methods ◽  
Writing Assessments ◽  
Mixed Methods Approach ◽  
Rater Accuracy

Modeling the Effects of Training and Trainers on Rater Accuracy

2013 ◽  
Author(s):  
Kevin R. Raczynski ◽  
Allan S. Cohen ◽  
Zhenqiu L. Lu
Keyword(s):  
Rater Accuracy

scholarly journals Approaching the self-dual point of the sinh-Gordon model

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Robert Konik ◽  
Márton Lájer ◽  
Giuseppe Mussardo
Keyword(s):  
Small Volume ◽  
Zero Mode ◽  
Form Factors ◽  
Lagrangian Formulation ◽  
The Self ◽  
Quantum Mechanical ◽  
Exact Form ◽  
Coupling Constant ◽  
Self Duality ◽  
Hyperbolic Cosine

Abstract One of the most striking but mysterious properties of the sinh-Gordon model (ShG) is the b → 1/b self-duality of its S-matrix, of which there is no trace in its Lagrangian formulation. Here b is the coupling appearing in the model’s eponymous hyperbolic cosine present in its Lagrangian, cosh(bϕ). In this paper we develop truncated spectrum methods (TSMs) for studying the sinh-Gordon model at a finite volume as we vary the coupling constant. We obtain the expected results for b ≪ 1 and intermediate values of b, but as the self-dual point b = 1 is approached, the basic application of the TSM to the ShG breaks down. We find that the TSM gives results with a strong cutoff Ec dependence, which disappears according only to a very slow power law in Ec. Standard renormalization group strategies — whether they be numerical or analytic — also fail to improve upon matters here. We thus explore three strategies to address the basic limitations of the TSM in the vicinity of b = 1. In the first, we focus on the small-volume spectrum. We attempt to understand how much of the physics of the ShG is encoded in the zero mode part of its Hamiltonian, in essence how ‘quantum mechanical’ vs ‘quantum field theoretic’ the problem is. In the second, we identify the divergencies present in perturbation theory and perform their resummation using a supra-Borel approximate. In the third approach, we use the exact form factors of the model to treat the ShG at one value of b as a perturbation of a ShG at a different coupling. In the light of this work, we argue that the strong coupling phase b > 1 of the Lagrangian formulation of model may be different from what is naïvely inferred from its S-matrix. In particular, we present an argument that the theory is massless for b > 1.

Nonparametric Unidimensional Unfolding for Multicategory Data

1992 ◽  
Vol 4 ◽  
pp. 41-74 ◽  
Author(s):  
Wijbrandt H. van Schuur
Keyword(s):  
Republican Party ◽  
Rating Data ◽  
Presidential Candidates ◽  
Unfolding Model ◽  
Scaling Model ◽  
Dichotomous Data ◽  
Party Activists ◽  
Preference Ratings

This article describes a nonparametric unidimensional unfolding model for dichotomous data (van Schuur 1984) and shows how it can be extended to multicategory data such as Likert-type rating data. This extension is analogous to Molenaar's (1982) application of Mokken's (1970) nonparametric unidimensional cumulative scaling model. The model is illustrated with an analysis of five-point preference ratings given in 1980 to five political presidential candidates by Democratic and Republican party activists in Missouri.

Reformulation in the Phase Plane Enhances Smoothness Rater Accuracy in Stroke

2012 ◽  
Vol 44 (3) ◽  
pp. 149-159 ◽  
Author(s):  
Michael Wininger ◽  
Nam H. Kim ◽  
William Craelius
Keyword(s):  
Phase Plane ◽  
Rater Accuracy

Electroosmotic Flow of Power-Law Fluids in a Slit Microchannel

2009 ◽  
Author(s):  
Cunlu Zhao ◽  
Chun Yang
Keyword(s):  
Shear Stress ◽  
Double Layer ◽  
Power Law ◽  
Dynamic Viscosity ◽  
Electroosmotic Flow ◽  
Flow Behavior ◽  
Flow Behavior Index ◽  
Power Law Fluids ◽  
Hyperbolic Cosine ◽  
Behavior Index

Electroosmotic flow of power-law fluids in a slit channel is analyzed. The governing equations including the linearized Poisson–Boltzmann equation, the Cauchy momentum equation and the continuity equation are solved to seek analytical expressions for the shear stress, dynamic viscosity and velocity distributions. Specifically, exact solutions of the velocity distributions are explicitly found for several special values of the flow behavior index. Furthermore, with the implementation of an approximate scheme for the hyperbolic cosine function, approximate solutions of the velocity distributions are obtained. In addition, a mathematical expression for the average electroosmotic velocity is derived for large values of the dimensionless electrokinetic parameter, κH, in a fashion similar to the Smoluchowski equation. Hence, a generalized Smoluchowski velocity is introduced by taking into account contributions due to the finite thickness of the electric double layer and the flow behavior index of power-law fluids. Finally, calculations are performed to examine the effects of κH, flow behavior index, double layer thickness, and applied electric field on the shear stress, dynamic viscosity, velocity distribution, and average velocity/flow rate of the electroosmotic flow of power-law fluids.

The Explanatory Generalized Graded Unfolding Model: Incorporating Collateral Information to Improve the Latent Trait Estimation Accuracy

2021 ◽  
pp. 014662162110517
Author(s):  
Seang-Hwane Joo ◽  
Philseok Lee ◽  
Stephen Stark
Keyword(s):  
Large Scale ◽  
Latent Trait ◽  
Theory Model ◽  
Estimation Accuracy ◽  
Cognitive Assessments ◽  
Collateral Information ◽  
Unfolding Model ◽  
Generalized Graded Unfolding Model ◽  
Scoring Accuracy ◽  
Trait Estimation

Collateral information has been used to address subpopulation heterogeneity and increase estimation accuracy in some large-scale cognitive assessments. The methodology that takes collateral information into account has not been developed and explored in published research with models designed specifically for noncognitive measurement. Because the accurate noncognitive measurement is becoming increasingly important, we sought to examine the benefits of using collateral information in latent trait estimation with an item response theory model that has proven valuable for noncognitive testing, namely, the generalized graded unfolding model (GGUM). Our presentation introduces an extension of the GGUM that incorporates collateral information, henceforth called Explanatory GGUM. We then present a simulation study that examined Explanatory GGUM latent trait estimation as a function of sample size, test length, number of background covariates, and correlation between the covariates and the latent trait. Results indicated the Explanatory GGUM approach provides scoring accuracy and precision superior to traditional expected a posteriori (EAP) and full Bayesian (FB) methods. Implications and recommendations are discussed.

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