scholarly journals Standard Errors of IRT Parameter Scale Transformation Coefficients: Comparison of Bootstrap Method, Delta Method, and Multiple Imputation Method

2019 ◽  
Vol 56 (2) ◽  
pp. 302-330 ◽  
Author(s):  
Zhonghua Zhang ◽  
Mingren Zhao
Keyword(s):  
Multiple Imputation ◽  
Bootstrap Method ◽  
Imputation Method ◽  
Delta Method ◽  
Scale Transformation ◽  
Standard Errors ◽  
Multiple Imputation Method

scholarly journals Asymptotic Standard Errors of Parameter Scale Transformation Coefficients in Test Equating Under the Nominal Response Model

2020 ◽  
pp. 014662162096574
Author(s):  
Zhonghua Zhang
Keyword(s):  
Multiple Imputation ◽  
Imputation Method ◽  
Delta Method ◽  
Scale Transformation ◽  
Standard Errors ◽  
Response Model ◽  
Test Equating ◽  
Nominal Response Model ◽  
Multiple Imputation Method ◽  
Nominal Response

Researchers have developed a characteristic curve procedure to estimate the parameter scale transformation coefficients in test equating under the nominal response model. In the study, the delta method was applied to derive the standard error expressions for computing the standard errors for the estimates of the parameter scale transformation coefficients. This brief report presents the results of a simulation study that examined the accuracy of the derived formulas and compared the performance of this analytical method with that of the multiple imputation method. The results indicated that the standard errors produced by the delta method were very close to the criterion standard errors as well as those yielded by the multiple imputation method under all the simulation conditions.

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 Reconstruction of spatially detailed global map of NH<sub>4</sub><sup>+</sup> and NO<sub>3</sub><sup>−</sup> application in synthetic nitrogen fertilizer

2016 ◽  
Author(s):  
Kazuya Nishina ◽  
Akihiko Ito ◽  
Naota Hanasaki ◽  
Seiji Hayashi
Keyword(s):  
Multiple Imputation ◽  
Nitrogen Fertilizer ◽  
Time Series Data ◽  
Fertilizer Application ◽  
Imputation Method ◽  
N Fertilizer ◽  
Series Data ◽  
Specific Information ◽  
Model Studies ◽  
Multiple Imputation Method

Abstract. This paper provides a method for constructing a new historical global nitrogen fertilizer application map (0.5° × 0.5° resolution) for the period 1961–2010 based on country-specific information from Food and Agriculture Organization statistics (FAOSTAT) and various global datasets. This new map incorporates the fraction of NH4+ (and NO3−) in N fertilizer inputs by utilizing fertilizer species information in FAOSTAT, in which species can be categorized as NH4+ and/or NO3−-forming N fertilizers. During data processing, we applied a statistical data imputation method for the missing data (19 % of national N fertilizer consumption) in FAOSTAT. The multiple imputation method enabled us to fill gaps in the time-series data using plausible values using covariates information (year, population, GDP, and crop area). After the imputation, we downscaled the national consumption data to a gridded cropland map. Also, we applied the multiple imputation method to the available chemical fertilizer species consumption, allowing for the estimation of the NH4+/NO3− ratio in national fertilizer consumption. In this study, the synthetic N fertilizer inputs in 2000 showed a general consistency with the existing N fertilizer map (Potter et al., 2010) in relation to the ranges of N fertilizer inputs. Globally, the estimated N fertilizer inputs based on the sum of filled data increased from 15 Tg-N to 110 Tg-N during 1961–2010. On the other hand, the global NO3− input started to decline after the late 1980s and the fraction of NO3− in global N fertilizer decreased consistently from 35 % to 13 % over a 50-year period. NH4+ based fertilizers are dominant in most countries; however, the NH4+/NO3− ratio in N fertilizer inputs shows clear differences temporally and geographically. This new map can be utilized as an input data to global model studies and bring new insights for the assessment of historical terrestrial N cycling changes. Datasets available at doi:10.1594/PANGAEA.861203.

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