scholarly journals A multidimensional generalized many-facet Rasch model for rubric-based performance assessment

2021 ◽  
Author(s):  
Masaki Uto
Keyword(s):  
Performance Assessment ◽  
Rasch Model ◽  
Measurement Accuracy ◽  
Estimation Method ◽  
Real Data ◽  
Monte Carlo Algorithm ◽  
Irt Model ◽  
Irt Models ◽  
Proposed Model ◽  
Problem Item

AbstractPerformance assessment, in which human raters assess examinee performance in a practical task, often involves the use of a scoring rubric consisting of multiple evaluation items to increase the objectivity of evaluation. However, even when using a rubric, assigned scores are known to depend on characteristics of the rubric’s evaluation items and the raters, thus decreasing ability measurement accuracy. To resolve this problem, item response theory (IRT) models that can estimate examinee ability while considering the effects of these characteristics have been proposed. These IRT models assume unidimensionality, meaning that a rubric measures one latent ability. In practice, however, this assumption might not be satisfied because a rubric’s evaluation items are often designed to measure multiple sub-abilities that constitute a targeted ability. To address this issue, this study proposes a multidimensional IRT model for rubric-based performance assessment. Specifically, the proposed model is formulated as a multidimensional extension of a generalized many-facet Rasch model. Moreover, a No-U-Turn variant of the Hamiltonian Markov chain Monte Carlo algorithm is adopted as a parameter estimation method for the proposed model. The proposed model is useful not only for improving the ability measurement accuracy, but also for detailed analysis of rubric quality and rubric construct validity. The study demonstrates the effectiveness of the proposed model through simulation experiments and application to real data.

scholarly journals The Weibull Birnbaum-Saunders Distribution And Its Applications

2020 ◽  
Vol 9 (1) ◽  
pp. 61-81
Author(s):  
Lazhar BENKHELIFA
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Reliability Estimation ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model ◽  
Modeling Data

A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.

A Mixture Price Trend Model for Long-Term Risk Management

2010 ◽  
pp. 157-173
Author(s):  
Eric S. Fung ◽  
Wai-Ki Ching ◽  
Tak-Kuen Siu
Keyword(s):  
Risk Management ◽  
Financial Risk ◽  
Estimation Method ◽  
Real Data ◽  
Price Trend ◽  
Trend Model ◽  
Proposed Model ◽  
Price Trends ◽  
Long Term Forecasting

In financial forecasting, a long-standing challenging issue is to develop an appropriate model for forecasting long-term risk management of enterprises. In this chapter, using financial markets as an example, we introduce a mixture price trend model for long-term forecasts of financial asset prices with a view to applying it for long-term financial risk management. The key idea of the mixture price trend model is to provide a general and flexible way to incorporate various price trend behaviors and to extract information from price trends for long-term forecasting. Indeed, the mixture price trend model can incorporate model uncertainty in the price trend model, which is a key element for risk management and is overlooked in some of the current literatures. The mixture price trend model also allows the incorporation of users’ subjective views on long-term price trends. An efficient estimation method is introduced. Statistical analysis of the proposed model based on real data will be conducted to illustrate the performance of the model.

On Longitudinal Item Response Theory Models: A Didactic

2019 ◽  
Vol 45 (3) ◽  
pp. 339-368 ◽  
Author(s):  
Chun Wang ◽  
Steven W. Nydick
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Real Data ◽  
Measurement Model ◽  
Higher Order ◽  
Response Theory ◽  
Latent Growth ◽  
Multidimensional Irt ◽  
Irt Model ◽  
Irt Models

Recent work on measuring growth with categorical outcome variables has combined the item response theory (IRT) measurement model with the latent growth curve model and extended the assessment of growth to multidimensional IRT models and higher order IRT models. However, there is a lack of synthetic studies that clearly evaluate the strength and limitations of different multilevel IRT models for measuring growth. This study aims to introduce the various longitudinal IRT models, including the longitudinal unidimensional IRT model, longitudinal multidimensional IRT model, and longitudinal higher order IRT model, which cover a broad range of applications in education and social science. Following a comparison of the parameterizations, identification constraints, strengths, and weaknesses of the different models, a real data example is provided to illustrate the application of different longitudinal IRT models to model students’ growth trajectories on multiple latent abilities.

scholarly journals Bayesian analysis of hierarchical IRT models: comparing and combining the unidimensional and multi-unidimensional IRT models

2005 ◽  
Author(s):  
◽  
Yanyan Sheng
Keyword(s):  
Item Response Theory ◽  
Bayesian Analysis ◽  
Item Response ◽  
Large Scale ◽  
Test Items ◽  
Irt Model ◽  
Irt Models ◽  
Proposed Model ◽  
Multidimensional Models ◽  
Item Response Theory Models

