Standard Error Estimation of 3PL IRT True Score Equating With an MCMC Method

2008 ◽  
Vol 33 (3) ◽  
pp. 257-278 ◽  
Author(s):  
Yuming Liu ◽  
E. Matthew Schulz ◽  
Lei Yu
Keyword(s):  
Bootstrap Method ◽  
Standard Errors ◽  
True Score ◽  
Mcmc Method ◽  
Test Form ◽  
True Score Equating ◽  
Standard Error Estimation ◽  
Equivalent Test ◽  
Mean Square Errors ◽  
The Bootstrap Method

A Markov chain Monte Carlo (MCMC) method and a bootstrap method were compared in the estimation of standard errors of item response theory (IRT) true score equating. Three test form relationships were examined: parallel, tau-equivalent, and congeneric. Data were simulated based on Reading Comprehension and Vocabulary tests of the Iowa Tests of Basic Skills®. For parallel and congeneric test forms within valid IRT true score ranges, the pattern and magnitude of standard errors of IRT true score equating estimated by the MCMC method were very close to those estimated by the bootstrap method. For tau-equivalent test forms, the pattern of standard errors estimated by the two methods was also similar. Bias and mean square errors of equating produced by the MCMC method were smaller than those produced by the bootstrap method; however, standard errors were larger. In educational testing, the MCMC method may be used as an additional or alternative procedure to the bootstrap method when evaluating the precision of equating results.

Asymptotic Standard Errors of Generalized Partial Credit Model True Score Equating Using Characteristic Curve Methods

2021 ◽  
pp. 014662162110131
Author(s):  
Zhonghua Zhang
Keyword(s):  
Bootstrap Method ◽  
Characteristic Curve ◽  
Delta Method ◽  
Standard Errors ◽  
Partial Credit Model ◽  
Generalized Partial Credit Model ◽  
True Score Equating ◽  
Generalized Partial Credit ◽  
Multiple Imputation Method ◽  
The Bootstrap Method

In this study, the delta method was applied to estimate the standard errors of the true score equating when using the characteristic curve methods with the generalized partial credit model in test equating under the context of the common-item nonequivalent groups equating design. Simulation studies were further conducted to compare the performance of the delta method with that of the bootstrap method and the multiple imputation method. The results indicated that the standard errors produced by the delta method were very close to the criterion empirical standard errors as well as those yielded by the bootstrap method and the multiple imputation method under all the manipulated conditions.

scholarly journals Influence Function and Bootstrap Methods of Estimating the Standard Errors of the Estimators of Mixture Exponential Distribution Parameter

2021 ◽  
pp. 113-136
Author(s):  
J. I. Udobi ◽  
G. A. Osuji ◽  
S. I. Onyeagu ◽  
H. O. Obiora-Ilouno
Keyword(s):  
Sample Size ◽  
Standard Error ◽  
Influence Function ◽  
Bootstrap Method ◽  
Standard Errors ◽  
Sample Sizes ◽  
Trimmed Mean ◽  
Contamination Levels ◽  
M Estimate ◽  
The Bootstrap Method

This work estimated the standard error of the maximum likelihood estimator (MLE) and the robust estimators of the exponential mixture parameter (θ) using the influence function and the bootstrap approaches. Mixture exponential random samples of sizes 10, 15, 20, 25, 50, and 100 were generated using 3 mixture exponential models at 2%, 5% and 10% contamination levels. The selected estimators namely: mean, median, alpha-trimmed mean, Huber M-estimate and their standard errors (Tn ) were estimated using the two approaches at the indicated sample sizes and contamination levels. The results were compared using the coefficient of variation, confidence interval and the asymptotic relative efficiency of Tn in order to find out which approach yields the more reliable, precise and efficient estimate of Tn. The results of the analysis show that the two approaches do not equally perform at all conditions. From the results, the bootstrap method was found to be more reliable and efficient method of estimating the standard error of the arithmetic mean at all sample sizes and contamination levels. In estimating the standard error of the median, the influence function method was found to be more effective especially when the sample size is small and yet contamination is high. The influence function based approach yielded more reliable, precise and efficient estimates of the standard errors of the alpha-trimmed mean and the Huber M-estimate for all sample sizes and levels of contamination although the reliability of the bootstrap method improved better as sample size increased to 50 and above. All simulations and analysis were carried out in R programming language.

scholarly journals New Models Used to Determine the Dioxins Total Amount and Toxicity (TEQ) in Atmospheric Emissions from Thermal Processes

Energies ◽  
2019 ◽  
Vol 12 (23) ◽  
pp. 4434
Author(s):  
Damià Palmer ◽  
Josep O. Pou ◽  
L. Gonzalez-Sabaté ◽  
Jordi Díaz-Ferrero ◽  
Juan A. Conesa ◽  
...  
Keyword(s):  
Regression Models ◽  
Bootstrap Method ◽  
Waste Incineration ◽  
Model Parameters ◽  
Thermal Processes ◽  
Multilinear Regression ◽  
Linearly Independent ◽  
Dioxins And Furans ◽  
Mean Square Errors ◽  
The Bootstrap Method

In order to reduce the calculation effort during the simulation of the emission of polychlorinated dibenzo-p-dioxins and furans (PCDD/F) during municipal solid waste incineration, minimizing the number of simulated components is mandatory. For this purpose, two new multilinear regression models capable of determining the dioxins total amount and toxicity of an atmospheric emission have been adjusted based on previously published ones. The new source of data used (almost 200 PCDD/F analyses) provides a wider range of application to the models, increasing also the diversity of the emission sources, from industrial and laboratory scale thermal processes. Only three of the 17 toxic congeners (1,2,3,6,7,8-HxCDD, 2,3,7,8-TCDF and OCDF), whose formation was found to be linearly independent, were necessary as inputs for the models. All model parameters have been statistically validated and their confidence intervals have been calculated using the Bootstrap method. The resulting coefficients of determination (R2) for the models are 0.9711 ± 0.0056 and 0.9583 ± 0.0085; its root mean square errors (RMSE) are 0.2115 and 0.2424, and its mean absolute errors (MAE) are 0.1541 and 0.1733 respectively.

scholarly journals Statistical Estimates of the Pulsar Glitch Activity

Universe ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 8
Author(s):  
Alessandro Montoli ◽  
Marco Antonelli ◽  
Brynmor Haskell ◽  
Pierre Pizzochero
Keyword(s):  
Linear Regression ◽  
Upper Bound ◽  
Bootstrap Method ◽  
Waiting Times ◽  
Statistical Estimates ◽  
Equal Variance ◽  
Linear Fit ◽  
The Moment ◽  
The Bootstrap Method

A common way to calculate the glitch activity of a pulsar is an ordinary linear regression of the observed cumulative glitch history. This method however is likely to underestimate the errors on the activity, as it implicitly assumes a (long-term) linear dependence between glitch sizes and waiting times, as well as equal variance, i.e., homoscedasticity, in the fit residuals, both assumptions that are not well justified from pulsar data. In this paper, we review the extrapolation of the glitch activity parameter and explore two alternatives: the relaxation of the homoscedasticity hypothesis in the linear fit and the use of the bootstrap technique. We find a larger uncertainty in the activity with respect to that obtained by ordinary linear regression, especially for those objects in which it can be significantly affected by a single glitch. We discuss how this affects the theoretical upper bound on the moment of inertia associated with the region of a neutron star containing the superfluid reservoir of angular momentum released in a stationary sequence of glitches. We find that this upper bound is less tight if one considers the uncertainty on the activity estimated with the bootstrap method and allows for models in which the superfluid reservoir is entirely in the crust.

The Bootstrap-Method: Discussion and Proposal for Improvement / Das bootstrap-Verfahren: Diskussion und Verbesserungsvorschlag

1998 ◽  
Vol 217 (1) ◽  
Author(s):  
Hans Schneeberger
Keyword(s):  
Bootstrap Method ◽  
Law School ◽  
Mean Deviation ◽  
Alternative Method ◽  
Doubling Method ◽  
The Mean ◽  
The Bootstrap Method

SummaryWith Efron’s law-school example the bootstrap method is compared with an alternative method, called doubling. It is shown, that the mean deviation of the estimator is always smaller for the doubling method.

Application of the bootstrap method to quantify uncertainty in seismic hazard estimates

1992 ◽  
Vol 82 (1) ◽  
pp. 104-119
Author(s):  
Michéle Lamarre ◽  
Brent Townshend ◽  
Haresh C. Shah
Keyword(s):  
Confidence Interval ◽  
Seismic Hazard ◽  
Statistical Method ◽  
Bootstrap Method ◽  
Earthquake Magnitude ◽  
Earthquake Catalog ◽  
Uncertainty Measure ◽  
Attenuation Models ◽  
The Bootstrap Method

Abstract This paper describes a methodology to assess the uncertainty in seismic hazard estimates at particular sites. A variant of the bootstrap statistical method is used to combine the uncertainty due to earthquake catalog incompleteness, earthquake magnitude, and recurrence and attenuation models used. The uncertainty measure is provided in the form of a confidence interval. Comparisons of this method applied to various sites in California with previous studies are used to confirm the validity of the method.

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