As item response theory models gain increased popularity in large scale educational and measurement testing situations, many studies have been conducted on the development and applications of unidimensional and multidimensional models. However, to date, no study has yet looked at models in the IRT framework with an overall ability dimension underlying all test items and several ability dimensions specific for each subtest. This study is to propose such a model and compare it with the conventional IRT models using Bayesian methodology. The results suggest that the proposed model offers a better way to represent the test situations not realized in existing models. The model specifications for the proposed model also give rise to implications for test developers on test designing. In addition, the proposed IRT model can be applied in other areas, such as intelligence or psychology, among others.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun
Keyword(s):  
Real Data ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Probability Weighted Moment ◽  
Record Statistics ◽  
Maximum Likelihood Criterion

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

The impact of duration observations on precision of results GNSS measurements

2017 ◽  
Vol 921 (3) ◽  
pp. 7-13 ◽  
Author(s):  
S.V. Grishko
Keyword(s):  
Measurement Accuracy ◽  
Functional Dependence ◽  
Observation Time ◽  
Satellite Networks ◽  
Satellite Measurements ◽  
Proposed Model ◽  
Actual Error ◽  
Gnss Measurements ◽  
The Impact ◽  
Qualitative Characteristics

This paper shows that the accuracy of relative satellite measurements depend not only on the length of the baseline, as it is regulated by the rating formula of accuracy of GNSS equipment, but also on the duration of observations. As a result of the strict adjustment much redundant satellite networks with different duration of observations obtained covariance matrix of baselines, the most realistic reflecting the actual error of satellite observations. Research of forms of communication of these errors from length of the baseline and duration of its measurement is executed. A significant influence of solar activity on accuracy of satellite measurements, in general, leads to unequal similar series of measurements made at different periods, for example, in the production of monitoring activities. The model of approximation of the functional dependence of accuracy of the baseline from its length and duration of observations having good qualitative characteristics is offered. Based on the proposed model, we analyzed the dynamics of changes in measurement accuracy with an increase in observation time.

scholarly journals An adaptive social distancing SIR model for COVID-19 disease spreading and forecasting

2021 ◽  
Vol 10 (s1) ◽  
Author(s):  
Said Gounane ◽  
Yassir Barkouch ◽  
Abdelghafour Atlas ◽  
Mostafa Bendahmane ◽  
Fahd Karami ◽  
...  
Keyword(s):  
Mathematical Theory ◽  
Real Data ◽  
Sir Model ◽  
Epidemic Threshold ◽  
Social Distancing ◽  
Sir Epidemic ◽  
Proposed Model ◽  
Disease Spreading ◽  
The Government ◽  
The Impact

Abstract Recently, various mathematical models have been proposed to model COVID-19 outbreak. These models are an effective tool to study the mechanisms of coronavirus spreading and to predict the future course of COVID-19 disease. They are also used to evaluate strategies to control this pandemic. Generally, SIR compartmental models are appropriate for understanding and predicting the dynamics of infectious diseases like COVID-19. The classical SIR model is initially introduced by Kermack and McKendrick (cf. (Anderson, R. M. 1991. “Discussion: the Kermack–McKendrick Epidemic Threshold Theorem.” Bulletin of Mathematical Biology 53 (1): 3–32; Kermack, W. O., and A. G. McKendrick. 1927. “A Contribution to the Mathematical Theory of Epidemics.” Proceedings of the Royal Society 115 (772): 700–21)) to describe the evolution of the susceptible, infected and recovered compartment. Focused on the impact of public policies designed to contain this pandemic, we develop a new nonlinear SIR epidemic problem modeling the spreading of coronavirus under the effect of a social distancing induced by the government measures to stop coronavirus spreading. To find the parameters adopted for each country (for e.g. Germany, Spain, Italy, France, Algeria and Morocco) we fit the proposed model with respect to the actual real data. We also evaluate the government measures in each country with respect to the evolution of the pandemic. Our numerical simulations can be used to provide an effective tool for predicting the spread of the disease.

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

2020 ◽  
Vol 70 (4) ◽  
pp. 953-978
Author(s):  
Mustafa Ç. Korkmaz ◽  
G. G. Hamedani
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Lorenz Curves ◽  
Proposed Model ◽  
New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

scholarly journals Transition models for count data: a flexible alternative to fixed distribution models

2021 ◽  
Author(s):  
Moritz Berger ◽  
Gerhard Tutz
Keyword(s):  
Count Data ◽  
Regression Models ◽  
Negative Binomial ◽  
Real Data ◽  
Distribution Models ◽  
Explanatory Variables ◽  
Excess Zeros ◽  
Proposed Model ◽  
Transition Models ◽  
Fixed Distribution

AbstractA flexible semiparametric class of models is introduced that offers an alternative to classical regression models for count data as the Poisson and Negative Binomial model, as well as to more general models accounting for excess zeros that are also based on fixed distributional assumptions. The model allows that the data itself determine the distribution of the response variable, but, in its basic form, uses a parametric term that specifies the effect of explanatory variables. In addition, an extended version is considered, in which the effects of covariates are specified nonparametrically. The proposed model and traditional models are compared in simulations and by utilizing several real data applications from the area of health and social science.

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